From a4ef4eff1c48e0678a4f6dc4c16d19aaa75b5906 Mon Sep 17 00:00:00 2001 From: Pablo Brubeck Date: Mon, 16 Feb 2026 17:25:09 +0000 Subject: [PATCH 01/51] GoalAdaptiveVariationalSolver --- firedrake/__init__.py | 4 + firedrake/adaptive_variational_solver.py | 677 +++++++++++++++++++++++ 2 files changed, 681 insertions(+) create mode 100644 firedrake/adaptive_variational_solver.py diff --git a/firedrake/__init__.py b/firedrake/__init__.py index e0009c2b0e..689c902b93 100644 --- a/firedrake/__init__.py +++ b/firedrake/__init__.py @@ -169,6 +169,10 @@ def init_petsc(): from firedrake.matrix import ( # noqa: F401 MatrixBase, Matrix, ImplicitMatrix, AssembledMatrix ) +from firedrake.adaptive_variational_solver import ( # noqa: F401 + GoalAdaptiveNonlinearVariationalSolver +) + # Set default log level set_log_level(WARNING) diff --git a/firedrake/adaptive_variational_solver.py b/firedrake/adaptive_variational_solver.py new file mode 100644 index 0000000000..26173c3e5f --- /dev/null +++ b/firedrake/adaptive_variational_solver.py @@ -0,0 +1,677 @@ +from firedrake.petsc import PETSc +from firedrake.function import Function +from firedrake.cofunction import Cofunction +from firedrake.functionspace import FunctionSpace, TensorFunctionSpace +from firedrake.ufl_expr import TestFunction, TrialFunction, derivative, action, adjoint +from firedrake.variational_solver import NonlinearVariationalProblem, NonlinearVariationalSolver +from firedrake.solving import solve + +from firedrake.preconditioners.pmg import PMGPC +from firedrake.mg.ufl_utils import coarsen +from firedrake.mg.adaptive_hierarchy import AdaptiveMeshHierarchy +from firedrake.mg.adaptive_transfer_manager import AdaptiveTransferManager +from firedrake.output import VTKFile + +from finat.ufl import BrokenElement, FiniteElement +from ufl import avg, dot, div, grad, dx, ds, dS, inner, jump, as_vector, replace, FacetNormal + +from functools import singledispatch +from pathlib import Path +import numpy as np +import csv + + +class SolverCtx: + def __init__(self, config: dict): + self.manual_indicators = config.get("manual_indicators", False) # Used for manual indicators (only implemented for Poisson but could be overriden) + self.dorfler_alpha = config.get("dorfler_alpha", 0.5) # Dorfler marking parameter, default 0.5 + self.max_iterations = config.get("max_iterations", 10) + self.output_dir = config.get("output_dir", "./output") + self.dual_extra_degree = config.get("dual_extra_degree", 1) + self.cell_residual_extra_degree = config.get("cell_residual_extra_degree", 0) + self.facet_residual_extra_degree = config.get("facet_residual_extra_degree", 0) + self.write_at_iteration = config.get("write_at_iteration", True) + self.use_adjoint_residual = config.get("use_adjoint_residual", False) # For switching between primal and primal + adjoint residuals + self.exact_indicators = config.get("exact_indicators", False) # Maybe remove + self.uniform_refinement = config.get("uniform_refinement", False) + self.primal_low_method = config.get("primal_low_method", "interpolate") + self.dual_low_method = config.get("dual_low_method", "interpolate") + self.write_mesh = config.get("write_mesh", "all") # Default all, options: "first_and_last" "by iteration" "none" + self.write_mesh_iteration_vector = config.get("write_iteration_vector", []) + self.write_mesh_iteration_interval = config.get("write_iteration_interval", 1) + self.write_solution = config.get("write_solution", "all") # Default all, options: "first_and_last" "by iteration" "none" + self.write_solution_iteration_vector = config.get("write_iteration_vector", []) + self.write_solution_iteration_interval = config.get("write_solution", "all") # Default all, options: "first_and_last" "by iteration" "none" + self.results_file_name = config.get("results_file_name", None) + self.nev = config.get("nev", 5) + self.run_name = config.get("run_name", None) + + # Solver parameters + sp_cell = { + "mat_type": "matfree", + "snes_type": "ksponly", + "ksp_type": "cg", + "pc_type": "jacobi", + } + sp_facet = { + "snes_type": "ksponly", + "ksp_type": "cg", + "pc_type": "jacobi", + } + # EXAMPLE DUAL SOLVE METHODS + sp_star = { + "snes_type": "ksponly", + "ksp_type": "cg", + "ksp_rtol": 1.0e-10, + "ksp_max_it": 20, + "ksp_convergence_test": "skip", + "ksp_monitor": None, + "pc_type": "python", + "pc_python_type": "firedrake.ASMStarPC", + "pc_star_mat_ordering_type": "metisnd", + "pc_star_sub_sub_pc_type": "cholesky", + } + sp_vanka = { + "snes_type": "ksponly", + "ksp_type": "gmres", + "ksp_rtol": 1.0e-10, + "ksp_max_it": 20, + "ksp_convergence_test": "skip", + "ksp_monitor": None, + "pc_type": "python", + "pc_python_type": "firedrake.ASMVankaPC", + "pc_vanka_mat_ordering_type": "metisnd", + "pc_vanka_sub_sub_pc_type": "cholesky", + "pc_vanka_construct_dim": 0, + } + sp_chol = { + "pc_type": "cholesky", + "pc_factor_mat_solver_type": "mumps" + } + + +class GoalAdaptiveNonlinearVariationalSolver(): + """ + Solves a nonlinear variational problem to minimise the error in a user-specified goal functional. + We do this by adaptively refining the mesh based on the solution to a dual problem - which links the goal functional + to the PDE. + """ + def __init__(self, problem: NonlinearVariationalProblem, goal_functional, tolerance: float, solver_parameters: dict, + *, primal_solver_parameters=None, dual_solver_parameters=None, exact_solution=None, exact_goal=None, verbose=True, + nullspace=None): + # User input vars + self.problem = problem + self.J = goal_functional + self.tolerance = tolerance + self.sp_primal = primal_solver_parameters + self.sp_dual = dual_solver_parameters + self.u_exact = as_mixed(exact_solution) if isinstance(exact_solution, (tuple, list)) else exact_solution + self.goal_exact = exact_goal + self.solverctx = SolverCtx(solver_parameters) # To store solver parameter data - Unnecessary, could remove in future. + # Derived vars + self.verbose = verbose + self.V = problem.u.function_space() + self.u = problem.u + self.bcs = problem.bcs + self.F = problem.F + self.element = self.V.ufl_element() + self.degree = self.element.degree() + self.test = TestFunction(self.V) + self.mesh = self.V.mesh() + self.nullspace = nullspace + self.atm = AdaptiveTransferManager() + self.amh = AdaptiveMeshHierarchy(self.mesh) + + # Data storage and writing + self.output_dir = Path(self.solverctx.output_dir) + self.output_dir.mkdir(parents=True, exist_ok=True) # ensures folder exists + self.N_vec = [] + self.Ndual_vec = [] + self.eta_vec = [] + self.etah_vec = [] + self.etaTsum_vec = [] + self.eff1_vec = [] + self.eff2_vec = [] + self.eff3_vec = [] + + def solve_primal(self): + from firedrake.assemble import assemble + s = self.solverctx + ndofs = self.V.dim() + self.N_vec.append(ndofs) + + def solve_uh(): + if self.sp_primal is None: + self.print(f"Solving primal (degree: {self.degree}, dofs: {ndofs}) [Method: Default nonlinear solve] ...") + else: + self.print(f"Solving primal (degree: {self.degree}, dofs: {ndofs}) [Method: User defined] ...") + solver = NonlinearVariationalSolver(self.problem, solver_parameters=self.sp_primal) + solver.set_transfer_manager(self.atm) + solver.solve() + + if s.use_adjoint_residual: + # Now solve in higher space + high_degree = self.degree + s.dual_extra_degree # By default use dual degree + high_element = PMGPC.reconstruct_degree(self.element, high_degree) + Vhigh = FunctionSpace(self.mesh, high_element) + solve_uh() + + self.print("u norm:", assemble(inner(self.u, self.u) * dx)) + self.u_high = Function(Vhigh).interpolate(self.u) # Dual soluton + self.print("u_high norm:", assemble(inner(self.u_high, self.u_high) * dx)) + (v_old,) = self.F.arguments() + v_high = TestFunction(Vhigh) + F_high = replace(self.F, {v_old: v_high, self.u: self.u_high}) + bcs_high = reconstruct_bcs(self.bcs, Vhigh) + self.problem_high = NonlinearVariationalProblem(F_high, self.u_high, bcs_high) + + if self.sp_primal is None: + self.print(f"Solving primal in higher space for error estimate (degree: {high_degree}, dofs: {Vhigh.dim()}) [Method: Default nonlinear solve] ...") + else: + self.print(f"Solving primal in higher space for error estimate (degree: {high_degree}, dofs: {Vhigh.dim()}) [Method: User defined] ...") + + solver = NonlinearVariationalSolver(self.problem_high, solver_parameters=self.sp_primal) + solver.set_transfer_manager(self.atm) + solver.solve() + + if s.primal_low_method == "solve": + solve_uh() + elif s.primal_low_method == "project": + self.u.project(self.u_high) + elif False: + # Default - but gives bad results? + self.u.interpolate(self.u_high) + self.u_err = self.u_high - self.u + else: + solve_uh() + + def solve_dual(self): + s = self.solverctx + + dual_degree = self.degree + s.dual_extra_degree + dual_element = PMGPC.reconstruct_degree(self.element, dual_degree) + + Vdual = FunctionSpace(self.mesh, dual_element) + vtest = TestFunction(Vdual) # Dual test function + self.z = Function(Vdual) # Dual soluton + + ndofs_dual = Vdual.dim() + self.Ndual_vec.append(ndofs_dual) + + self.G = (action(adjoint(derivative(self.F, self.u, TrialFunction(Vdual))), self.z) + - derivative(self.J, self.u, vtest)) + + bcs_dual = [bc.reconstruct(V=Vdual, indices=bc._indices, g=0) for bc in self.bcs] + + if self.sp_dual is None: + self.print(f"Solving dual (degree: {dual_degree}, dofs: {ndofs_dual}) [Method: Default nonlinear solve] ...") + else: + self.print(f"Solving dual (degree: {dual_degree}, dofs: {ndofs_dual}) [Method: User defined] ...") + solve(self.G == 0, self.z, bcs_dual, solver_parameters=self.sp_dual) + + # zlo + self.z_lo = Function(self.V) # Dual soluton + if s.dual_low_method == "solve": + ndofs = self.V.dim() + test = TestFunction(self.V) + G_lo = (action(adjoint(derivative(self.F, self.u, TrialFunction(self.V))), self.z_lo) + - derivative(self.J, self.u, test)) + + bcs_dual_low = [bc.reconstruct(V=self.V, indices=bc._indices, g=0) for bc in self.bcs] + + if self.sp_dual is None: + self.print(f"Solving dual in V (degree: {self.degree}, dofs: {ndofs}) [Method: Default nonlinear solve] ...") + else: + self.print(f"Solving dual in V (degree: {self.degree}, dofs: {ndofs}) [Method: User defined] ...") + solve(G_lo == 0, self.z_lo, bcs_dual_low, solver_parameters=self.sp_dual) + + elif s.dual_low_method == "project": + self.z_lo.project(self.z) + else: + self.z_lo.interpolate(self.z) # Default method + + self.z_err = self.z - self.z_lo + + def compute_etah(self): + from firedrake.assemble import assemble + s = self.solverctx + # Compute error estimate F(z) + if s.use_adjoint_residual: + primal_err = abs(assemble(residual(self.F, self.z_err))) + + G = (action(adjoint(derivative(self.F, self.u, TrialFunction(self.V))), self.z_lo) + - derivative(self.J, self.u, TestFunction(self.V))) + dual_err = abs(assemble(residual(G, self.u_err))) + self.eta_h = 0.5 * abs(primal_err + dual_err) + else: + self.eta_h = abs(assemble(residual(self.F, self.z_err))) + + self.etah_vec.append(self.eta_h) + + self.Juh = assemble(self.J) + self.print(f"{"Computed goal":45s}{"J(uh):":8s}{self.Juh:15.12f}") + + if self.u_exact is not None: + quad_opts = {"quadrature_degree": 20} + self.Ju = assemble(replace(self.J, {self.u: self.u_exact}), form_compiler_parameters=quad_opts) + elif self.goal_exact is not None: + self.Ju = self.goal_exact + + if self.u_exact is not None or self.goal_exact is not None: + self.eta = abs(self.Juh - self.Ju) + self.eta_vec.append(self.eta) + self.print(f"{"Exact goal":45s}{"J(u):":8s}{self.Ju:15.12f}") + self.print(f"{"True error, |J(u) - J(u_h)|":45s}{"eta:":8s}{self.eta:15.12f}") + + if s.use_adjoint_residual: + self.print(f"{"Primal error, |rho(u_h;z-z_h)|:":45s}{"eta_pri:":8s}{primal_err:15.12f}") + self.print(f"{"Dual error, |rho*(z_h;u-u_h)|:":45s}{"eta_adj:":8s}{dual_err:15.12f}") + self.print(f"{"Difference":35s}{"|eta_pri - η_adj|:":18s}{abs(primal_err-dual_err):19.12e}") + self.print(f"{"Predicted error, 0.5|rho+rho*|":45s}{"eta_h:":8s}{self.eta_h:15.12f}") + else: + self.print(f"{"Predicted error, |rho(u_h;z-z_h)|":45s}{"eta_h:":8s}{self.eta_h:15.12f}") + + def automatic_error_indicators(self): + from firedrake.assemble import assemble + self.print("Computing local refinement indicators, eta_K...") + # 7. Compute cell and facet residuals R_T, R_\partialT + z_lo = Function(self.V) + z_lo.interpolate(self.z) # Default method + self.z_err = self.z - z_lo + if self.solverctx.use_adjoint_residual: + u_lo = Function(self.V) + u_lo.interpolate(self.u_high) + self.u_err = self.u_high - u_lo + + s = self.solverctx + dim = self.mesh.topological_dimension + cell = self.mesh.ufl_cell() + variant = "integral" # Finite element type + cell_residual_degree = self.degree + s.cell_residual_extra_degree + facet_residuaL_degree = self.degree + s.facet_residual_extra_degree + # ------------------------------- Primal residual ------------------------------- + # Rcell + B = FunctionSpace(self.mesh, "B", dim+1, variant=variant) # Bubble function space + bubbles = Function(B).assign(1) # Bubbles + # Discontinuous function space of Rcell polynomials + if self.V.value_shape == (): + DG = FunctionSpace(self.mesh, "DG", cell_residual_degree, variant=variant) + else: + DG = TensorFunctionSpace(self.mesh, "DG", cell_residual_degree, variant=variant, shape=self.V.value_shape) + uc = TrialFunction(DG) + vc = TestFunction(DG) + ac = inner(uc, bubbles*vc)*dx + Lc = residual(self.F, bubbles*vc) + Rcell = Function(DG, name="Rcell") # Rcell polynomial + assemble(Lc) + solve(ac == Lc, Rcell, solver_parameters=s.sp_cell) # solve for Rcell polynonmial + + # Rfacet + FB = FunctionSpace(self.mesh, "FB", dim, variant=variant) # Cone function space + cones = Function(FB).assign(1) # Cones + # Broken discontinuous function space of facet polynomials + el = BrokenElement(FiniteElement("FB", cell=cell, degree=facet_residuaL_degree+dim, variant=variant)) + if self.V.value_shape == (): + Q = FunctionSpace(self.mesh, el) + else: + Q = TensorFunctionSpace(self.mesh, el, shape=self.V.value_shape) + Qtest = TestFunction(Q) + Qtrial = TrialFunction(Q) + Lf = residual(self.F, Qtest) - inner(Rcell, Qtest)*dx + af = both(inner(Qtrial/cones, Qtest))*dS + inner(Qtrial/cones, Qtest)*ds + Rhat = Function(Q) + solve(af == Lf, Rhat, solver_parameters=s.sp_facet) + Rfacet = Rhat/cones + + # Primal error indicators + DG0 = FunctionSpace(self.mesh, "DG", degree=0) + test = TestFunction(DG0) + + eta_primal = assemble( + inner(inner(Rcell, self.z_err), test)*dx + + + inner(avg(inner(Rfacet, self.z_err)), both(test))*dS + + + inner(inner(Rfacet, self.z_err), test)*ds + ) + + # ------------------------------- Adjoint residual ------------------------------- + if s.use_adjoint_residual: + (vF,) = self.F.arguments() # test Argument used in self.F + # r*(v) = J"(u)[v] - A"_u(u)[v, z] since self.F = A(u;v) - L(v) + # rstar_form = -derivative(self.J, self.u, vF) + derivative(replace(self.F, {vF: self.z}), self.u, vF) + rstar_form = (action(adjoint(derivative(self.F, self.u, TrialFunction(self.V))), self.z_lo) + - derivative(self.J, self.u, TestFunction(self.V))) + # dual: project r* -> Rcell*, Rfacet* + Lc_star = residual(rstar_form, bubbles*vc) + Rcell_star = Function(DG, name="Rcell_star") + solve(ac == Lc_star, Rcell_star, solver_parameters=s.sp_cell) + + Lf_star = residual(rstar_form, Qtest) - inner(Rcell_star, Qtest)*dx + Rhat_star = Function(Q) + solve(af == Lf_star, Rhat_star, solver_parameters=s.sp_facet) + Rfacet_star = Rhat_star/cones + + # indicators: 0.5 * (primal + dual) + eta_dual = assemble( + inner(inner(Rcell_star, self.u_err), test)*dx + + inner(avg(inner(Rfacet_star, self.u_err)), both(test))*dS + + inner(inner(Rfacet_star, self.u_err), test)*ds + ) + with eta_dual.dat.vec as evec: + evec.abs() + etaT_array = evec.getArray() + + self.eta_dual_total = abs(np.sum(etaT_array)) + self.print(f"{"Sum of dual refinement indicators":45s}{"Σeta_K:":8s}{self.eta_dual_total:15.12f}") + with eta_primal.dat.vec as evec: + evec.abs() + etaT_array = evec.getArray() + + self.eta_dual_total = abs(np.sum(etaT_array)) + self.print(f"{"Sum of primal refinement indicators":45s}{"Σeta_K:":8s}{self.eta_dual_total:15.12f}") + + self.etaT = assemble(0.5*(eta_primal + eta_dual)) + else: + self.etaT = eta_primal + + # Exact error indicators (experimental - ignore) + if self.solverctx.exact_indicators: + u_err_exact = self.u_exact - self.u + eta_dual_exact = assemble( + inner(inner(Rcell_star, u_err_exact), test)*dx + + inner(avg(inner(Rfacet_star, u_err_exact)), both(test))*dS + + inner(inner(Rfacet_star, u_err_exact), test)*ds + ) + udiff = assemble(eta_dual_exact - eta_dual) + with udiff.dat.vec as uvec: + unorm = uvec.norm() + self.print("L2 error in (dual) refinement indicators: ", unorm) + + def manual_error_indicators(self): + """ Currently only implemented for Poisson, but can be overriden. To adapt to other PDEs, replace the form of + self.etaT = assemble() to the symbolic form of the error indicators. This form is usually obtained by integrating + the weak form by parts (to recover the strong form) and redistributing facet fluxes. + """ + from firedrake.assemble import assemble + self.print("[MANUAL] Computing local refinement indicators (η_K)...") + n = FacetNormal(self.mesh) + DG0 = FunctionSpace(self.mesh, "DG", degree=0) + test = TestFunction(DG0) + self.etaT = assemble( + inner(self.f + div(grad(self.u)), self.z_err * test) * dx + - inner(0.5*jump(grad(self.u), n), self.z_err * both(test)) * dS + - inner(dot(grad(self.u), n), self.z_err * test) * ds + ) + + def compute_efficiency(self): + with self.etaT.dat.vec as evec: + evec.abs() + self.etaT_array = evec.getArray() + + self.etaT_total = abs(np.sum(self.etaT_array)) + self.etaTsum_vec.append(self.etaT_total) + self.print(f"{"Sum of refinement indicators":45s}{"Ση_K:":8s}{self.etaT_total:15.12f}") + + if self.u_exact is not None or self.goal_exact is not None: + # Compute efficiency indices + self.eff1 = self.eta_h/self.eta + self.eff2 = self.etaT_total/self.eta + self.print(f"{"Effectivity index 1":45s}{"η_h/η:":8s}{self.eff1:7.4f}") + self.print(f"{"Effectivity index 2":45s}{"Ση_K/η:":8s}{self.eff2:7.4f}") + self.eff1_vec.append(self.eff1) + self.eff2_vec.append(self.eff2) + else: + self.eff3 = self.etaT_total/self.eta_h + self.print(f"{"Effectivity index:":45s}{"Ση_K/η_h:":8s}{self.eff3:7.4f}") + self.eff3_vec.append(self.eff3) + + def mark_cells(self): + """ Only Dorfler marking is implemented currently. Can be overridden if other marking strategies are desired. + """ + s = self.solverctx + # 9. Mark cells for refinement (Dorfler marking) + sorted_indices = np.argsort(-self.etaT_array) + sorted_etaT = self.etaT_array[sorted_indices] + cumulative_sum = np.cumsum(sorted_etaT) + threshold = s.dorfler_alpha * self.etaT_total + M = np.searchsorted(cumulative_sum, threshold) + 1 + marked_cells = sorted_indices[:M] + + markers_space = FunctionSpace(self.mesh, "DG", 0) + self.markers = Function(markers_space) + with self.markers.dat.vec as mv: + marr = mv.getArray() + marr[:] = 0 + marr[marked_cells] = 1 + + def refine_mesh(self): + self.print("Refining mesh ...") + new_mesh = self.mesh.refine_marked_elements(self.markers) + self.print("Transferring problem to new mesh ...") + + # FIXME + self.amh = AdaptiveMeshHierarchy(self.mesh) + self.amh.add_mesh(new_mesh) + + coef_map = {} + if self.u_exact is not None: + self.u_exact = refine(self.u_exact, refine, coefficient_mapping=coef_map) + + self.problem = refine(self.problem, refine, coefficient_mapping=coef_map) + self.J = refine(self.J, refine, coefficient_mapping=coef_map) + self.F = self.problem.F + self.u = self.problem.u + self.bcs = self.problem.bcs + self.V = self.u.function_space() + self.mesh = new_mesh + + def uniform_refine(self): + # Uniform marking for comparison tests + markers_space = FunctionSpace(self.mesh, "DG", 0) + self.markers = Function(markers_space) + self.markers.assign(1) + + def write_data(self): + s = self.solverctx + # Write to file + if s.results_file_name is None: + file_path = self.output_dir / "results.csv" + else: + file_path = self.output_dir / s.results_file_name + rows = list(zip(self.N_vec, self.Ndual_vec, self.eta_vec, self.etah_vec, self.etaTsum_vec, self.eff1_vec, self.eff2_vec)) + headers = ("N", "Ndual", "eta", "eta_h", "sum_eta_T", "eff1", "eff2") + with open(file_path, "w", newline="") as file: + w = csv.writer(file) + w.writerow(headers) + w.writerows(rows) + + def append_data(self, it): + s = self.solverctx + if s.run_name is None: + file_path = self.output_dir / "results.csv" + else: + file_path = self.output_dir / f"{s.run_name}/{s.run_name}_results.csv" + if self.u_exact is None and self.goal_exact is None and not self.solverctx.uniform_refinement: + headers = ("iteration", "N", "Ndual", "Juh", "eta_h", "sum_eta_T") + row = ( + it, + self.N_vec[-1], self.Ndual_vec[-1], self.Juh, self.etah_vec[-1], self.etaTsum_vec[-1] + ) + elif self.solverctx.uniform_refinement: + headers = ("iteration", "N", "Ndual", "Juh", "eta", "eta_h") + row = ( + it, + self.N_vec[-1], self.Ndual_vec[-1], self.Juh, self.eta_vec[-1], self.etah_vec[-1] + ) + else: + headers = ("iteration", "N", "Ndual", "Juh", "eta", "eta_h", "sum_eta_T", "eff1", "eff2") + row = ( + it, + self.N_vec[-1], self.Ndual_vec[-1], self.Juh, self.eta_vec[-1], self.etah_vec[-1], self.etaTsum_vec[-1], self.eff1_vec[-1], self.eff2_vec[-1] + ) + + file_path.parent.mkdir(parents=True, exist_ok=True) # create directories if missing + if it == 0: + with open(file_path, "w", newline="") as file: + writer = csv.writer(file) + writer.writerow(headers) + writer.writerow(row) + else: + with open(file_path, "a", newline="") as file: + writer = csv.writer(file) + writer.writerow(row) + + def print(self, *args, **kwargs): + if self.verbose: + PETSc.Sys.Print(*args, **kwargs) + + def solve(self): + s = self.solverctx + + for it in range(s.max_iterations): + self.print(f"---------------------------- [MESH LEVEL {it}] ----------------------------") + self.write_mesh(it) + self.solve_primal() + self.solve_dual() + self.write_solution(it) + self.compute_etah() + if self.eta_h < self.tolerance: + self.print("Error estimate below tolerance, finished.") + break + if it == s.max_iterations - 1: + self.print(f"Maximum iteration ({s.max_iterations}) reached. Exiting.") + break + if s.uniform_refinement: + self.print("Refining uniformly") + self.uniform_refine() + else: + if s.manual_indicators: + self.manual_error_indicators() + else: + self.automatic_error_indicators() + self.compute_efficiency() + self.mark_cells() + if s.write_at_iteration: + self.print("Appending data ...") + self.append_data(it) + self.refine_mesh() + + if not s.write_at_iteration: + self.print("Writing data ...") + self.write_data() + + # Writing functions: -------------------------------------- + + def write_solution(self, it): + s = self.solverctx + should_write = False + if s.write_solution == "all": + should_write = True + elif s.write_solution == "first_and_last": + if it == 0 or it == s.max_iterations: + should_write = True + elif s.write_solution == "by_iteration": + # Case A: user gave specific iterations (list/tuple/set) + if getattr(s, "write_solution_iteration_vector", None) is not None: + # allow any iterable; convert to set for O(1) lookup + targets = set(s.write_iteration_vector) + should_write = it in targets + # Case B: otherwise use interval (positive int) + elif getattr(s, "write_solution_iteration_interval", None) is not None: + interval = int(s.write_iteration_interval) + if interval <= 0: + raise ValueError("write_solution_iteration_interval must be a positive integer") + should_write = (it % interval == 0) # includes it=0 + if should_write: + self.print("Writing (primal) solution ...") + VTKFile(self.output_dir / f"{s.run_name}/{s.run_name}_solution_{it}.pvd").write(*self.u.subfunctions) + self.print("Writing (dual) solution ...") + VTKFile(self.output_dir / f"{s.run_name}/{s.run_name}_dual_solution_{it}.pvd").write(*self.z.subfunctions) + + def write_mesh(self, it): + s = self.solverctx + should_write = False + if s.write_mesh == "all": + should_write = True + elif s.write_mesh == "first_and_last": + if it == 0 or it == s.max_iterations: + should_write = True + elif s.write_mesh == "by_iteration": + # Case A: user gave specific iterations (list/tuple/set) + if getattr(s, "write_mesh_iteration_vector", None) is not None: + # allow any iterable; convert to set for O(1) lookup + targets = set(s.write_iteration_vector) + should_write = it in targets + # Case B: otherwise use interval (positive int) + elif getattr(s, "write_mesh_iteration_interval", None) is not None: + interval = int(s.write_iteration_interval) + if interval <= 0: + raise ValueError("write_mesh_iteration_interval must be a positive integer") + should_write = (it % interval == 0) # includes it=0 + if should_write: + self.print("Writing mesh ...") + VTKFile(self.output_dir / f"{s.run_name}/{s.run_name}_mesh_{it}.pvd").write(self.mesh) + + +# Utility functions + +def residual(F, test): + v, = F.arguments() + return replace(F, {v: test}) + + +def both(u): + return u("+") + u("-") + + +def as_mixed(exprs): + return as_vector([e[idx] for e in exprs for idx in np.ndindex(e.ufl_shape)]) + + +# Should no longer be needed +def reconstruct_bc_value(bc, V): + if not isinstance(bc._original_arg, Function): + return bc._original_arg + return Function(V).interpolate(bc._original_arg) + + +def reconstruct_bcs(bcs, V): + """Reconstruct a list of bcs""" + new_bcs = [] + for bc in bcs: + V_ = V + for index in bc._indices: + V_ = V_.sub(index) + g = reconstruct_bc_value(bc, V_) + new_bcs.append(bc.reconstruct(V=V_, g=g)) + + return new_bcs + + +@singledispatch +def refine(expr, self, coefficient_mapping=None): + return coarsen(expr, self, coefficient_mapping=coefficient_mapping) # fallback to original + + +@refine.register(Cofunction) +@refine.register(Function) +def refine_function(expr, self, coefficient_mapping=None): + if coefficient_mapping is None: + coefficient_mapping = {} + new = coefficient_mapping.get(expr) + if new is None: + Vf = expr.function_space() + Vc = self(Vf, self) + new = Function(Vc, name=f"coarse_{expr.name()}") + new.interpolate(expr) + coefficient_mapping[expr] = new + return new + + +# Only required for my examples: +def getlabels(mesh, codim): + ngmesh = mesh.netgen_mesh + names = ngmesh.GetRegionNames(codim=codim) + names_to_labels = {} + for l in names: + names_to_labels[l] = tuple(i+1 for i, name in enumerate(names) if name == l) + return names_to_labels From 42a68b8eb31d7c2dfb6a9480563a194625b93289 Mon Sep 17 00:00:00 2001 From: Pablo Brubeck Date: Tue, 17 Feb 2026 14:04:47 +0000 Subject: [PATCH 02/51] fixes --- firedrake/adaptive_variational_solver.py | 549 +++++++++++------------ firedrake/mg/ufl_utils.py | 4 +- 2 files changed, 273 insertions(+), 280 deletions(-) diff --git a/firedrake/adaptive_variational_solver.py b/firedrake/adaptive_variational_solver.py index 26173c3e5f..c156ae9683 100644 --- a/firedrake/adaptive_variational_solver.py +++ b/firedrake/adaptive_variational_solver.py @@ -3,17 +3,21 @@ from firedrake.cofunction import Cofunction from firedrake.functionspace import FunctionSpace, TensorFunctionSpace from firedrake.ufl_expr import TestFunction, TrialFunction, derivative, action, adjoint -from firedrake.variational_solver import NonlinearVariationalProblem, NonlinearVariationalSolver +from firedrake.variational_solver import (NonlinearVariationalProblem, NonlinearVariationalSolver, + LinearVariationalProblem, LinearVariationalSolver) from firedrake.solving import solve +from firedrake.norms import norm from firedrake.preconditioners.pmg import PMGPC -from firedrake.mg.ufl_utils import coarsen +from firedrake.mg import utils +from firedrake.mg.ufl_utils import coarsen, CoarseningError from firedrake.mg.adaptive_hierarchy import AdaptiveMeshHierarchy from firedrake.mg.adaptive_transfer_manager import AdaptiveTransferManager from firedrake.output import VTKFile from finat.ufl import BrokenElement, FiniteElement from ufl import avg, dot, div, grad, dx, ds, dS, inner, jump, as_vector, replace, FacetNormal +import ufl from functools import singledispatch from pathlib import Path @@ -21,7 +25,7 @@ import csv -class SolverCtx: +class GoalAdaptiveOptions: def __init__(self, config: dict): self.manual_indicators = config.get("manual_indicators", False) # Used for manual indicators (only implemented for Poisson but could be overriden) self.dorfler_alpha = config.get("dorfler_alpha", 0.5) # Dorfler marking parameter, default 0.5 @@ -45,6 +49,7 @@ def __init__(self, config: dict): self.results_file_name = config.get("results_file_name", None) self.nev = config.get("nev", 5) self.run_name = config.get("run_name", None) + self.form_compiler_parameters = config.get("form_compiler_parameters", None) # Solver parameters sp_cell = { @@ -58,42 +63,12 @@ def __init__(self, config: dict): "ksp_type": "cg", "pc_type": "jacobi", } - # EXAMPLE DUAL SOLVE METHODS - sp_star = { - "snes_type": "ksponly", - "ksp_type": "cg", - "ksp_rtol": 1.0e-10, - "ksp_max_it": 20, - "ksp_convergence_test": "skip", - "ksp_monitor": None, - "pc_type": "python", - "pc_python_type": "firedrake.ASMStarPC", - "pc_star_mat_ordering_type": "metisnd", - "pc_star_sub_sub_pc_type": "cholesky", - } - sp_vanka = { - "snes_type": "ksponly", - "ksp_type": "gmres", - "ksp_rtol": 1.0e-10, - "ksp_max_it": 20, - "ksp_convergence_test": "skip", - "ksp_monitor": None, - "pc_type": "python", - "pc_python_type": "firedrake.ASMVankaPC", - "pc_vanka_mat_ordering_type": "metisnd", - "pc_vanka_sub_sub_pc_type": "cholesky", - "pc_vanka_construct_dim": 0, - } - sp_chol = { - "pc_type": "cholesky", - "pc_factor_mat_solver_type": "mumps" - } class GoalAdaptiveNonlinearVariationalSolver(): - """ - Solves a nonlinear variational problem to minimise the error in a user-specified goal functional. - We do this by adaptively refining the mesh based on the solution to a dual problem - which links the goal functional + """Solves a nonlinear variational problem to minimise the error in a + user-specified goal functional. We do this by adaptively refining the mesh + based on the solution to a dual problem - which links the goal functional to the PDE. """ def __init__(self, problem: NonlinearVariationalProblem, goal_functional, tolerance: float, solver_parameters: dict, @@ -101,29 +76,26 @@ def __init__(self, problem: NonlinearVariationalProblem, goal_functional, tolera nullspace=None): # User input vars self.problem = problem - self.J = goal_functional + self.goal_functional = goal_functional self.tolerance = tolerance self.sp_primal = primal_solver_parameters self.sp_dual = dual_solver_parameters self.u_exact = as_mixed(exact_solution) if isinstance(exact_solution, (tuple, list)) else exact_solution self.goal_exact = exact_goal - self.solverctx = SolverCtx(solver_parameters) # To store solver parameter data - Unnecessary, could remove in future. + self.options = GoalAdaptiveOptions(solver_parameters) + # Derived vars self.verbose = verbose - self.V = problem.u.function_space() + V = problem.u.function_space() self.u = problem.u - self.bcs = problem.bcs - self.F = problem.F - self.element = self.V.ufl_element() + self.element = V.ufl_element() self.degree = self.element.degree() - self.test = TestFunction(self.V) - self.mesh = self.V.mesh() self.nullspace = nullspace self.atm = AdaptiveTransferManager() - self.amh = AdaptiveMeshHierarchy(self.mesh) + self.amh = AdaptiveMeshHierarchy(V.mesh()) # Data storage and writing - self.output_dir = Path(self.solverctx.output_dir) + self.output_dir = Path(self.options.output_dir) self.output_dir.mkdir(parents=True, exist_ok=True) # ensures folder exists self.N_vec = [] self.Ndual_vec = [] @@ -135,48 +107,44 @@ def __init__(self, problem: NonlinearVariationalProblem, goal_functional, tolera self.eff3_vec = [] def solve_primal(self): - from firedrake.assemble import assemble - s = self.solverctx - ndofs = self.V.dim() + F = self.problem.F + V = self.problem.u.function_space() + bcs = self.problem.bcs + mesh = V.mesh() + ndofs = V.dim() self.N_vec.append(ndofs) + self.u = self.problem.u def solve_uh(): - if self.sp_primal is None: - self.print(f"Solving primal (degree: {self.degree}, dofs: {ndofs}) [Method: Default nonlinear solve] ...") - else: - self.print(f"Solving primal (degree: {self.degree}, dofs: {ndofs}) [Method: User defined] ...") + self.print(f"Solving primal (degree: {self.degree}, dofs: {ndofs}) ...") solver = NonlinearVariationalSolver(self.problem, solver_parameters=self.sp_primal) solver.set_transfer_manager(self.atm) solver.solve() - if s.use_adjoint_residual: + if self.options.use_adjoint_residual: # Now solve in higher space - high_degree = self.degree + s.dual_extra_degree # By default use dual degree + high_degree = self.degree + self.options.dual_extra_degree # By default use dual degree high_element = PMGPC.reconstruct_degree(self.element, high_degree) - Vhigh = FunctionSpace(self.mesh, high_element) + Vhigh = FunctionSpace(mesh, high_element) solve_uh() - self.print("u norm:", assemble(inner(self.u, self.u) * dx)) + self.print("u norm:", norm(self.u)) self.u_high = Function(Vhigh).interpolate(self.u) # Dual soluton - self.print("u_high norm:", assemble(inner(self.u_high, self.u_high) * dx)) - (v_old,) = self.F.arguments() + self.print("u_high norm:", norm(self.u_high)) + v_old, = F.arguments() v_high = TestFunction(Vhigh) - F_high = replace(self.F, {v_old: v_high, self.u: self.u_high}) - bcs_high = reconstruct_bcs(self.bcs, Vhigh) + F_high = replace(F, {v_old: v_high, self.u: self.u_high}) + bcs_high = reconstruct_bcs(bcs, Vhigh) self.problem_high = NonlinearVariationalProblem(F_high, self.u_high, bcs_high) - if self.sp_primal is None: - self.print(f"Solving primal in higher space for error estimate (degree: {high_degree}, dofs: {Vhigh.dim()}) [Method: Default nonlinear solve] ...") - else: - self.print(f"Solving primal in higher space for error estimate (degree: {high_degree}, dofs: {Vhigh.dim()}) [Method: User defined] ...") - + self.print(f"Solving primal in higher space for error estimate (degree: {high_degree}, dofs: {Vhigh.dim()}) ...") solver = NonlinearVariationalSolver(self.problem_high, solver_parameters=self.sp_primal) solver.set_transfer_manager(self.atm) solver.solve() - if s.primal_low_method == "solve": + if self.options.primal_low_method == "solve": solve_uh() - elif s.primal_low_method == "project": + elif self.options.primal_low_method == "project": self.u.project(self.u_high) elif False: # Default - but gives bad results? @@ -186,84 +154,94 @@ def solve_uh(): solve_uh() def solve_dual(self): - s = self.solverctx + J = self.goal_functional + F = self.problem.F + self.u = self.problem.u + bcs = self.problem.bcs + V = self.u.function_space() + mesh = V.mesh() - dual_degree = self.degree + s.dual_extra_degree + # Higher-order dual soluton + dual_degree = self.degree + self.options.dual_extra_degree dual_element = PMGPC.reconstruct_degree(self.element, dual_degree) - - Vdual = FunctionSpace(self.mesh, dual_element) - vtest = TestFunction(Vdual) # Dual test function - self.z = Function(Vdual) # Dual soluton + Vdual = FunctionSpace(mesh, dual_element) + self.z = Function(Vdual) ndofs_dual = Vdual.dim() self.Ndual_vec.append(ndofs_dual) + self.print(f"Solving higher-order dual (degree: {dual_degree}, dofs: {ndofs_dual}) ...") + + dF = derivative(F, self.u, TrialFunction(Vdual)) + dJ = derivative(J, self.u, TestFunction(Vdual)) + G = action(adjoint(dF), self.z) - dJ + a = derivative(G, self.z) + bcs_dual = [bc.reconstruct(V=Vdual, indices=bc._indices, g=0) for bc in bcs] + problem = LinearVariationalProblem(a, dJ, self.z, bcs_dual) + solver = LinearVariationalSolver(problem, solver_parameters=self.sp_dual) + solver.set_transfer_manager(self.atm) + solver.solve() + + # Lower-order dual soluton + self.z_lo = Function(V) + if self.options.dual_low_method == "solve": + ndofs = V.dim() + self.print(f"Solving lower-order dual (degree: {self.degree}, dofs: {ndofs}) ...") + + dF = derivative(F, self.u, TrialFunction(V)) + dJ = derivative(J, self.u, TestFunction(V)) + G_lo = action(adjoint(dF), self.z_lo) - dJ + a = derivative(G_lo, self.z_lo) + bcs_dual_low = [bc.reconstruct(V=V, indices=bc._indices, g=0) for bc in bcs] + problem = LinearVariationalProblem(a, dJ, self.z_lo, bcs_dual_low) + solver = LinearVariationalSolver(problem, solver_parameters=self.sp_dual) + solver.set_transfer_manager(self.atm) + solver.solve() - self.G = (action(adjoint(derivative(self.F, self.u, TrialFunction(Vdual))), self.z) - - derivative(self.J, self.u, vtest)) - - bcs_dual = [bc.reconstruct(V=Vdual, indices=bc._indices, g=0) for bc in self.bcs] - - if self.sp_dual is None: - self.print(f"Solving dual (degree: {dual_degree}, dofs: {ndofs_dual}) [Method: Default nonlinear solve] ...") - else: - self.print(f"Solving dual (degree: {dual_degree}, dofs: {ndofs_dual}) [Method: User defined] ...") - solve(self.G == 0, self.z, bcs_dual, solver_parameters=self.sp_dual) - - # zlo - self.z_lo = Function(self.V) # Dual soluton - if s.dual_low_method == "solve": - ndofs = self.V.dim() - test = TestFunction(self.V) - G_lo = (action(adjoint(derivative(self.F, self.u, TrialFunction(self.V))), self.z_lo) - - derivative(self.J, self.u, test)) - - bcs_dual_low = [bc.reconstruct(V=self.V, indices=bc._indices, g=0) for bc in self.bcs] - - if self.sp_dual is None: - self.print(f"Solving dual in V (degree: {self.degree}, dofs: {ndofs}) [Method: Default nonlinear solve] ...") - else: - self.print(f"Solving dual in V (degree: {self.degree}, dofs: {ndofs}) [Method: User defined] ...") - solve(G_lo == 0, self.z_lo, bcs_dual_low, solver_parameters=self.sp_dual) - - elif s.dual_low_method == "project": + elif self.options.dual_low_method == "project": self.z_lo.project(self.z) else: - self.z_lo.interpolate(self.z) # Default method + # Default method + self.z_lo.interpolate(self.z) self.z_err = self.z - self.z_lo def compute_etah(self): + """Compute error estimate""" from firedrake.assemble import assemble - s = self.solverctx - # Compute error estimate F(z) - if s.use_adjoint_residual: - primal_err = abs(assemble(residual(self.F, self.z_err))) + J = self.goal_functional + F = self.problem.F + u = self.problem.u + + primal_err = abs(assemble(residual(F, self.z_err))) + if self.options.use_adjoint_residual: + dF = derivative(F, u) + dJ = derivative(J, u) + G = action(adjoint(dF), self.z_lo) - dJ - G = (action(adjoint(derivative(self.F, self.u, TrialFunction(self.V))), self.z_lo) - - derivative(self.J, self.u, TestFunction(self.V))) dual_err = abs(assemble(residual(G, self.u_err))) self.eta_h = 0.5 * abs(primal_err + dual_err) else: - self.eta_h = abs(assemble(residual(self.F, self.z_err))) + self.eta_h = primal_err self.etah_vec.append(self.eta_h) - self.Juh = assemble(self.J) - self.print(f"{"Computed goal":45s}{"J(uh):":8s}{self.Juh:15.12f}") + Juh = assemble(J) + self.print(f"{"Computed goal":45s}{"J(uh):":8s}{Juh:15.12f}") + self.Juh = Juh - if self.u_exact is not None: - quad_opts = {"quadrature_degree": 20} - self.Ju = assemble(replace(self.J, {self.u: self.u_exact}), form_compiler_parameters=quad_opts) - elif self.goal_exact is not None: - self.Ju = self.goal_exact + if self.goal_exact is not None: + Ju = self.goal_exact + elif self.u_exact is not None: + fcp = self.options.form_compiler_parameters + Ju = assemble(replace(J, {u: self.u_exact}), form_compiler_parameters=fcp) if self.u_exact is not None or self.goal_exact is not None: - self.eta = abs(self.Juh - self.Ju) + self.eta = abs(Juh - Ju) self.eta_vec.append(self.eta) - self.print(f"{"Exact goal":45s}{"J(u):":8s}{self.Ju:15.12f}") + self.print(f"{"Exact goal":45s}{"J(u):":8s}{Ju:15.12f}") self.print(f"{"True error, |J(u) - J(u_h)|":45s}{"eta:":8s}{self.eta:15.12f}") - if s.use_adjoint_residual: + if self.options.use_adjoint_residual: self.print(f"{"Primal error, |rho(u_h;z-z_h)|:":45s}{"eta_pri:":8s}{primal_err:15.12f}") self.print(f"{"Dual error, |rho*(z_h;u-u_h)|:":45s}{"eta_adj:":8s}{dual_err:15.12f}") self.print(f"{"Difference":35s}{"|eta_pri - η_adj|:":18s}{abs(primal_err-dual_err):19.12e}") @@ -272,59 +250,63 @@ def compute_etah(self): self.print(f"{"Predicted error, |rho(u_h;z-z_h)|":45s}{"eta_h:":8s}{self.eta_h:15.12f}") def automatic_error_indicators(self): + """Compute cell and facet residuals R_cell, R_facet""" from firedrake.assemble import assemble - self.print("Computing local refinement indicators, eta_K...") - # 7. Compute cell and facet residuals R_T, R_\partialT - z_lo = Function(self.V) - z_lo.interpolate(self.z) # Default method + J = self.goal_functional + F = self.problem.F + V = self.problem.u.function_space() + + z_lo = Function(V) + z_lo.interpolate(self.z) self.z_err = self.z - z_lo - if self.solverctx.use_adjoint_residual: - u_lo = Function(self.V) + if self.options.use_adjoint_residual: + u_lo = Function(V) u_lo.interpolate(self.u_high) self.u_err = self.u_high - u_lo - s = self.solverctx - dim = self.mesh.topological_dimension - cell = self.mesh.ufl_cell() + mesh = V.mesh() + dim = mesh.topological_dimension + cell = mesh.ufl_cell() variant = "integral" # Finite element type - cell_residual_degree = self.degree + s.cell_residual_extra_degree - facet_residuaL_degree = self.degree + s.facet_residual_extra_degree + cell_residual_degree = self.degree + self.options.cell_residual_extra_degree + facet_residuaL_degree = self.degree + self.options.facet_residual_extra_degree # ------------------------------- Primal residual ------------------------------- - # Rcell - B = FunctionSpace(self.mesh, "B", dim+1, variant=variant) # Bubble function space + # Cell bubbles + B = FunctionSpace(mesh, "B", dim+1, variant=variant) # Bubble function space bubbles = Function(B).assign(1) # Bubbles - # Discontinuous function space of Rcell polynomials - if self.V.value_shape == (): - DG = FunctionSpace(self.mesh, "DG", cell_residual_degree, variant=variant) + # DG space on cell interiors + if V.value_shape == (): + DG = FunctionSpace(mesh, "DG", cell_residual_degree, variant=variant) else: - DG = TensorFunctionSpace(self.mesh, "DG", cell_residual_degree, variant=variant, shape=self.V.value_shape) + DG = TensorFunctionSpace(mesh, "DG", cell_residual_degree, variant=variant, shape=V.value_shape) uc = TrialFunction(DG) vc = TestFunction(DG) ac = inner(uc, bubbles*vc)*dx - Lc = residual(self.F, bubbles*vc) - Rcell = Function(DG, name="Rcell") # Rcell polynomial - assemble(Lc) - solve(ac == Lc, Rcell, solver_parameters=s.sp_cell) # solve for Rcell polynonmial - - # Rfacet - FB = FunctionSpace(self.mesh, "FB", dim, variant=variant) # Cone function space - cones = Function(FB).assign(1) # Cones - # Broken discontinuous function space of facet polynomials + Lc = residual(F, bubbles*vc) + # solve for Rcell + Rcell = Function(DG) + solve(ac == Lc, Rcell, solver_parameters=self.options.sp_cell) + + # Facet bubbles + FB = FunctionSpace(mesh, "FB", dim, variant=variant) + cones = Function(FB).assign(1) + # Broken facet bubble space el = BrokenElement(FiniteElement("FB", cell=cell, degree=facet_residuaL_degree+dim, variant=variant)) - if self.V.value_shape == (): - Q = FunctionSpace(self.mesh, el) + if V.value_shape == (): + Q = FunctionSpace(mesh, el) else: - Q = TensorFunctionSpace(self.mesh, el, shape=self.V.value_shape) + Q = TensorFunctionSpace(mesh, el, shape=V.value_shape) Qtest = TestFunction(Q) Qtrial = TrialFunction(Q) - Lf = residual(self.F, Qtest) - inner(Rcell, Qtest)*dx + Lf = residual(F, Qtest) - inner(Rcell, Qtest)*dx af = both(inner(Qtrial/cones, Qtest))*dS + inner(Qtrial/cones, Qtest)*ds + # solve for Rfacet Rhat = Function(Q) - solve(af == Lf, Rhat, solver_parameters=s.sp_facet) + solve(af == Lf, Rhat, solver_parameters=self.options.sp_facet) Rfacet = Rhat/cones # Primal error indicators - DG0 = FunctionSpace(self.mesh, "DG", degree=0) + DG0 = FunctionSpace(mesh, "DG", degree=0) test = TestFunction(DG0) eta_primal = assemble( @@ -334,20 +316,22 @@ def automatic_error_indicators(self): ) # ------------------------------- Adjoint residual ------------------------------- - if s.use_adjoint_residual: - (vF,) = self.F.arguments() # test Argument used in self.F - # r*(v) = J"(u)[v] - A"_u(u)[v, z] since self.F = A(u;v) - L(v) - # rstar_form = -derivative(self.J, self.u, vF) + derivative(replace(self.F, {vF: self.z}), self.u, vF) - rstar_form = (action(adjoint(derivative(self.F, self.u, TrialFunction(self.V))), self.z_lo) - - derivative(self.J, self.u, TestFunction(self.V))) + if self.options.use_adjoint_residual: + (vF,) = F.arguments() # test Argument used in F + # r*(v) = J"(u)[v] - A"_u(u)[v, z] since F = A(u;v) - L(v) + # rstar = -derivative(J, self.u, vF) + derivative(replace(F, {vF: self.z}), self.u, vF) + dF = derivative(F, self.u, TrialFunction(V)) + dJ = derivative(J, self.u, TestFunction(V)) + rstar = action(adjoint(dF), self.z_lo) - dJ + # dual: project r* -> Rcell*, Rfacet* - Lc_star = residual(rstar_form, bubbles*vc) - Rcell_star = Function(DG, name="Rcell_star") - solve(ac == Lc_star, Rcell_star, solver_parameters=s.sp_cell) + Lc_star = residual(rstar, bubbles*vc) + Rcell_star = Function(DG) + solve(ac == Lc_star, Rcell_star, solver_parameters=self.options.sp_cell) - Lf_star = residual(rstar_form, Qtest) - inner(Rcell_star, Qtest)*dx + Lf_star = residual(rstar, Qtest) - inner(Rcell_star, Qtest)*dx Rhat_star = Function(Q) - solve(af == Lf_star, Rhat_star, solver_parameters=s.sp_facet) + solve(af == Lf_star, Rhat_star, solver_parameters=self.options.sp_facet) Rfacet_star = Rhat_star/cones # indicators: 0.5 * (primal + dual) @@ -358,23 +342,21 @@ def automatic_error_indicators(self): ) with eta_dual.dat.vec as evec: evec.abs() - etaT_array = evec.getArray() + self.eta_dual_total = abs(evec.sum()) - self.eta_dual_total = abs(np.sum(etaT_array)) self.print(f"{"Sum of dual refinement indicators":45s}{"Σeta_K:":8s}{self.eta_dual_total:15.12f}") with eta_primal.dat.vec as evec: evec.abs() - etaT_array = evec.getArray() + self.eta_dual_total = abs(evec.sum()) - self.eta_dual_total = abs(np.sum(etaT_array)) self.print(f"{"Sum of primal refinement indicators":45s}{"Σeta_K:":8s}{self.eta_dual_total:15.12f}") self.etaT = assemble(0.5*(eta_primal + eta_dual)) else: self.etaT = eta_primal - # Exact error indicators (experimental - ignore) - if self.solverctx.exact_indicators: + # XXX Exact error indicators (experimental - ignore) + if self.options.exact_indicators: u_err_exact = self.u_exact - self.u eta_dual_exact = assemble( inner(inner(Rcell_star, u_err_exact), test)*dx @@ -392,22 +374,21 @@ def manual_error_indicators(self): the weak form by parts (to recover the strong form) and redistributing facet fluxes. """ from firedrake.assemble import assemble - self.print("[MANUAL] Computing local refinement indicators (η_K)...") - n = FacetNormal(self.mesh) - DG0 = FunctionSpace(self.mesh, "DG", degree=0) + mesh = self.amh[-1] + n = FacetNormal(mesh) + DG0 = FunctionSpace(mesh, "DG", degree=0) test = TestFunction(DG0) self.etaT = assemble( inner(self.f + div(grad(self.u)), self.z_err * test) * dx - - inner(0.5*jump(grad(self.u), n), self.z_err * both(test)) * dS + - inner(jump(grad(self.u), n), self.z_err * avg(test)) * dS - inner(dot(grad(self.u), n), self.z_err * test) * ds ) def compute_efficiency(self): with self.etaT.dat.vec as evec: evec.abs() - self.etaT_array = evec.getArray() + self.etaT_total = abs(evec.sum()) - self.etaT_total = abs(np.sum(self.etaT_array)) self.etaTsum_vec.append(self.etaT_total) self.print(f"{"Sum of refinement indicators":45s}{"Ση_K:":8s}{self.etaT_total:15.12f}") @@ -424,59 +405,98 @@ def compute_efficiency(self): self.print(f"{"Effectivity index:":45s}{"Ση_K/η_h:":8s}{self.eff3:7.4f}") self.eff3_vec.append(self.eff3) - def mark_cells(self): - """ Only Dorfler marking is implemented currently. Can be overridden if other marking strategies are desired. - """ - s = self.solverctx - # 9. Mark cells for refinement (Dorfler marking) - sorted_indices = np.argsort(-self.etaT_array) - sorted_etaT = self.etaT_array[sorted_indices] + def set_uniform_cell_markers(self): + """Uniform marking for comparison tests""" + mesh = self.amh[-1] + markers_space = FunctionSpace(mesh, "DG", 0) + self.markers = Function(markers_space) + self.markers.assign(1) + + def set_adaptive_cell_markers(self): + """Mark cells for refinement (Dorfler marking)""" + sorted_indices = np.argsort(-self.etaT.dat.data_ro) + sorted_etaT = self.etaT.dat.data[sorted_indices] cumulative_sum = np.cumsum(sorted_etaT) - threshold = s.dorfler_alpha * self.etaT_total + threshold = self.options.dorfler_alpha * self.etaT_total M = np.searchsorted(cumulative_sum, threshold) + 1 marked_cells = sorted_indices[:M] - markers_space = FunctionSpace(self.mesh, "DG", 0) + mesh = self.amh[-1] + markers_space = FunctionSpace(mesh, "DG", 0) self.markers = Function(markers_space) with self.markers.dat.vec as mv: marr = mv.getArray() - marr[:] = 0 marr[marked_cells] = 1 - def refine_mesh(self): - self.print("Refining mesh ...") - new_mesh = self.mesh.refine_marked_elements(self.markers) - self.print("Transferring problem to new mesh ...") - - # FIXME - self.amh = AdaptiveMeshHierarchy(self.mesh) + def refine_problem(self): + mesh = self.amh[-1] + new_mesh = mesh.refine_marked_elements(self.markers) self.amh.add_mesh(new_mesh) coef_map = {} + self.problem = refine(self.problem, refine, coefficient_mapping=coef_map) + self.goal_functional = refine(self.goal_functional, refine, coefficient_mapping=coef_map) if self.u_exact is not None: self.u_exact = refine(self.u_exact, refine, coefficient_mapping=coef_map) - - self.problem = refine(self.problem, refine, coefficient_mapping=coef_map) - self.J = refine(self.J, refine, coefficient_mapping=coef_map) - self.F = self.problem.F self.u = self.problem.u - self.bcs = self.problem.bcs - self.V = self.u.function_space() - self.mesh = new_mesh + self.print("******* dim =", self.u.function_space().dim()) - def uniform_refine(self): - # Uniform marking for comparison tests - markers_space = FunctionSpace(self.mesh, "DG", 0) - self.markers = Function(markers_space) - self.markers.assign(1) + def solve(self): + for it in range(self.options.max_iterations): + if self.step(): + break + + def step(self): + it = len(self.amh) - 1 + self.print(f"---------------------------- [MESH LEVEL {it}] ----------------------------") + self.write_mesh(it) + self.solve_primal() + self.solve_dual() + self.write_solution(it) + self.compute_etah() + if self.eta_h < self.tolerance: + self.print("Error estimate below tolerance, finished.") + return 1 + + if it == self.options.max_iterations - 1: + self.print(f"Maximum iteration ({self.options.max_iterations}) reached. Exiting.") + return 1 + + if self.options.uniform_refinement: + self.print("Refining uniformly") + self.set_uniform_cell_markers() + else: + if self.options.manual_indicators: + self.print("[MANUAL] Computing local refinement indicators (η_K)...") + self.manual_error_indicators() + else: + self.print("Computing local refinement indicators, eta_K...") + self.automatic_error_indicators() + self.compute_efficiency() + self.set_adaptive_cell_markers() + + if self.options.write_at_iteration: + self.print("Appending data ...") + self.append_data() + self.print("Transferring problem to new mesh ...") + self.refine_problem() + if not self.options.write_at_iteration: + self.print("Writing data ...") + self.write_data() + return 0 + + # Writing functions: -------------------------------------- + + def print(self, *args, **kwargs): + if self.verbose: + PETSc.Sys.Print(*args, **kwargs) def write_data(self): - s = self.solverctx # Write to file - if s.results_file_name is None: + if self.options.results_file_name is None: file_path = self.output_dir / "results.csv" else: - file_path = self.output_dir / s.results_file_name + file_path = self.output_dir / self.options.results_file_name rows = list(zip(self.N_vec, self.Ndual_vec, self.eta_vec, self.etah_vec, self.etaTsum_vec, self.eff1_vec, self.eff2_vec)) headers = ("N", "Ndual", "eta", "eta_h", "sum_eta_T", "eff1", "eff2") with open(file_path, "w", newline="") as file: @@ -484,29 +504,31 @@ def write_data(self): w.writerow(headers) w.writerows(rows) - def append_data(self, it): - s = self.solverctx - if s.run_name is None: + def append_data(self): + it = len(self.amh) - 1 + Juh = self.Juh + run_name = self.options.run_name + if run_name is None: file_path = self.output_dir / "results.csv" else: - file_path = self.output_dir / f"{s.run_name}/{s.run_name}_results.csv" - if self.u_exact is None and self.goal_exact is None and not self.solverctx.uniform_refinement: + file_path = self.output_dir / f"{run_name}/{run_name}_results.csv" + if self.u_exact is None and self.goal_exact is None and not self.options.uniform_refinement: headers = ("iteration", "N", "Ndual", "Juh", "eta_h", "sum_eta_T") row = ( it, - self.N_vec[-1], self.Ndual_vec[-1], self.Juh, self.etah_vec[-1], self.etaTsum_vec[-1] + self.N_vec[-1], self.Ndual_vec[-1], Juh, self.etah_vec[-1], self.etaTsum_vec[-1] ) - elif self.solverctx.uniform_refinement: + elif self.options.uniform_refinement: headers = ("iteration", "N", "Ndual", "Juh", "eta", "eta_h") row = ( it, - self.N_vec[-1], self.Ndual_vec[-1], self.Juh, self.eta_vec[-1], self.etah_vec[-1] + self.N_vec[-1], self.Ndual_vec[-1], Juh, self.eta_vec[-1], self.etah_vec[-1] ) else: headers = ("iteration", "N", "Ndual", "Juh", "eta", "eta_h", "sum_eta_T", "eff1", "eff2") row = ( it, - self.N_vec[-1], self.Ndual_vec[-1], self.Juh, self.eta_vec[-1], self.etah_vec[-1], self.etaTsum_vec[-1], self.eff1_vec[-1], self.eff2_vec[-1] + self.N_vec[-1], self.Ndual_vec[-1], Juh, self.eta_vec[-1], self.etah_vec[-1], self.etaTsum_vec[-1], self.eff1_vec[-1], self.eff2_vec[-1] ) file_path.parent.mkdir(parents=True, exist_ok=True) # create directories if missing @@ -520,96 +542,58 @@ def append_data(self, it): writer = csv.writer(file) writer.writerow(row) - def print(self, *args, **kwargs): - if self.verbose: - PETSc.Sys.Print(*args, **kwargs) - - def solve(self): - s = self.solverctx - - for it in range(s.max_iterations): - self.print(f"---------------------------- [MESH LEVEL {it}] ----------------------------") - self.write_mesh(it) - self.solve_primal() - self.solve_dual() - self.write_solution(it) - self.compute_etah() - if self.eta_h < self.tolerance: - self.print("Error estimate below tolerance, finished.") - break - if it == s.max_iterations - 1: - self.print(f"Maximum iteration ({s.max_iterations}) reached. Exiting.") - break - if s.uniform_refinement: - self.print("Refining uniformly") - self.uniform_refine() - else: - if s.manual_indicators: - self.manual_error_indicators() - else: - self.automatic_error_indicators() - self.compute_efficiency() - self.mark_cells() - if s.write_at_iteration: - self.print("Appending data ...") - self.append_data(it) - self.refine_mesh() - - if not s.write_at_iteration: - self.print("Writing data ...") - self.write_data() - - # Writing functions: -------------------------------------- - def write_solution(self, it): - s = self.solverctx should_write = False - if s.write_solution == "all": + write_solution = self.options.write_mesh + if write_solution == "all": should_write = True - elif s.write_solution == "first_and_last": - if it == 0 or it == s.max_iterations: + elif write_solution == "first_and_last": + if it == 0 or it == self.options.max_iterations: should_write = True - elif s.write_solution == "by_iteration": + elif write_solution == "by_iteration": # Case A: user gave specific iterations (list/tuple/set) - if getattr(s, "write_solution_iteration_vector", None) is not None: + if getattr(self.options, "write_solution_iteration_vector", None) is not None: # allow any iterable; convert to set for O(1) lookup - targets = set(s.write_iteration_vector) + targets = set(self.options.write_iteration_vector) should_write = it in targets # Case B: otherwise use interval (positive int) - elif getattr(s, "write_solution_iteration_interval", None) is not None: - interval = int(s.write_iteration_interval) + elif getattr(self.options, "write_solution_iteration_interval", None) is not None: + interval = int(self.options.write_iteration_interval) if interval <= 0: raise ValueError("write_solution_iteration_interval must be a positive integer") should_write = (it % interval == 0) # includes it=0 if should_write: + run_name = self.options.run_name self.print("Writing (primal) solution ...") - VTKFile(self.output_dir / f"{s.run_name}/{s.run_name}_solution_{it}.pvd").write(*self.u.subfunctions) + VTKFile(self.output_dir / f"{run_name}/{run_name}_solution_{it}.pvd").write(*self.u.subfunctions) self.print("Writing (dual) solution ...") - VTKFile(self.output_dir / f"{s.run_name}/{s.run_name}_dual_solution_{it}.pvd").write(*self.z.subfunctions) + VTKFile(self.output_dir / f"{run_name}/{run_name}_dual_solution_{it}.pvd").write(*self.z.subfunctions) def write_mesh(self, it): - s = self.solverctx + mesh = self.problem.u.function_space().mesh() should_write = False - if s.write_mesh == "all": + write_mesh = self.options.write_mesh + if write_mesh == "all": should_write = True - elif s.write_mesh == "first_and_last": - if it == 0 or it == s.max_iterations: + elif write_mesh == "first_and_last": + if it == 0 or it == self.options.max_iterations: should_write = True - elif s.write_mesh == "by_iteration": + elif write_mesh == "by_iteration": # Case A: user gave specific iterations (list/tuple/set) - if getattr(s, "write_mesh_iteration_vector", None) is not None: + if getattr(self.options, "write_mesh_iteration_vector", None) is not None: # allow any iterable; convert to set for O(1) lookup - targets = set(s.write_iteration_vector) + targets = set(self.options.write_iteration_vector) should_write = it in targets # Case B: otherwise use interval (positive int) - elif getattr(s, "write_mesh_iteration_interval", None) is not None: - interval = int(s.write_iteration_interval) + elif getattr(self.options, "write_mesh_iteration_interval", None) is not None: + interval = int(self.options.write_iteration_interval) if interval <= 0: raise ValueError("write_mesh_iteration_interval must be a positive integer") should_write = (it % interval == 0) # includes it=0 if should_write: self.print("Writing mesh ...") - VTKFile(self.output_dir / f"{s.run_name}/{s.run_name}_mesh_{it}.pvd").write(self.mesh) + run_name = self.options.run_name + VTKFile(self.output_dir / f"{run_name}/{run_name}_mesh_{it}.pvd").write(mesh) # Utility functions @@ -652,6 +636,15 @@ def refine(expr, self, coefficient_mapping=None): return coarsen(expr, self, coefficient_mapping=coefficient_mapping) # fallback to original +@refine.register(ufl.Mesh) +@refine.register(ufl.MeshSequence) +def refine_mesh(mesh, self, coefficient_mapping=None): + hierarchy, level = utils.get_level(mesh) + if hierarchy is None: + raise CoarseningError("No mesh hierarchy available") + return hierarchy[level + 1] + + @refine.register(Cofunction) @refine.register(Function) def refine_function(expr, self, coefficient_mapping=None): diff --git a/firedrake/mg/ufl_utils.py b/firedrake/mg/ufl_utils.py index d5a26a36e6..99ffd19309 100644 --- a/firedrake/mg/ufl_utils.py +++ b/firedrake/mg/ufl_utils.py @@ -145,7 +145,7 @@ def coarsen_equation_bc(ebc, self, coefficient_mapping=None): @coarsen.register(firedrake.functionspaceimpl.WithGeometryBase) def coarsen_function_space(V, self, coefficient_mapping=None): - if hasattr(V, "_coarse"): + if hasattr(V, "_coarse") and self == coarsen: return V._coarse V_fine = V @@ -180,7 +180,7 @@ def coarsen_function(expr, self, coefficient_mapping=None): @coarsen.register(firedrake.NonlinearVariationalProblem) def coarsen_nlvp(problem, self, coefficient_mapping=None): - if hasattr(problem, "_coarse"): + if hasattr(problem, "_coarse") and self == coarsen: return problem._coarse def inject_on_restrict(fine, restriction, rscale, injection, coarse): From 2c3b4f5d8cbb67428f485172746d86f0994c2f2d Mon Sep 17 00:00:00 2001 From: Pablo Brubeck Date: Tue, 17 Feb 2026 16:05:51 +0000 Subject: [PATCH 03/51] Switch off Dorfler marking in parallel --- firedrake/adaptive_variational_solver.py | 35 ++++++++++++------------ 1 file changed, 18 insertions(+), 17 deletions(-) diff --git a/firedrake/adaptive_variational_solver.py b/firedrake/adaptive_variational_solver.py index c156ae9683..cd100d3302 100644 --- a/firedrake/adaptive_variational_solver.py +++ b/firedrake/adaptive_variational_solver.py @@ -269,7 +269,7 @@ def automatic_error_indicators(self): cell = mesh.ufl_cell() variant = "integral" # Finite element type cell_residual_degree = self.degree + self.options.cell_residual_extra_degree - facet_residuaL_degree = self.degree + self.options.facet_residual_extra_degree + facet_residual_degree = self.degree + self.options.facet_residual_extra_degree # ------------------------------- Primal residual ------------------------------- # Cell bubbles B = FunctionSpace(mesh, "B", dim+1, variant=variant) # Bubble function space @@ -291,7 +291,7 @@ def automatic_error_indicators(self): FB = FunctionSpace(mesh, "FB", dim, variant=variant) cones = Function(FB).assign(1) # Broken facet bubble space - el = BrokenElement(FiniteElement("FB", cell=cell, degree=facet_residuaL_degree+dim, variant=variant)) + el = BrokenElement(FiniteElement("FB", cell=cell, degree=facet_residual_degree+dim, variant=variant)) if V.value_shape == (): Q = FunctionSpace(mesh, el) else: @@ -317,9 +317,7 @@ def automatic_error_indicators(self): # ------------------------------- Adjoint residual ------------------------------- if self.options.use_adjoint_residual: - (vF,) = F.arguments() # test Argument used in F # r*(v) = J"(u)[v] - A"_u(u)[v, z] since F = A(u;v) - L(v) - # rstar = -derivative(J, self.u, vF) + derivative(replace(F, {vF: self.z}), self.u, vF) dF = derivative(F, self.u, TrialFunction(V)) dJ = derivative(J, self.u, TestFunction(V)) rstar = action(adjoint(dF), self.z_lo) - dJ @@ -414,19 +412,24 @@ def set_uniform_cell_markers(self): def set_adaptive_cell_markers(self): """Mark cells for refinement (Dorfler marking)""" - sorted_indices = np.argsort(-self.etaT.dat.data_ro) - sorted_etaT = self.etaT.dat.data[sorted_indices] - cumulative_sum = np.cumsum(sorted_etaT) - threshold = self.options.dorfler_alpha * self.etaT_total - M = np.searchsorted(cumulative_sum, threshold) + 1 - marked_cells = sorted_indices[:M] - mesh = self.amh[-1] + if mesh.comm.size == 1: + threshold = self.options.dorfler_alpha * self.etaT_total + sorted_indices = np.argsort(-self.etaT.dat.data_ro) + sorted_etaT = self.etaT.dat.data[sorted_indices] + cumulative_sum = np.cumsum(sorted_etaT) + M = np.searchsorted(cumulative_sum, threshold) + 1 + marked_cells = sorted_indices[:M] + else: + # TODO implemented a parallel sort + with self.etaT.dat.vec_ro as evec: + _, eta_max = evec.max() + threshold = self.options.dorfler_alpha * eta_max + marked_cells = self.etaT.dat.data_ro > threshold + markers_space = FunctionSpace(mesh, "DG", 0) self.markers = Function(markers_space) - with self.markers.dat.vec as mv: - marr = mv.getArray() - marr[marked_cells] = 1 + self.markers.dat.data_wo[marked_cells] = 1 def refine_problem(self): mesh = self.amh[-1] @@ -439,7 +442,6 @@ def refine_problem(self): if self.u_exact is not None: self.u_exact = refine(self.u_exact, refine, coefficient_mapping=coef_map) self.u = self.problem.u - self.print("******* dim =", self.u.function_space().dim()) def solve(self): for it in range(self.options.max_iterations): @@ -466,11 +468,10 @@ def step(self): self.print("Refining uniformly") self.set_uniform_cell_markers() else: + self.print("Computing local refinement indicators eta_K ...") if self.options.manual_indicators: - self.print("[MANUAL] Computing local refinement indicators (η_K)...") self.manual_error_indicators() else: - self.print("Computing local refinement indicators, eta_K...") self.automatic_error_indicators() self.compute_efficiency() self.set_adaptive_cell_markers() From 82a707123231e66c81e5e53cbaa069cf127be169 Mon Sep 17 00:00:00 2001 From: Pablo Brubeck Date: Tue, 17 Feb 2026 17:14:39 +0000 Subject: [PATCH 04/51] refactoring --- firedrake/adaptive_variational_solver.py | 238 +++++++++++------------ 1 file changed, 119 insertions(+), 119 deletions(-) diff --git a/firedrake/adaptive_variational_solver.py b/firedrake/adaptive_variational_solver.py index cd100d3302..cdafbc9fcb 100644 --- a/firedrake/adaptive_variational_solver.py +++ b/firedrake/adaptive_variational_solver.py @@ -108,99 +108,88 @@ def __init__(self, problem: NonlinearVariationalProblem, goal_functional, tolera def solve_primal(self): F = self.problem.F - V = self.problem.u.function_space() + u = self.problem.u bcs = self.problem.bcs - mesh = V.mesh() - ndofs = V.dim() - self.N_vec.append(ndofs) - self.u = self.problem.u + V = self.problem.u.function_space() + self.N_vec.append(V.dim()) def solve_uh(): - self.print(f"Solving primal (degree: {self.degree}, dofs: {ndofs}) ...") + self.print(f"Solving primal (degree: {self.degree}, dofs: {V.dim()}) ...") solver = NonlinearVariationalSolver(self.problem, solver_parameters=self.sp_primal) solver.set_transfer_manager(self.atm) solver.solve() if self.options.use_adjoint_residual: # Now solve in higher space - high_degree = self.degree + self.options.dual_extra_degree # By default use dual degree + high_degree = self.degree + self.options.dual_extra_degree # Use dual degree high_element = PMGPC.reconstruct_degree(self.element, high_degree) - Vhigh = FunctionSpace(mesh, high_element) + Vhigh = V.reconstruct(element=high_element) solve_uh() - self.print("u norm:", norm(self.u)) - self.u_high = Function(Vhigh).interpolate(self.u) # Dual soluton - self.print("u_high norm:", norm(self.u_high)) + u_high = Function(Vhigh).interpolate(u) + self.print("u norm:", norm(u)) + self.print("u_high norm:", norm(u_high)) + v_old, = F.arguments() v_high = TestFunction(Vhigh) - F_high = replace(F, {v_old: v_high, self.u: self.u_high}) + F_high = replace(F, {v_old: v_high, u: u_high}) bcs_high = reconstruct_bcs(bcs, Vhigh) - self.problem_high = NonlinearVariationalProblem(F_high, self.u_high, bcs_high) + problem_high = NonlinearVariationalProblem(F_high, u_high, bcs_high) self.print(f"Solving primal in higher space for error estimate (degree: {high_degree}, dofs: {Vhigh.dim()}) ...") - solver = NonlinearVariationalSolver(self.problem_high, solver_parameters=self.sp_primal) + solver = NonlinearVariationalSolver(problem_high, solver_parameters=self.sp_primal) solver.set_transfer_manager(self.atm) solver.solve() if self.options.primal_low_method == "solve": solve_uh() elif self.options.primal_low_method == "project": - self.u.project(self.u_high) - elif False: - # Default - but gives bad results? - self.u.interpolate(self.u_high) - self.u_err = self.u_high - self.u + u.project(self.u_high) + else: + # Default to interpolation - but gives bad results? + u.interpolate(self.u_high) + self.u_err = self.u_high - u else: solve_uh() def solve_dual(self): J = self.goal_functional F = self.problem.F - self.u = self.problem.u + u = self.problem.u bcs = self.problem.bcs - V = self.u.function_space() - mesh = V.mesh() + V = u.function_space() + + def solve_zh(z): + Z = z.function_space() + degree = Z.ufl_element().degree() + self.print(f"Solving dual (degree: {degree}, dofs: {Z.dim()}) ...") + dF = derivative(F, u, TrialFunction(Z)) + dJ = derivative(J, u, TestFunction(Z)) + G = action(adjoint(dF), z) - dJ + a = derivative(G, z) + bcs_dual = [bc.reconstruct(V=Z, indices=bc._indices, g=0) for bc in bcs] + problem = LinearVariationalProblem(a, dJ, z, bcs_dual) + solver = LinearVariationalSolver(problem, solver_parameters=self.sp_dual) + solver.set_transfer_manager(self.atm) + solver.solve() # Higher-order dual soluton dual_degree = self.degree + self.options.dual_extra_degree dual_element = PMGPC.reconstruct_degree(self.element, dual_degree) - Vdual = FunctionSpace(mesh, dual_element) + Vdual = V.reconstruct(element=dual_element) self.z = Function(Vdual) - ndofs_dual = Vdual.dim() - self.Ndual_vec.append(ndofs_dual) - self.print(f"Solving higher-order dual (degree: {dual_degree}, dofs: {ndofs_dual}) ...") - - dF = derivative(F, self.u, TrialFunction(Vdual)) - dJ = derivative(J, self.u, TestFunction(Vdual)) - G = action(adjoint(dF), self.z) - dJ - a = derivative(G, self.z) - bcs_dual = [bc.reconstruct(V=Vdual, indices=bc._indices, g=0) for bc in bcs] - problem = LinearVariationalProblem(a, dJ, self.z, bcs_dual) - solver = LinearVariationalSolver(problem, solver_parameters=self.sp_dual) - solver.set_transfer_manager(self.atm) - solver.solve() + self.Ndual_vec.append(Vdual.dim()) + solve_zh(self.z) # Lower-order dual soluton self.z_lo = Function(V) if self.options.dual_low_method == "solve": - ndofs = V.dim() - self.print(f"Solving lower-order dual (degree: {self.degree}, dofs: {ndofs}) ...") - - dF = derivative(F, self.u, TrialFunction(V)) - dJ = derivative(J, self.u, TestFunction(V)) - G_lo = action(adjoint(dF), self.z_lo) - dJ - a = derivative(G_lo, self.z_lo) - bcs_dual_low = [bc.reconstruct(V=V, indices=bc._indices, g=0) for bc in bcs] - problem = LinearVariationalProblem(a, dJ, self.z_lo, bcs_dual_low) - solver = LinearVariationalSolver(problem, solver_parameters=self.sp_dual) - solver.set_transfer_manager(self.atm) - solver.solve() - + solve_zh(self.z_lo) elif self.options.dual_low_method == "project": self.z_lo.project(self.z) else: - # Default method + # Default to interpolation self.z_lo.interpolate(self.z) self.z_err = self.z - self.z_lo @@ -219,11 +208,11 @@ def compute_etah(self): G = action(adjoint(dF), self.z_lo) - dJ dual_err = abs(assemble(residual(G, self.u_err))) - self.eta_h = 0.5 * abs(primal_err + dual_err) + eta_h = 0.5 * abs(primal_err + dual_err) else: - self.eta_h = primal_err + eta_h = primal_err - self.etah_vec.append(self.eta_h) + self.etah_vec.append(eta_h) Juh = assemble(J) self.print(f"{"Computed goal":45s}{"J(uh):":8s}{Juh:15.12f}") @@ -236,25 +225,29 @@ def compute_etah(self): Ju = assemble(replace(J, {u: self.u_exact}), form_compiler_parameters=fcp) if self.u_exact is not None or self.goal_exact is not None: - self.eta = abs(Juh - Ju) - self.eta_vec.append(self.eta) + eta = abs(Juh - Ju) + self.eta_vec.append(eta) self.print(f"{"Exact goal":45s}{"J(u):":8s}{Ju:15.12f}") - self.print(f"{"True error, |J(u) - J(u_h)|":45s}{"eta:":8s}{self.eta:15.12f}") + self.print(f"{"True error, |J(u) - J(u_h)|":45s}{"eta:":8s}{eta:15.12f}") + else: + eta = None if self.options.use_adjoint_residual: self.print(f"{"Primal error, |rho(u_h;z-z_h)|:":45s}{"eta_pri:":8s}{primal_err:15.12f}") self.print(f"{"Dual error, |rho*(z_h;u-u_h)|:":45s}{"eta_adj:":8s}{dual_err:15.12f}") self.print(f"{"Difference":35s}{"|eta_pri - η_adj|:":18s}{abs(primal_err-dual_err):19.12e}") - self.print(f"{"Predicted error, 0.5|rho+rho*|":45s}{"eta_h:":8s}{self.eta_h:15.12f}") + self.print(f"{"Predicted error, 0.5|rho+rho*|":45s}{"eta_h:":8s}{eta_h:15.12f}") else: - self.print(f"{"Predicted error, |rho(u_h;z-z_h)|":45s}{"eta_h:":8s}{self.eta_h:15.12f}") + self.print(f"{"Predicted error, |rho(u_h;z-z_h)|":45s}{"eta_h:":8s}{eta_h:15.12f}") + return eta_h, eta def automatic_error_indicators(self): """Compute cell and facet residuals R_cell, R_facet""" from firedrake.assemble import assemble J = self.goal_functional F = self.problem.F - V = self.problem.u.function_space() + u = self.problem.u + V = u.function_space() z_lo = Function(V) z_lo.interpolate(self.z) @@ -264,10 +257,10 @@ def automatic_error_indicators(self): u_lo.interpolate(self.u_high) self.u_err = self.u_high - u_lo - mesh = V.mesh() + mesh = V.mesh().unique() dim = mesh.topological_dimension cell = mesh.ufl_cell() - variant = "integral" # Finite element type + variant = "integral" cell_residual_degree = self.degree + self.options.cell_residual_extra_degree facet_residual_degree = self.degree + self.options.facet_residual_extra_degree # ------------------------------- Primal residual ------------------------------- @@ -314,12 +307,14 @@ def automatic_error_indicators(self): + inner(avg(inner(Rfacet, self.z_err)), both(test))*dS + + inner(inner(Rfacet, self.z_err), test)*ds ) + with eta_primal.dat.vec as evec: + evec.abs() # ------------------------------- Adjoint residual ------------------------------- if self.options.use_adjoint_residual: # r*(v) = J"(u)[v] - A"_u(u)[v, z] since F = A(u;v) - L(v) - dF = derivative(F, self.u, TrialFunction(V)) - dJ = derivative(J, self.u, TestFunction(V)) + dF = derivative(F, u, TrialFunction(V)) + dJ = derivative(J, u, TestFunction(V)) rstar = action(adjoint(dF), self.z_lo) - dJ # dual: project r* -> Rcell*, Rfacet* @@ -332,7 +327,6 @@ def automatic_error_indicators(self): solve(af == Lf_star, Rhat_star, solver_parameters=self.options.sp_facet) Rfacet_star = Rhat_star/cones - # indicators: 0.5 * (primal + dual) eta_dual = assemble( inner(inner(Rcell_star, self.u_err), test)*dx + inner(avg(inner(Rfacet_star, self.u_err)), both(test))*dS @@ -340,22 +334,21 @@ def automatic_error_indicators(self): ) with eta_dual.dat.vec as evec: evec.abs() - self.eta_dual_total = abs(evec.sum()) + # indicators: 0.5 * (primal + dual) + etaT = assemble(0.5*(eta_primal + eta_dual)) - self.print(f"{"Sum of dual refinement indicators":45s}{"Σeta_K:":8s}{self.eta_dual_total:15.12f}") with eta_primal.dat.vec as evec: - evec.abs() + self.eta_primal_total = abs(evec.sum()) + with eta_dual.dat.vec as evec: self.eta_dual_total = abs(evec.sum()) - self.print(f"{"Sum of primal refinement indicators":45s}{"Σeta_K:":8s}{self.eta_dual_total:15.12f}") - - self.etaT = assemble(0.5*(eta_primal + eta_dual)) + self.print(f"{"Sum of dual refinement indicators":45s}{"Σeta_K:":8s}{self.eta_dual_total:15.12f}") else: - self.etaT = eta_primal + etaT = eta_primal # XXX Exact error indicators (experimental - ignore) if self.options.exact_indicators: - u_err_exact = self.u_exact - self.u + u_err_exact = self.u_exact - u eta_dual_exact = assemble( inner(inner(Rcell_star, u_err_exact), test)*dx + inner(avg(inner(Rfacet_star, u_err_exact)), both(test))*dS @@ -365,75 +358,82 @@ def automatic_error_indicators(self): with udiff.dat.vec as uvec: unorm = uvec.norm() self.print("L2 error in (dual) refinement indicators: ", unorm) + return etaT def manual_error_indicators(self): """ Currently only implemented for Poisson, but can be overriden. To adapt to other PDEs, replace the form of - self.etaT = assemble() to the symbolic form of the error indicators. This form is usually obtained by integrating + etaT = assemble() to the symbolic form of the error indicators. This form is usually obtained by integrating the weak form by parts (to recover the strong form) and redistributing facet fluxes. """ from firedrake.assemble import assemble - mesh = self.amh[-1] + u = self.problem.u + mesh = u.function_space().mesh().unique() n = FacetNormal(mesh) DG0 = FunctionSpace(mesh, "DG", degree=0) test = TestFunction(DG0) - self.etaT = assemble( - inner(self.f + div(grad(self.u)), self.z_err * test) * dx - - inner(jump(grad(self.u), n), self.z_err * avg(test)) * dS - - inner(dot(grad(self.u), n), self.z_err * test) * ds + etaT = assemble( + inner(self.f + div(grad(u)), self.z_err * test) * dx + - inner(jump(grad(u), n), self.z_err * avg(test)) * dS + - inner(dot(grad(u), n), self.z_err * test) * ds ) - - def compute_efficiency(self): - with self.etaT.dat.vec as evec: + with etaT.dat.vec as evec: evec.abs() - self.etaT_total = abs(evec.sum()) + return etaT - self.etaTsum_vec.append(self.etaT_total) - self.print(f"{"Sum of refinement indicators":45s}{"Ση_K:":8s}{self.etaT_total:15.12f}") + def compute_efficiency(self, etaT, eta_h, eta): + with etaT.dat.vec as evec: + etaT_total = abs(evec.sum()) + + self.etaTsum_vec.append(etaT_total) + self.print(f"{"Sum of refinement indicators":45s}{"Ση_K:":8s}{etaT_total:15.12f}") if self.u_exact is not None or self.goal_exact is not None: # Compute efficiency indices - self.eff1 = self.eta_h/self.eta - self.eff2 = self.etaT_total/self.eta - self.print(f"{"Effectivity index 1":45s}{"η_h/η:":8s}{self.eff1:7.4f}") - self.print(f"{"Effectivity index 2":45s}{"Ση_K/η:":8s}{self.eff2:7.4f}") - self.eff1_vec.append(self.eff1) - self.eff2_vec.append(self.eff2) + eff1 = eta_h / eta + eff2 = etaT_total / eta + self.eff1_vec.append(eff1) + self.eff2_vec.append(eff2) + self.print(f"{"Effectivity index 1":45s}{"η_h/η:":8s}{eff1:7.4f}") + self.print(f"{"Effectivity index 2":45s}{"Ση_K/η:":8s}{eff2:7.4f}") else: - self.eff3 = self.etaT_total/self.eta_h - self.print(f"{"Effectivity index:":45s}{"Ση_K/η_h:":8s}{self.eff3:7.4f}") - self.eff3_vec.append(self.eff3) - - def set_uniform_cell_markers(self): - """Uniform marking for comparison tests""" - mesh = self.amh[-1] - markers_space = FunctionSpace(mesh, "DG", 0) - self.markers = Function(markers_space) - self.markers.assign(1) + eff3 = etaT_total / eta_h + self.eff3_vec.append(eff3) + self.print(f"{"Effectivity index:":45s}{"Ση_K/η_h:":8s}{eff3:7.4f}") - def set_adaptive_cell_markers(self): + def set_adaptive_cell_markers(self, etaT): """Mark cells for refinement (Dorfler marking)""" mesh = self.amh[-1] if mesh.comm.size == 1: - threshold = self.options.dorfler_alpha * self.etaT_total - sorted_indices = np.argsort(-self.etaT.dat.data_ro) - sorted_etaT = self.etaT.dat.data[sorted_indices] + with etaT.dat.vec as evec: + etaT_total = abs(evec.sum()) + threshold = self.options.dorfler_alpha * etaT_total + sorted_indices = np.argsort(-etaT.dat.data_ro) + sorted_etaT = etaT.dat.data[sorted_indices] cumulative_sum = np.cumsum(sorted_etaT) M = np.searchsorted(cumulative_sum, threshold) + 1 marked_cells = sorted_indices[:M] else: - # TODO implemented a parallel sort - with self.etaT.dat.vec_ro as evec: + # TODO implement a parallel sort + with etaT.dat.vec_ro as evec: _, eta_max = evec.max() threshold = self.options.dorfler_alpha * eta_max - marked_cells = self.etaT.dat.data_ro > threshold + marked_cells = etaT.dat.data_ro > threshold + + markers = Function(etaT.function_space()) + markers.dat.data_wo[marked_cells] = 1 + return markers + def set_uniform_cell_markers(self): + """Uniform marking for comparison tests""" + mesh = self.amh[-1] markers_space = FunctionSpace(mesh, "DG", 0) - self.markers = Function(markers_space) - self.markers.dat.data_wo[marked_cells] = 1 + markers = Function(markers_space) + markers.assign(1) + return markers - def refine_problem(self): + def refine_problem(self, markers): mesh = self.amh[-1] - new_mesh = mesh.refine_marked_elements(self.markers) + new_mesh = mesh.refine_marked_elements(markers) self.amh.add_mesh(new_mesh) coef_map = {} @@ -455,8 +455,8 @@ def step(self): self.solve_primal() self.solve_dual() self.write_solution(it) - self.compute_etah() - if self.eta_h < self.tolerance: + eta_h, eta = self.compute_etah() + if eta_h < self.tolerance: self.print("Error estimate below tolerance, finished.") return 1 @@ -466,21 +466,21 @@ def step(self): if self.options.uniform_refinement: self.print("Refining uniformly") - self.set_uniform_cell_markers() + markers = self.set_uniform_cell_markers() else: self.print("Computing local refinement indicators eta_K ...") if self.options.manual_indicators: - self.manual_error_indicators() + etaT = self.manual_error_indicators() else: - self.automatic_error_indicators() - self.compute_efficiency() - self.set_adaptive_cell_markers() + etaT = self.automatic_error_indicators() + self.compute_efficiency(etaT, eta_h, eta) + markers = self.set_adaptive_cell_markers(etaT) if self.options.write_at_iteration: self.print("Appending data ...") self.append_data() self.print("Transferring problem to new mesh ...") - self.refine_problem() + self.refine_problem(markers) if not self.options.write_at_iteration: self.print("Writing data ...") self.write_data() From e75a38e0f06425da3860713b92be8c2b8c16390d Mon Sep 17 00:00:00 2001 From: Pablo Brubeck Date: Tue, 17 Feb 2026 17:54:49 +0000 Subject: [PATCH 05/51] cleanup --- firedrake/adaptive_variational_solver.py | 78 +++++++++++------------- 1 file changed, 36 insertions(+), 42 deletions(-) diff --git a/firedrake/adaptive_variational_solver.py b/firedrake/adaptive_variational_solver.py index cdafbc9fcb..f801cd94d5 100644 --- a/firedrake/adaptive_variational_solver.py +++ b/firedrake/adaptive_variational_solver.py @@ -72,7 +72,7 @@ class GoalAdaptiveNonlinearVariationalSolver(): to the PDE. """ def __init__(self, problem: NonlinearVariationalProblem, goal_functional, tolerance: float, solver_parameters: dict, - *, primal_solver_parameters=None, dual_solver_parameters=None, exact_solution=None, exact_goal=None, verbose=True, + *, primal_solver_parameters=None, dual_solver_parameters=None, exact_solution=None, exact_goal=None, source_term, verbose=True, nullspace=None): # User input vars self.problem = problem @@ -83,11 +83,11 @@ def __init__(self, problem: NonlinearVariationalProblem, goal_functional, tolera self.u_exact = as_mixed(exact_solution) if isinstance(exact_solution, (tuple, list)) else exact_solution self.goal_exact = exact_goal self.options = GoalAdaptiveOptions(solver_parameters) + self.source_term = source_term # Derived vars self.verbose = verbose V = problem.u.function_space() - self.u = problem.u self.element = V.ufl_element() self.degree = self.element.degree() self.nullspace = nullspace @@ -119,13 +119,12 @@ def solve_uh(): solver.set_transfer_manager(self.atm) solver.solve() + solve_uh() if self.options.use_adjoint_residual: # Now solve in higher space high_degree = self.degree + self.options.dual_extra_degree # Use dual degree high_element = PMGPC.reconstruct_degree(self.element, high_degree) Vhigh = V.reconstruct(element=high_element) - solve_uh() - u_high = Function(Vhigh).interpolate(u) self.print("u norm:", norm(u)) self.print("u_high norm:", norm(u_high)) @@ -144,13 +143,14 @@ def solve_uh(): if self.options.primal_low_method == "solve": solve_uh() elif self.options.primal_low_method == "project": - u.project(self.u_high) + u.project(u_high) else: # Default to interpolation - but gives bad results? - u.interpolate(self.u_high) - self.u_err = self.u_high - u + u.interpolate(u_high) + u_err = u_high - u else: - solve_uh() + u_err = None + return u_err def solve_dual(self): J = self.goal_functional @@ -161,8 +161,7 @@ def solve_dual(self): def solve_zh(z): Z = z.function_space() - degree = Z.ufl_element().degree() - self.print(f"Solving dual (degree: {degree}, dofs: {Z.dim()}) ...") + self.print(f"Solving dual (degree: {Z.ufl_element().degree()}, dofs: {Z.dim()}) ...") dF = derivative(F, u, TrialFunction(Z)) dJ = derivative(J, u, TestFunction(Z)) G = action(adjoint(dF), z) - dJ @@ -191,23 +190,23 @@ def solve_zh(z): else: # Default to interpolation self.z_lo.interpolate(self.z) + z_err = self.z - self.z_lo + return z_err - self.z_err = self.z - self.z_lo - - def compute_etah(self): + def compute_etah(self, u_err, z_err): """Compute error estimate""" from firedrake.assemble import assemble J = self.goal_functional F = self.problem.F u = self.problem.u - primal_err = abs(assemble(residual(F, self.z_err))) + primal_err = abs(assemble(residual(F, z_err))) if self.options.use_adjoint_residual: dF = derivative(F, u) dJ = derivative(J, u) G = action(adjoint(dF), self.z_lo) - dJ - dual_err = abs(assemble(residual(G, self.u_err))) + dual_err = abs(assemble(residual(G, u_err))) eta_h = 0.5 * abs(primal_err + dual_err) else: eta_h = primal_err @@ -235,13 +234,13 @@ def compute_etah(self): if self.options.use_adjoint_residual: self.print(f"{"Primal error, |rho(u_h;z-z_h)|:":45s}{"eta_pri:":8s}{primal_err:15.12f}") self.print(f"{"Dual error, |rho*(z_h;u-u_h)|:":45s}{"eta_adj:":8s}{dual_err:15.12f}") - self.print(f"{"Difference":35s}{"|eta_pri - η_adj|:":18s}{abs(primal_err-dual_err):19.12e}") + self.print(f"{"Difference":35s}{"|eta_pri - eta_adj|:":18s}{abs(primal_err-dual_err):19.12e}") self.print(f"{"Predicted error, 0.5|rho+rho*|":45s}{"eta_h:":8s}{eta_h:15.12f}") else: self.print(f"{"Predicted error, |rho(u_h;z-z_h)|":45s}{"eta_h:":8s}{eta_h:15.12f}") return eta_h, eta - def automatic_error_indicators(self): + def automatic_error_indicators(self, u_err, z_err): """Compute cell and facet residuals R_cell, R_facet""" from firedrake.assemble import assemble J = self.goal_functional @@ -249,14 +248,6 @@ def automatic_error_indicators(self): u = self.problem.u V = u.function_space() - z_lo = Function(V) - z_lo.interpolate(self.z) - self.z_err = self.z - z_lo - if self.options.use_adjoint_residual: - u_lo = Function(V) - u_lo.interpolate(self.u_high) - self.u_err = self.u_high - u_lo - mesh = V.mesh().unique() dim = mesh.topological_dimension cell = mesh.ufl_cell() @@ -303,9 +294,9 @@ def automatic_error_indicators(self): test = TestFunction(DG0) eta_primal = assemble( - inner(inner(Rcell, self.z_err), test)*dx + - + inner(avg(inner(Rfacet, self.z_err)), both(test))*dS + - + inner(inner(Rfacet, self.z_err), test)*ds + inner(inner(Rcell, z_err), test)*dx + + + inner(avg(inner(Rfacet, z_err)), both(test))*dS + + + inner(inner(Rfacet, z_err), test)*ds ) with eta_primal.dat.vec as evec: evec.abs() @@ -328,9 +319,9 @@ def automatic_error_indicators(self): Rfacet_star = Rhat_star/cones eta_dual = assemble( - inner(inner(Rcell_star, self.u_err), test)*dx - + inner(avg(inner(Rfacet_star, self.u_err)), both(test))*dS - + inner(inner(Rfacet_star, self.u_err), test)*ds + inner(inner(Rcell_star, u_err), test)*dx + + inner(avg(inner(Rfacet_star, u_err)), both(test))*dS + + inner(inner(Rfacet_star, u_err), test)*ds ) with eta_dual.dat.vec as evec: evec.abs() @@ -360,7 +351,7 @@ def automatic_error_indicators(self): self.print("L2 error in (dual) refinement indicators: ", unorm) return etaT - def manual_error_indicators(self): + def manual_error_indicators(self, u_err, z_err): """ Currently only implemented for Poisson, but can be overriden. To adapt to other PDEs, replace the form of etaT = assemble() to the symbolic form of the error indicators. This form is usually obtained by integrating the weak form by parts (to recover the strong form) and redistributing facet fluxes. @@ -369,12 +360,13 @@ def manual_error_indicators(self): u = self.problem.u mesh = u.function_space().mesh().unique() n = FacetNormal(mesh) + f = self.source_term DG0 = FunctionSpace(mesh, "DG", degree=0) test = TestFunction(DG0) etaT = assemble( - inner(self.f + div(grad(u)), self.z_err * test) * dx - - inner(jump(grad(u), n), self.z_err * avg(test)) * dS - - inner(dot(grad(u), n), self.z_err * test) * ds + inner(f + div(grad(u)), z_err * test) * dx + - inner(jump(grad(u), n), z_err * avg(test)) * dS + - inner(dot(grad(u), n), z_err * test) * ds ) with etaT.dat.vec as evec: evec.abs() @@ -441,7 +433,8 @@ def refine_problem(self, markers): self.goal_functional = refine(self.goal_functional, refine, coefficient_mapping=coef_map) if self.u_exact is not None: self.u_exact = refine(self.u_exact, refine, coefficient_mapping=coef_map) - self.u = self.problem.u + if self.source_term is not None: + self.source_term = refine(self.source_term, refine, coefficient_mapping=coef_map) def solve(self): for it in range(self.options.max_iterations): @@ -452,10 +445,10 @@ def step(self): it = len(self.amh) - 1 self.print(f"---------------------------- [MESH LEVEL {it}] ----------------------------") self.write_mesh(it) - self.solve_primal() - self.solve_dual() + u_err = self.solve_primal() + z_err = self.solve_dual() self.write_solution(it) - eta_h, eta = self.compute_etah() + eta_h, eta = self.compute_etah(u_err, z_err) if eta_h < self.tolerance: self.print("Error estimate below tolerance, finished.") return 1 @@ -470,9 +463,9 @@ def step(self): else: self.print("Computing local refinement indicators eta_K ...") if self.options.manual_indicators: - etaT = self.manual_error_indicators() + etaT = self.manual_error_indicators(u_err, z_err) else: - etaT = self.automatic_error_indicators() + etaT = self.automatic_error_indicators(u_err, z_err) self.compute_efficiency(etaT, eta_h, eta) markers = self.set_adaptive_cell_markers(etaT) @@ -566,7 +559,8 @@ def write_solution(self, it): if should_write: run_name = self.options.run_name self.print("Writing (primal) solution ...") - VTKFile(self.output_dir / f"{run_name}/{run_name}_solution_{it}.pvd").write(*self.u.subfunctions) + u = self.problem.u + VTKFile(self.output_dir / f"{run_name}/{run_name}_solution_{it}.pvd").write(*u.subfunctions) self.print("Writing (dual) solution ...") VTKFile(self.output_dir / f"{run_name}/{run_name}_dual_solution_{it}.pvd").write(*self.z.subfunctions) From 156805552dbfe603830e74fd1886d9b8ed348c94 Mon Sep 17 00:00:00 2001 From: Pablo Brubeck Date: Fri, 20 Feb 2026 09:22:24 +0000 Subject: [PATCH 06/51] fix fstrings --- firedrake/adaptive_variational_solver.py | 30 ++++++++++++------------ 1 file changed, 15 insertions(+), 15 deletions(-) diff --git a/firedrake/adaptive_variational_solver.py b/firedrake/adaptive_variational_solver.py index f801cd94d5..ef078e7d70 100644 --- a/firedrake/adaptive_variational_solver.py +++ b/firedrake/adaptive_variational_solver.py @@ -114,7 +114,7 @@ def solve_primal(self): self.N_vec.append(V.dim()) def solve_uh(): - self.print(f"Solving primal (degree: {self.degree}, dofs: {V.dim()}) ...") + self.print(f'Solving primal (degree: {self.degree}, dofs: {V.dim()}) ...') solver = NonlinearVariationalSolver(self.problem, solver_parameters=self.sp_primal) solver.set_transfer_manager(self.atm) solver.solve() @@ -214,7 +214,7 @@ def compute_etah(self, u_err, z_err): self.etah_vec.append(eta_h) Juh = assemble(J) - self.print(f"{"Computed goal":45s}{"J(uh):":8s}{Juh:15.12f}") + self.print(f'{"Computed goal":45s}{"J(uh):":8s}{Juh:15.12f}') self.Juh = Juh if self.goal_exact is not None: @@ -226,18 +226,18 @@ def compute_etah(self, u_err, z_err): if self.u_exact is not None or self.goal_exact is not None: eta = abs(Juh - Ju) self.eta_vec.append(eta) - self.print(f"{"Exact goal":45s}{"J(u):":8s}{Ju:15.12f}") - self.print(f"{"True error, |J(u) - J(u_h)|":45s}{"eta:":8s}{eta:15.12f}") + self.print(f'{"Exact goal":45s}{"J(u):":8s}{Ju:15.12f}') + self.print(f'{"True error, |J(u) - J(u_h)|":45s}{"eta:":8s}{eta:15.12f}') else: eta = None if self.options.use_adjoint_residual: - self.print(f"{"Primal error, |rho(u_h;z-z_h)|:":45s}{"eta_pri:":8s}{primal_err:15.12f}") - self.print(f"{"Dual error, |rho*(z_h;u-u_h)|:":45s}{"eta_adj:":8s}{dual_err:15.12f}") - self.print(f"{"Difference":35s}{"|eta_pri - eta_adj|:":18s}{abs(primal_err-dual_err):19.12e}") - self.print(f"{"Predicted error, 0.5|rho+rho*|":45s}{"eta_h:":8s}{eta_h:15.12f}") + self.print(f'{"Primal error, |rho(u_h;z-z_h)|:":45s}{"eta_pri:":8s}{primal_err:15.12f}') + self.print(f'{"Dual error, |rho*(z_h;u-u_h)|:":45s}{"eta_adj:":8s}{dual_err:15.12f}') + self.print(f'{"Difference":35s}{"|eta_pri - eta_adj|:":18s}{abs(primal_err-dual_err):19.12e}') + self.print(f'{"Predicted error, 0.5|rho+rho*|":45s}{"eta_h:":8s}{eta_h:15.12f}') else: - self.print(f"{"Predicted error, |rho(u_h;z-z_h)|":45s}{"eta_h:":8s}{eta_h:15.12f}") + self.print(f'{"Predicted error, |rho(u_h;z-z_h)|":45s}{"eta_h:":8s}{eta_h:15.12f}') return eta_h, eta def automatic_error_indicators(self, u_err, z_err): @@ -332,8 +332,8 @@ def automatic_error_indicators(self, u_err, z_err): self.eta_primal_total = abs(evec.sum()) with eta_dual.dat.vec as evec: self.eta_dual_total = abs(evec.sum()) - self.print(f"{"Sum of primal refinement indicators":45s}{"Σeta_K:":8s}{self.eta_dual_total:15.12f}") - self.print(f"{"Sum of dual refinement indicators":45s}{"Σeta_K:":8s}{self.eta_dual_total:15.12f}") + self.print(f'{"Sum of primal refinement indicators":45s}{"Σeta_K:":8s}{self.eta_dual_total:15.12f}') + self.print(f'{"Sum of dual refinement indicators":45s}{"Σeta_K:":8s}{self.eta_dual_total:15.12f}') else: etaT = eta_primal @@ -377,7 +377,7 @@ def compute_efficiency(self, etaT, eta_h, eta): etaT_total = abs(evec.sum()) self.etaTsum_vec.append(etaT_total) - self.print(f"{"Sum of refinement indicators":45s}{"Ση_K:":8s}{etaT_total:15.12f}") + self.print(f'{"Sum of refinement indicators":45s}{"Ση_K:":8s}{etaT_total:15.12f}') if self.u_exact is not None or self.goal_exact is not None: # Compute efficiency indices @@ -385,12 +385,12 @@ def compute_efficiency(self, etaT, eta_h, eta): eff2 = etaT_total / eta self.eff1_vec.append(eff1) self.eff2_vec.append(eff2) - self.print(f"{"Effectivity index 1":45s}{"η_h/η:":8s}{eff1:7.4f}") - self.print(f"{"Effectivity index 2":45s}{"Ση_K/η:":8s}{eff2:7.4f}") + self.print(f'{"Effectivity index 1":45s}{"η_h/η:":8s}{eff1:7.4f}') + self.print(f'{"Effectivity index 2":45s}{"Ση_K/η:":8s}{eff2:7.4f}') else: eff3 = etaT_total / eta_h self.eff3_vec.append(eff3) - self.print(f"{"Effectivity index:":45s}{"Ση_K/η_h:":8s}{eff3:7.4f}") + self.print(f'{"Effectivity index:":45s}{"Ση_K/η_h:":8s}{eff3:7.4f}') def set_adaptive_cell_markers(self, etaT): """Mark cells for refinement (Dorfler marking)""" From af31c94b358d1ead0e7e0b143bd9d070309e7e4e Mon Sep 17 00:00:00 2001 From: Pablo Brubeck Date: Mon, 23 Feb 2026 12:06:46 +0000 Subject: [PATCH 07/51] fixes --- firedrake/adaptive_variational_solver.py | 13 ++++++------- 1 file changed, 6 insertions(+), 7 deletions(-) diff --git a/firedrake/adaptive_variational_solver.py b/firedrake/adaptive_variational_solver.py index ef078e7d70..44c8dc036c 100644 --- a/firedrake/adaptive_variational_solver.py +++ b/firedrake/adaptive_variational_solver.py @@ -141,11 +141,10 @@ def solve_uh(): solver.solve() if self.options.primal_low_method == "solve": - solve_uh() + pass elif self.options.primal_low_method == "project": u.project(u_high) else: - # Default to interpolation - but gives bad results? u.interpolate(u_high) u_err = u_high - u else: @@ -332,7 +331,7 @@ def automatic_error_indicators(self, u_err, z_err): self.eta_primal_total = abs(evec.sum()) with eta_dual.dat.vec as evec: self.eta_dual_total = abs(evec.sum()) - self.print(f'{"Sum of primal refinement indicators":45s}{"Σeta_K:":8s}{self.eta_dual_total:15.12f}') + self.print(f'{"Sum of primal refinement indicators":45s}{"Σeta_K:":8s}{self.eta_primal_total:15.12f}') self.print(f'{"Sum of dual refinement indicators":45s}{"Σeta_K:":8s}{self.eta_dual_total:15.12f}') else: etaT = eta_primal @@ -377,7 +376,7 @@ def compute_efficiency(self, etaT, eta_h, eta): etaT_total = abs(evec.sum()) self.etaTsum_vec.append(etaT_total) - self.print(f'{"Sum of refinement indicators":45s}{"Ση_K:":8s}{etaT_total:15.12f}') + self.print(f'{"Sum of refinement indicators":45s}{"Σeta_K:":8s}{etaT_total:15.12f}') if self.u_exact is not None or self.goal_exact is not None: # Compute efficiency indices @@ -385,12 +384,12 @@ def compute_efficiency(self, etaT, eta_h, eta): eff2 = etaT_total / eta self.eff1_vec.append(eff1) self.eff2_vec.append(eff2) - self.print(f'{"Effectivity index 1":45s}{"η_h/η:":8s}{eff1:7.4f}') - self.print(f'{"Effectivity index 2":45s}{"Ση_K/η:":8s}{eff2:7.4f}') + self.print(f'{"Effectivity index 1":45s}{"eta_h/eta:":8s}{eff1:7.4f}') + self.print(f'{"Effectivity index 2":45s}{"Σeta_K/eta:":8s}{eff2:7.4f}') else: eff3 = etaT_total / eta_h self.eff3_vec.append(eff3) - self.print(f'{"Effectivity index:":45s}{"Ση_K/η_h:":8s}{eff3:7.4f}') + self.print(f'{"Effectivity index:":45s}{"Σeta_K/eta_h:":8s}{eff3:7.4f}') def set_adaptive_cell_markers(self, etaT): """Mark cells for refinement (Dorfler marking)""" From 54a2690c7f7de1321fb19d60ab4600d1409127f0 Mon Sep 17 00:00:00 2001 From: Pablo Brubeck Date: Mon, 23 Feb 2026 12:23:41 +0000 Subject: [PATCH 08/51] style --- firedrake/adaptive_variational_solver.py | 71 ++++++++++++------------ 1 file changed, 34 insertions(+), 37 deletions(-) diff --git a/firedrake/adaptive_variational_solver.py b/firedrake/adaptive_variational_solver.py index 44c8dc036c..9c235c0506 100644 --- a/firedrake/adaptive_variational_solver.py +++ b/firedrake/adaptive_variational_solver.py @@ -6,7 +6,6 @@ from firedrake.variational_solver import (NonlinearVariationalProblem, NonlinearVariationalSolver, LinearVariationalProblem, LinearVariationalSolver) from firedrake.solving import solve -from firedrake.norms import norm from firedrake.preconditioners.pmg import PMGPC from firedrake.mg import utils @@ -72,7 +71,7 @@ class GoalAdaptiveNonlinearVariationalSolver(): to the PDE. """ def __init__(self, problem: NonlinearVariationalProblem, goal_functional, tolerance: float, solver_parameters: dict, - *, primal_solver_parameters=None, dual_solver_parameters=None, exact_solution=None, exact_goal=None, source_term, verbose=True, + *, primal_solver_parameters=None, dual_solver_parameters=None, exact_solution=None, exact_goal=None, source_term=None, verbose=True, nullspace=None): # User input vars self.problem = problem @@ -101,7 +100,7 @@ def __init__(self, problem: NonlinearVariationalProblem, goal_functional, tolera self.Ndual_vec = [] self.eta_vec = [] self.etah_vec = [] - self.etaTsum_vec = [] + self.eta_cell_sum_vec = [] self.eff1_vec = [] self.eff2_vec = [] self.eff3_vec = [] @@ -126,8 +125,6 @@ def solve_uh(): high_element = PMGPC.reconstruct_degree(self.element, high_degree) Vhigh = V.reconstruct(element=high_element) u_high = Function(Vhigh).interpolate(u) - self.print("u norm:", norm(u)) - self.print("u_high norm:", norm(u_high)) v_old, = F.arguments() v_high = TestFunction(Vhigh) @@ -233,7 +230,7 @@ def compute_etah(self, u_err, z_err): if self.options.use_adjoint_residual: self.print(f'{"Primal error, |rho(u_h;z-z_h)|:":45s}{"eta_pri:":8s}{primal_err:15.12f}') self.print(f'{"Dual error, |rho*(z_h;u-u_h)|:":45s}{"eta_adj:":8s}{dual_err:15.12f}') - self.print(f'{"Difference":35s}{"|eta_pri - eta_adj|:":18s}{abs(primal_err-dual_err):19.12e}') + self.print(f'{"Difference":35s}{"|eta_pri-eta_adj|:":18s}{abs(primal_err-dual_err):19.12e}') self.print(f'{"Predicted error, 0.5|rho+rho*|":45s}{"eta_h:":8s}{eta_h:15.12f}') else: self.print(f'{"Predicted error, |rho(u_h;z-z_h)|":45s}{"eta_h:":8s}{eta_h:15.12f}') @@ -325,7 +322,7 @@ def automatic_error_indicators(self, u_err, z_err): with eta_dual.dat.vec as evec: evec.abs() # indicators: 0.5 * (primal + dual) - etaT = assemble(0.5*(eta_primal + eta_dual)) + eta_cell = assemble(0.5*(eta_primal + eta_dual)) with eta_primal.dat.vec as evec: self.eta_primal_total = abs(evec.sum()) @@ -334,7 +331,7 @@ def automatic_error_indicators(self, u_err, z_err): self.print(f'{"Sum of primal refinement indicators":45s}{"Σeta_K:":8s}{self.eta_primal_total:15.12f}') self.print(f'{"Sum of dual refinement indicators":45s}{"Σeta_K:":8s}{self.eta_dual_total:15.12f}') else: - etaT = eta_primal + eta_cell = eta_primal # XXX Exact error indicators (experimental - ignore) if self.options.exact_indicators: @@ -348,11 +345,11 @@ def automatic_error_indicators(self, u_err, z_err): with udiff.dat.vec as uvec: unorm = uvec.norm() self.print("L2 error in (dual) refinement indicators: ", unorm) - return etaT + return eta_cell def manual_error_indicators(self, u_err, z_err): """ Currently only implemented for Poisson, but can be overriden. To adapt to other PDEs, replace the form of - etaT = assemble() to the symbolic form of the error indicators. This form is usually obtained by integrating + eta_cell = assemble() to the symbolic form of the error indicators. This form is usually obtained by integrating the weak form by parts (to recover the strong form) and redistributing facet fluxes. """ from firedrake.assemble import assemble @@ -362,55 +359,55 @@ def manual_error_indicators(self, u_err, z_err): f = self.source_term DG0 = FunctionSpace(mesh, "DG", degree=0) test = TestFunction(DG0) - etaT = assemble( + eta_cell = assemble( inner(f + div(grad(u)), z_err * test) * dx - inner(jump(grad(u), n), z_err * avg(test)) * dS - inner(dot(grad(u), n), z_err * test) * ds ) - with etaT.dat.vec as evec: + with eta_cell.dat.vec as evec: evec.abs() - return etaT + return eta_cell - def compute_efficiency(self, etaT, eta_h, eta): - with etaT.dat.vec as evec: - etaT_total = abs(evec.sum()) + def compute_efficiency(self, eta_cell, eta_h, eta): + with eta_cell.dat.vec as evec: + eta_cell_total = abs(evec.sum()) - self.etaTsum_vec.append(etaT_total) - self.print(f'{"Sum of refinement indicators":45s}{"Σeta_K:":8s}{etaT_total:15.12f}') + self.eta_cell_sum_vec.append(eta_cell_total) + self.print(f'{"Sum of refinement indicators":45s}{"Σeta_K:":8s}{eta_cell_total:15.12f}') if self.u_exact is not None or self.goal_exact is not None: # Compute efficiency indices eff1 = eta_h / eta - eff2 = etaT_total / eta + eff2 = eta_cell_total / eta self.eff1_vec.append(eff1) self.eff2_vec.append(eff2) self.print(f'{"Effectivity index 1":45s}{"eta_h/eta:":8s}{eff1:7.4f}') self.print(f'{"Effectivity index 2":45s}{"Σeta_K/eta:":8s}{eff2:7.4f}') else: - eff3 = etaT_total / eta_h + eff3 = eta_cell_total / eta_h self.eff3_vec.append(eff3) self.print(f'{"Effectivity index:":45s}{"Σeta_K/eta_h:":8s}{eff3:7.4f}') - def set_adaptive_cell_markers(self, etaT): + def set_adaptive_cell_markers(self, eta_cell): """Mark cells for refinement (Dorfler marking)""" mesh = self.amh[-1] if mesh.comm.size == 1: - with etaT.dat.vec as evec: - etaT_total = abs(evec.sum()) - threshold = self.options.dorfler_alpha * etaT_total - sorted_indices = np.argsort(-etaT.dat.data_ro) - sorted_etaT = etaT.dat.data[sorted_indices] - cumulative_sum = np.cumsum(sorted_etaT) + with eta_cell.dat.vec as evec: + eta_cell_total = abs(evec.sum()) + threshold = self.options.dorfler_alpha * eta_cell_total + sorted_indices = np.argsort(-eta_cell.dat.data_ro) + sorted_eta_cell = eta_cell.dat.data[sorted_indices] + cumulative_sum = np.cumsum(sorted_eta_cell) M = np.searchsorted(cumulative_sum, threshold) + 1 marked_cells = sorted_indices[:M] else: # TODO implement a parallel sort - with etaT.dat.vec_ro as evec: + with eta_cell.dat.vec_ro as evec: _, eta_max = evec.max() threshold = self.options.dorfler_alpha * eta_max - marked_cells = etaT.dat.data_ro > threshold + marked_cells = eta_cell.dat.data_ro > threshold - markers = Function(etaT.function_space()) + markers = Function(eta_cell.function_space()) markers.dat.data_wo[marked_cells] = 1 return markers @@ -462,11 +459,11 @@ def step(self): else: self.print("Computing local refinement indicators eta_K ...") if self.options.manual_indicators: - etaT = self.manual_error_indicators(u_err, z_err) + eta_cell = self.manual_error_indicators(u_err, z_err) else: - etaT = self.automatic_error_indicators(u_err, z_err) - self.compute_efficiency(etaT, eta_h, eta) - markers = self.set_adaptive_cell_markers(etaT) + eta_cell = self.automatic_error_indicators(u_err, z_err) + self.compute_efficiency(eta_cell, eta_h, eta) + markers = self.set_adaptive_cell_markers(eta_cell) if self.options.write_at_iteration: self.print("Appending data ...") @@ -490,7 +487,7 @@ def write_data(self): file_path = self.output_dir / "results.csv" else: file_path = self.output_dir / self.options.results_file_name - rows = list(zip(self.N_vec, self.Ndual_vec, self.eta_vec, self.etah_vec, self.etaTsum_vec, self.eff1_vec, self.eff2_vec)) + rows = list(zip(self.N_vec, self.Ndual_vec, self.eta_vec, self.etah_vec, self.eta_cell_sum_vec, self.eff1_vec, self.eff2_vec)) headers = ("N", "Ndual", "eta", "eta_h", "sum_eta_T", "eff1", "eff2") with open(file_path, "w", newline="") as file: w = csv.writer(file) @@ -509,7 +506,7 @@ def append_data(self): headers = ("iteration", "N", "Ndual", "Juh", "eta_h", "sum_eta_T") row = ( it, - self.N_vec[-1], self.Ndual_vec[-1], Juh, self.etah_vec[-1], self.etaTsum_vec[-1] + self.N_vec[-1], self.Ndual_vec[-1], Juh, self.etah_vec[-1], self.eta_cell_sum_vec[-1] ) elif self.options.uniform_refinement: headers = ("iteration", "N", "Ndual", "Juh", "eta", "eta_h") @@ -521,7 +518,7 @@ def append_data(self): headers = ("iteration", "N", "Ndual", "Juh", "eta", "eta_h", "sum_eta_T", "eff1", "eff2") row = ( it, - self.N_vec[-1], self.Ndual_vec[-1], Juh, self.eta_vec[-1], self.etah_vec[-1], self.etaTsum_vec[-1], self.eff1_vec[-1], self.eff2_vec[-1] + self.N_vec[-1], self.Ndual_vec[-1], Juh, self.eta_vec[-1], self.etah_vec[-1], self.eta_cell_sum_vec[-1], self.eff1_vec[-1], self.eff2_vec[-1] ) file_path.parent.mkdir(parents=True, exist_ok=True) # create directories if missing From 709dba7ab8bbb555c99b29c386044719e30f2692 Mon Sep 17 00:00:00 2001 From: Pablo Brubeck Date: Mon, 23 Feb 2026 12:57:38 +0000 Subject: [PATCH 09/51] Fix refinement of DirichletBC --- firedrake/adaptive_variational_solver.py | 30 +++++++++++++----------- firedrake/mg/ufl_utils.py | 24 +++++++++++++++---- 2 files changed, 36 insertions(+), 18 deletions(-) diff --git a/firedrake/adaptive_variational_solver.py b/firedrake/adaptive_variational_solver.py index 9c235c0506..4c917da9f9 100644 --- a/firedrake/adaptive_variational_solver.py +++ b/firedrake/adaptive_variational_solver.py @@ -434,7 +434,9 @@ def refine_problem(self, markers): def solve(self): for it in range(self.options.max_iterations): - if self.step(): + try: + self.step() + except StopIteration: break def step(self): @@ -447,11 +449,11 @@ def step(self): eta_h, eta = self.compute_etah(u_err, z_err) if eta_h < self.tolerance: self.print("Error estimate below tolerance, finished.") - return 1 + raise StopIteration if it == self.options.max_iterations - 1: self.print(f"Maximum iteration ({self.options.max_iterations}) reached. Exiting.") - return 1 + raise StopIteration if self.options.uniform_refinement: self.print("Refining uniformly") @@ -473,7 +475,6 @@ def step(self): if not self.options.write_at_iteration: self.print("Writing data ...") self.write_data() - return 0 # Writing functions: -------------------------------------- @@ -602,12 +603,6 @@ def as_mixed(exprs): return as_vector([e[idx] for e in exprs for idx in np.ndindex(e.ufl_shape)]) -# Should no longer be needed -def reconstruct_bc_value(bc, V): - if not isinstance(bc._original_arg, Function): - return bc._original_arg - return Function(V).interpolate(bc._original_arg) - def reconstruct_bcs(bcs, V): """Reconstruct a list of bcs""" @@ -616,9 +611,7 @@ def reconstruct_bcs(bcs, V): V_ = V for index in bc._indices: V_ = V_.sub(index) - g = reconstruct_bc_value(bc, V_) - new_bcs.append(bc.reconstruct(V=V_, g=g)) - + new_bcs.append(bc.reconstruct(V=V_)) return new_bcs @@ -645,7 +638,16 @@ def refine_function(expr, self, coefficient_mapping=None): if new is None: Vf = expr.function_space() Vc = self(Vf, self) - new = Function(Vc, name=f"coarse_{expr.name()}") + name = expr.name() + if name is not None: + level_increment = -1 if self == coarsen else 1 + try: + name, prev_level = name.split("_level_") + except ValueError: + prev_level = 0 + level = int(prev_level) + level_increment + name = f"{name}_level_{level}" + new = Function(Vc, name=name) new.interpolate(expr) coefficient_mapping[expr] = new return new diff --git a/firedrake/mg/ufl_utils.py b/firedrake/mg/ufl_utils.py index 99ffd19309..a98293d49e 100644 --- a/firedrake/mg/ufl_utils.py +++ b/firedrake/mg/ufl_utils.py @@ -122,7 +122,7 @@ def coarsen_formsum(form, self, coefficient_mapping=None): @coarsen.register(firedrake.DirichletBC) def coarsen_bc(bc, self, coefficient_mapping=None): V = self(bc.function_space(), self, coefficient_mapping=coefficient_mapping) - val = self(bc.function_arg, self, coefficient_mapping=coefficient_mapping) + val = self(bc._original_arg, self, coefficient_mapping=coefficient_mapping) subdomain = bc.sub_domain return type(bc)(V, val, subdomain) @@ -147,12 +147,19 @@ def coarsen_equation_bc(ebc, self, coefficient_mapping=None): def coarsen_function_space(V, self, coefficient_mapping=None): if hasattr(V, "_coarse") and self == coarsen: return V._coarse - V_fine = V # Handle MixedFunctionSpace : V_fine.reconstruct requires MeshSequence. fine_mesh = V_fine.mesh() if V_fine.index is None else V_fine.parent.mesh() mesh_coarse = self(fine_mesh, self) - name = f"coarse_{V.name}" if V.name else None + name = V.name + if name is not None: + level_increment = -1 if self == coarsen else 1 + try: + name, prev_level = name.split("_level_") + except ValueError: + prev_level = 0 + level = prev_level + level_increment + name = f"{name}_level_{level}" V_coarse = V_fine.reconstruct(mesh=mesh_coarse, name=name) V_coarse._fine = V_fine V_fine._coarse = V_coarse @@ -168,7 +175,16 @@ def coarsen_function(expr, self, coefficient_mapping=None): if new is None: Vf = expr.function_space() Vc = self(Vf, self) - new = firedrake.Function(Vc, name=f"coarse_{expr.name()}") + name = expr.name() + if name is not None: + level_increment = -1 if self == coarsen else 1 + try: + name, prev_level = name.split("_level_") + except ValueError: + prev_level = 0 + level = int(prev_level) + level_increment + name = f"{name}_level_{level}" + new = firedrake.Function(Vc, name=name) manager = get_transfer_manager(Vf.dm) if is_dual(expr): manager.restrict(expr, new) From cd7bd194a07ad8441511658598ad06cead65cc18 Mon Sep 17 00:00:00 2001 From: Pablo Brubeck Date: Mon, 23 Feb 2026 14:25:54 +0000 Subject: [PATCH 10/51] fix --- firedrake/adaptive_variational_solver.py | 18 +++++++++--------- 1 file changed, 9 insertions(+), 9 deletions(-) diff --git a/firedrake/adaptive_variational_solver.py b/firedrake/adaptive_variational_solver.py index 4c917da9f9..58801db13b 100644 --- a/firedrake/adaptive_variational_solver.py +++ b/firedrake/adaptive_variational_solver.py @@ -118,7 +118,6 @@ def solve_uh(): solver.set_transfer_manager(self.atm) solver.solve() - solve_uh() if self.options.use_adjoint_residual: # Now solve in higher space high_degree = self.degree + self.options.dual_extra_degree # Use dual degree @@ -138,17 +137,19 @@ def solve_uh(): solver.solve() if self.options.primal_low_method == "solve": - pass + solve_uh() elif self.options.primal_low_method == "project": u.project(u_high) - else: + elif self.options.primal_low_method == "interpolate": u.interpolate(u_high) u_err = u_high - u else: + solve_uh() u_err = None return u_err def solve_dual(self): + from firedrake.assemble import assemble J = self.goal_functional F = self.problem.F u = self.problem.u @@ -167,6 +168,7 @@ def solve_zh(z): solver = LinearVariationalSolver(problem, solver_parameters=self.sp_dual) solver.set_transfer_manager(self.atm) solver.solve() + return problem # Higher-order dual soluton dual_degree = self.degree + self.options.dual_extra_degree @@ -180,7 +182,8 @@ def solve_zh(z): # Lower-order dual soluton self.z_lo = Function(V) if self.options.dual_low_method == "solve": - solve_zh(self.z_lo) + self.z_lo.interpolate(self.z) + self.adjoint_problem = solve_zh(self.z_lo) elif self.options.dual_low_method == "project": self.z_lo.project(self.z) else: @@ -198,14 +201,11 @@ def compute_etah(self, u_err, z_err): primal_err = abs(assemble(residual(F, z_err))) if self.options.use_adjoint_residual: - dF = derivative(F, u) - dJ = derivative(J, u) - G = action(adjoint(dF), self.z_lo) - dJ - + G = self.adjoint_problem.F dual_err = abs(assemble(residual(G, u_err))) eta_h = 0.5 * abs(primal_err + dual_err) else: - eta_h = primal_err + eta_h = abs(primal_err) self.etah_vec.append(eta_h) From 1bd16e364d4c94b229b0f2fdb230bd7dd06fd7a9 Mon Sep 17 00:00:00 2001 From: Pablo Brubeck Date: Tue, 24 Feb 2026 09:27:48 +0000 Subject: [PATCH 11/51] Netgen: copy the mesh before refining to support multiple hierarchies --- firedrake/adaptive_variational_solver.py | 79 ++++++++++-------------- firedrake/mesh.py | 9 +-- 2 files changed, 39 insertions(+), 49 deletions(-) diff --git a/firedrake/adaptive_variational_solver.py b/firedrake/adaptive_variational_solver.py index 58801db13b..6d819dccc4 100644 --- a/firedrake/adaptive_variational_solver.py +++ b/firedrake/adaptive_variational_solver.py @@ -119,19 +119,19 @@ def solve_uh(): solver.solve() if self.options.use_adjoint_residual: - # Now solve in higher space + # Now solve in higher-order space high_degree = self.degree + self.options.dual_extra_degree # Use dual degree high_element = PMGPC.reconstruct_degree(self.element, high_degree) - Vhigh = V.reconstruct(element=high_element) - u_high = Function(Vhigh).interpolate(u) + V_high = V.reconstruct(element=high_element) + u_high = Function(V_high).interpolate(u) v_old, = F.arguments() - v_high = TestFunction(Vhigh) + v_high = TestFunction(V_high) F_high = replace(F, {v_old: v_high, u: u_high}) - bcs_high = reconstruct_bcs(bcs, Vhigh) + bcs_high = [bc.reconstruct(V=V_high, indices=bc._indices) for bc in bcs] problem_high = NonlinearVariationalProblem(F_high, u_high, bcs_high) - self.print(f"Solving primal in higher space for error estimate (degree: {high_degree}, dofs: {Vhigh.dim()}) ...") + self.print(f"Solving primal in higher space for error estimate (degree: {high_degree}, dofs: {V_high.dim()}) ...") solver = NonlinearVariationalSolver(problem_high, solver_parameters=self.sp_primal) solver.set_transfer_manager(self.atm) solver.solve() @@ -149,41 +149,42 @@ def solve_uh(): return u_err def solve_dual(self): - from firedrake.assemble import assemble - J = self.goal_functional - F = self.problem.F - u = self.problem.u - bcs = self.problem.bcs - V = u.function_space() + V = self.problem.u.function_space() def solve_zh(z): + bcs = self.problem.bcs + J = self.goal_functional + F = self.problem.F + u = self.problem.u + Z = z.function_space() self.print(f"Solving dual (degree: {Z.ufl_element().degree()}, dofs: {Z.dim()}) ...") - dF = derivative(F, u, TrialFunction(Z)) + + Fz = residual(F, TestFunction(Z)) + dF = derivative(Fz, u, TrialFunction(Z)) dJ = derivative(J, u, TestFunction(Z)) - G = action(adjoint(dF), z) - dJ - a = derivative(G, z) + a = adjoint(dF) + bcs_dual = [bc.reconstruct(V=Z, indices=bc._indices, g=0) for bc in bcs] problem = LinearVariationalProblem(a, dJ, z, bcs_dual) solver = LinearVariationalSolver(problem, solver_parameters=self.sp_dual) solver.set_transfer_manager(self.atm) solver.solve() - return problem # Higher-order dual soluton dual_degree = self.degree + self.options.dual_extra_degree dual_element = PMGPC.reconstruct_degree(self.element, dual_degree) - Vdual = V.reconstruct(element=dual_element) - self.z = Function(Vdual) + V_dual = V.reconstruct(element=dual_element) + self.z = Function(V_dual) - self.Ndual_vec.append(Vdual.dim()) + self.Ndual_vec.append(V_dual.dim()) solve_zh(self.z) # Lower-order dual soluton self.z_lo = Function(V) if self.options.dual_low_method == "solve": self.z_lo.interpolate(self.z) - self.adjoint_problem = solve_zh(self.z_lo) + solve_zh(self.z_lo) elif self.options.dual_low_method == "project": self.z_lo.project(self.z) else: @@ -201,7 +202,11 @@ def compute_etah(self, u_err, z_err): primal_err = abs(assemble(residual(F, z_err))) if self.options.use_adjoint_residual: - G = self.adjoint_problem.F + Z = self.z_lo.function_space() + dF = derivative(F, u, TrialFunction(Z)) + dJ = derivative(J, u) + G = action(adjoint(dF), self.z_lo) - dJ + dual_err = abs(assemble(residual(G, u_err))) eta_h = 0.5 * abs(primal_err + dual_err) else: @@ -390,22 +395,12 @@ def compute_efficiency(self, eta_cell, eta_h, eta): def set_adaptive_cell_markers(self, eta_cell): """Mark cells for refinement (Dorfler marking)""" - mesh = self.amh[-1] - if mesh.comm.size == 1: - with eta_cell.dat.vec as evec: - eta_cell_total = abs(evec.sum()) - threshold = self.options.dorfler_alpha * eta_cell_total - sorted_indices = np.argsort(-eta_cell.dat.data_ro) - sorted_eta_cell = eta_cell.dat.data[sorted_indices] - cumulative_sum = np.cumsum(sorted_eta_cell) - M = np.searchsorted(cumulative_sum, threshold) + 1 - marked_cells = sorted_indices[:M] - else: - # TODO implement a parallel sort - with eta_cell.dat.vec_ro as evec: - _, eta_max = evec.max() - threshold = self.options.dorfler_alpha * eta_max - marked_cells = eta_cell.dat.data_ro > threshold + # NOTE this is not quite Dorfler marking + # For Dorfler marking we need to implement a parallel sort + with eta_cell.dat.vec_ro as evec: + _, eta_max = evec.max() + threshold = self.options.dorfler_alpha * eta_max + marked_cells = eta_cell.dat.data_ro > threshold markers = Function(eta_cell.function_space()) markers.dat.data_wo[marked_cells] = 1 @@ -603,16 +598,10 @@ def as_mixed(exprs): return as_vector([e[idx] for e in exprs for idx in np.ndindex(e.ufl_shape)]) - def reconstruct_bcs(bcs, V): """Reconstruct a list of bcs""" - new_bcs = [] - for bc in bcs: - V_ = V - for index in bc._indices: - V_ = V_.sub(index) - new_bcs.append(bc.reconstruct(V=V_)) - return new_bcs + bcs = [bc.reconstruct(V=V, indices=bc._indices) for bc in bcs] + return bcs @singledispatch diff --git a/firedrake/mesh.py b/firedrake/mesh.py index a05d93c3ed..ece240e0e4 100644 --- a/firedrake/mesh.py +++ b/firedrake/mesh.py @@ -2996,7 +2996,8 @@ def refine_marked_elements(self, mark, netgen_flags=None): if netgen_flags is None: netgen_flags = {} DistParams = self._distribution_parameters - els = {2: self.netgen_mesh.Elements2D, 3: self.netgen_mesh.Elements3D} + netgen_mesh = self.netgen_mesh.Copy() + els = {2: netgen_mesh.Elements2D, 3: netgen_mesh.Elements3D} dim = self.geometric_dimension refine_faces = netgen_flags.get("refine_faces", False) if dim in [2, 3]: @@ -3019,10 +3020,10 @@ def refine_marked_elements(self, mark, netgen_flags=None): else: el.refine = False if not refine_faces and dim == 3: - self.netgen_mesh.Elements2D().NumPy()["refine"] = 0 - self.netgen_mesh.Refine(adaptive=True) + netgen_mesh.Elements2D().NumPy()["refine"] = 0 + netgen_mesh.Refine(adaptive=True) mark = mark-np.ones(mark.shape) - return fd.Mesh(self.netgen_mesh, distribution_parameters=DistParams, comm=self.comm) + return fd.Mesh(netgen_mesh, distribution_parameters=DistParams, comm=self.comm) return fd.Mesh(netgen.libngpy._meshing.Mesh(dim), distribution_parameters=DistParams, comm=self.comm) else: From c16ad9d0ec44f463707b6044d3565c3eea65923b Mon Sep 17 00:00:00 2001 From: Patrick Farrell Date: Thu, 26 Feb 2026 10:43:45 +0000 Subject: [PATCH 12/51] Reorganise how netgen meshes are curved --- firedrake/mesh.py | 26 +++++++++++++++++++++++--- firedrake/mg/netgen.py | 23 ++++++++++------------- 2 files changed, 33 insertions(+), 16 deletions(-) diff --git a/firedrake/mesh.py b/firedrake/mesh.py index ece240e0e4..2c4177db2a 100644 --- a/firedrake/mesh.py +++ b/firedrake/mesh.py @@ -2994,7 +2994,7 @@ def refine_marked_elements(self, mark, netgen_flags=None): utils.check_netgen_installed() if netgen_flags is None: - netgen_flags = {} + netgen_flags = self.netgen_flags DistParams = self._distribution_parameters netgen_mesh = self.netgen_mesh.Copy() els = {2: netgen_mesh.Elements2D, 3: netgen_mesh.Elements3D} @@ -3023,9 +3023,11 @@ def refine_marked_elements(self, mark, netgen_flags=None): netgen_mesh.Elements2D().NumPy()["refine"] = 0 netgen_mesh.Refine(adaptive=True) mark = mark-np.ones(mark.shape) - return fd.Mesh(netgen_mesh, distribution_parameters=DistParams, comm=self.comm) + return fd.Mesh(netgen_mesh, distribution_parameters=DistParams, + netgen_flags=netgen_flags, comm=self.comm) return fd.Mesh(netgen.libngpy._meshing.Mesh(dim), - distribution_parameters=DistParams, comm=self.comm) + distribution_parameters=DistParams, + netgen_flags=netgen_flags, comm=self.comm) else: raise NotImplementedError("No implementation for dimension other than 2 and 3.") @@ -3432,6 +3434,24 @@ def Mesh(meshfile, **kwargs): if from_netgen: mesh.netgen_mesh = netgen_firedrake_mesh.meshMap.ngMesh + mesh.netgen_flags = netgen_flags + + # Curve the mesh, if requested + degree = netgen_flags.get("degree", 1) + if degree != 1: + permutation_tol = netgen_flags.get("permutation_tol", 1e-8) + cg = netgen_flags.get("cg", False) + ho_field = mesh.curve_field( + order=degree, + permutation_tol=permutation_tol, + cg_field=cg + ) + temp = Mesh(ho_field, distribution_parameters=mesh._distribution_parameters, + comm=mesh.comm) + temp.netgen_mesh = mesh.netgen_mesh + temp.netgen_flags = netgen_flags + temp._tolerance = mesh.tolerance + mesh = temp mesh.submesh_parent = submesh_parent mesh._tolerance = tolerance diff --git a/firedrake/mg/netgen.py b/firedrake/mg/netgen.py index 82acab25aa..1e3420f104 100644 --- a/firedrake/mg/netgen.py +++ b/firedrake/mg/netgen.py @@ -266,15 +266,11 @@ def NetgenHierarchy(mesh, levs, flags, distribution_parameters=None): parameters.update(mesh._distribution_parameters) parameters["partition"] = False # Curve the mesh - if order[0] > 1: - ho_field = mesh.curve_field( - order=order[0], - permutation_tol=permutation_tol, - cg_field=cg - ) - temp = fd.Mesh(ho_field, distribution_parameters=parameters, comm=comm) - temp.netgen_mesh = mesh.netgen_mesh - temp._tolerance = mesh.tolerance + if order[0] != mesh.coordinates.function_space().ufl_element().degree(): + temp_flags = dict(flags) + temp_flags['degree'] = order[0] + temp = fd.Mesh(mesh.netgen_mesh, distribution_parameters=parameters, + netgen_flags=temp_flags, comm=comm) mesh = temp # Make a plex (cdm) without overlap. dm_cell_type, = mesh.dm_cell_types @@ -313,15 +309,16 @@ def NetgenHierarchy(mesh, levs, flags, distribution_parameters=None): raise ValueError("Only 2D and 3D meshes can be optimised.") mesh.netgen_mesh = ngmesh # Curve the mesh - if order[l+1] > 1: + if order[l+1] != mesh.coordinates.function_space().ufl_element().degree(): logger.info("\t\t\tCurving the mesh ...") tic = time.time() if snap == "geometry": + temp_flags = dict(flags) + temp_flags['degree'] = order[l+1] mesh = fd.Mesh( - mesh.curve_field(order=order[l+1], - location_tol=location_tol, - permutation_tol=permutation_tol), + mesh.netgen_mesh, distribution_parameters=parameters, + netgen_flags=temp_flags, comm=comm) elif snap == "coarse": mesh = snapToCoarse(ho_field, mesh, order[l+1], snap_smoothing, cg) From b28fbf50066ab63381782c0db2948a92ecce300e Mon Sep 17 00:00:00 2001 From: Pablo Brubeck Date: Thu, 26 Feb 2026 11:56:42 +0000 Subject: [PATCH 13/51] support reusing the solver with different guesses --- firedrake/adaptive_variational_solver.py | 15 ++++++++++++++- firedrake/mg/adaptive_hierarchy.py | 9 +++++++-- firedrake/mg/netgen.py | 5 ++--- firedrake/mg/ufl_utils.py | 5 +++-- 4 files changed, 26 insertions(+), 8 deletions(-) diff --git a/firedrake/adaptive_variational_solver.py b/firedrake/adaptive_variational_solver.py index 6d819dccc4..940f0d03d1 100644 --- a/firedrake/adaptive_variational_solver.py +++ b/firedrake/adaptive_variational_solver.py @@ -1,3 +1,4 @@ +from firedrake import dmhooks from firedrake.petsc import PETSc from firedrake.function import Function from firedrake.cofunction import Cofunction @@ -91,7 +92,19 @@ def __init__(self, problem: NonlinearVariationalProblem, goal_functional, tolera self.degree = self.element.degree() self.nullspace = nullspace self.atm = AdaptiveTransferManager() - self.amh = AdaptiveMeshHierarchy(V.mesh()) + + mesh = V.mesh().unique() + amh, level = utils.get_level(mesh) + if amh is None: + amh = AdaptiveMeshHierarchy(mesh) + if not isinstance(amh, AdaptiveMeshHierarchy): + raise ValueError("Problem needs to be defined on an AdaptiveMeshHierarchy") + + # FIXME we should construct a subset of the original hierarchy instead + amh, level = utils.get_level(mesh) + while len(amh) > level+1: + amh.pop_mesh() + self.amh = amh # Data storage and writing self.output_dir = Path(self.options.output_dir) diff --git a/firedrake/mg/adaptive_hierarchy.py b/firedrake/mg/adaptive_hierarchy.py index fc6c2f728a..c0e37414db 100644 --- a/firedrake/mg/adaptive_hierarchy.py +++ b/firedrake/mg/adaptive_hierarchy.py @@ -21,7 +21,7 @@ class AdaptiveMeshHierarchy(HierarchyBase): """ def __init__(self, base_mesh: MeshGeometry, nested: bool = True): self.meshes = [] - self._meshes = [] + self._meshes = self.meshes self.nested = nested self.add_mesh(base_mesh) @@ -35,10 +35,15 @@ def add_mesh(self, mesh: MeshGeometry): The mesh to be added to the finest level. """ level = len(self.meshes) - self._meshes.append(mesh) self.meshes.append(mesh) set_level(mesh, self, level) + def pop_mesh(self): + """ + Removes the finest mesh from the hierarchy. + """ + self.meshes.pop() + def adapt(self, eta: Function | Cofunction, theta: float): """ Adds a new mesh to the hierarchy by locally refining the finest mesh diff --git a/firedrake/mg/netgen.py b/firedrake/mg/netgen.py index 1e3420f104..ae3edb7a6b 100644 --- a/firedrake/mg/netgen.py +++ b/firedrake/mg/netgen.py @@ -246,8 +246,6 @@ def NetgenHierarchy(mesh, levs, flags, distribution_parameters=None): logger.info(f"\tOrder of the hierarchy: {order}") if isinstance(order, int): order = [order]*(levs+1) - permutation_tol = flags.get("permutation_tol", 1e-8) - location_tol = flags.get("location_tol", 1e-8) refType = flags.get("refinement_type", "uniform") logger.info(f"\tRefinement type: {refType}") optMoves = flags.get("optimisation_moves", False) @@ -270,7 +268,7 @@ def NetgenHierarchy(mesh, levs, flags, distribution_parameters=None): temp_flags = dict(flags) temp_flags['degree'] = order[0] temp = fd.Mesh(mesh.netgen_mesh, distribution_parameters=parameters, - netgen_flags=temp_flags, comm=comm) + netgen_flags=temp_flags, comm=comm) mesh = temp # Make a plex (cdm) without overlap. dm_cell_type, = mesh.dm_cell_types @@ -321,6 +319,7 @@ def NetgenHierarchy(mesh, levs, flags, distribution_parameters=None): netgen_flags=temp_flags, comm=comm) elif snap == "coarse": + ho_field = meshes[0].coordinates mesh = snapToCoarse(ho_field, mesh, order[l+1], snap_smoothing, cg) toc = time.time() logger.info(f"\t\t\tMeshed curved. Time taken: {toc-tic}") diff --git a/firedrake/mg/ufl_utils.py b/firedrake/mg/ufl_utils.py index a98293d49e..7505f19e9c 100644 --- a/firedrake/mg/ufl_utils.py +++ b/firedrake/mg/ufl_utils.py @@ -145,8 +145,9 @@ def coarsen_equation_bc(ebc, self, coefficient_mapping=None): @coarsen.register(firedrake.functionspaceimpl.WithGeometryBase) def coarsen_function_space(V, self, coefficient_mapping=None): - if hasattr(V, "_coarse") and self == coarsen: - return V._coarse + # FIXME support multiple hierarchies + # if hasattr(V, "_coarse") and self == coarsen: + # return V._coarse V_fine = V # Handle MixedFunctionSpace : V_fine.reconstruct requires MeshSequence. fine_mesh = V_fine.mesh() if V_fine.index is None else V_fine.parent.mesh() From 25209e1b7dbbd465123f50477f5d77b199cc355b Mon Sep 17 00:00:00 2001 From: Patrick Farrell Date: Thu, 26 Feb 2026 15:32:20 +0000 Subject: [PATCH 14/51] Bugfix with deflation --- firedrake/deflation.py | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/firedrake/deflation.py b/firedrake/deflation.py index 66ff62cdc4..030ec9b92e 100644 --- a/firedrake/deflation.py +++ b/firedrake/deflation.py @@ -94,7 +94,8 @@ def solve(self, snes, b, x): snes.reason = self.inner.reason # Record the solution we've just found - self.deflation.append(Function(self.problem.u)) + if snes.reason > 0: + self.deflation.append(Function(self.problem.u)) return out From 178fbf560a96ebfea057215e4cbd095563533e7b Mon Sep 17 00:00:00 2001 From: Patrick Farrell Date: Fri, 27 Feb 2026 17:20:53 +0000 Subject: [PATCH 15/51] Initial stab at a demo --- demos/demo_references.bib | 22 +++++ .../goal_based_adaptivity.py.rst | 93 +++++++++++++++++++ 2 files changed, 115 insertions(+) create mode 100644 demos/goal_based_adaptivity/goal_based_adaptivity.py.rst diff --git a/demos/demo_references.bib b/demos/demo_references.bib index ce29d3c2e8..7179174452 100644 --- a/demos/demo_references.bib +++ b/demos/demo_references.bib @@ -391,3 +391,25 @@ @Article{Farrell2015 pages = {A2026--A2045}, doi = {10.1137/140984798}, } + +@article{Becker2001, + author = {Roland Becker and Rolf Rannacher}, + title = {An optimal control approach to a posteriori error estimation in finite element methods}, + journal = {Acta Numerica}, + volume = {10}, + pages = {1-102}, + year = {2001}, + doi = {10.1017/S0962492901000010}, +} + +@article{Rognes2010, +author = {Rognes, Marie E. and Logg, Anders}, +title = {Automated goal-oriented error control {I}: stationary variational problems}, +journal = {SIAM Journal on Scientific Computing}, +volume = {35}, +number = {3}, +pages = {C173--C193}, +year = {2013}, +doi = {10.1137/10081962X}, +} + diff --git a/demos/goal_based_adaptivity/goal_based_adaptivity.py.rst b/demos/goal_based_adaptivity/goal_based_adaptivity.py.rst new file mode 100644 index 0000000000..d727feec91 --- /dev/null +++ b/demos/goal_based_adaptivity/goal_based_adaptivity.py.rst @@ -0,0 +1,93 @@ +Goal-based adaptivity for computing functionals of the solution +=============================================================== + +.. rst-class:: emphasis + + The dual-weighted residual (DWR) method is a technique for designing global and local + error estimators for the error in a goal functional :math:`J(u)`, where :math:`u` + is the solution of a partial differential equation. Deriving the DWR method for + a specific problem usually involves substantial expertise, in deriving the appropriate + adjoint equation, residual formulation, etc. In this demo we show how the DWR method + can be automatically implemented using the :code:`GoalAdaptiveNonlinearVariationalSolver` + class in Firedrake. + + The demo was contributed by `Patrick Farrell + `__, based on the MSc project of Joseph Flood. + +The dual-weighted residual (DWR) method :cite:`Becker2001` is a technique for designing global and local error estimators for the error in a goal functional :math:`J(u)`. While implementing DWR by hand involves substantial expertise, the high-level symbolic UFL representation of the problem to solve permits the *automation* of DWR :cite:`Rognes2010`. + +In this demo we demonstrate how to automatically apply DWR to a nonlinear stationary boundary-value problem, the 𝑝-Laplacian: + +.. math:: + :name: eq:plaplace + + -\nabla \cdot \left( |\nabla u|^{p-2} \nabla u \right) = f \text{ in } \Omega, \quad u = 0 \text{ on } \partial \Omega. + +We solve the problem on a unit square with known analytical solution, so that we can compute effectivity indices of our error estimates. +Since we will be adapting the mesh, :doc:`we must build the domain with Netgen `: :: + + from firedrake import * + from netgen.occ import * + square = WorkPlane().Rectangle(1, 1).Face().bc("all") + square.edges.Max(Y).name = "top" + geo = OCCGeometry(square, dim=2) + ngmesh = geo.GenerateMesh(maxh=0.2) + mesh = Mesh(ngmesh) + + V = FunctionSpace(mesh, "CG", 3) + (x, y) = SpatialCoordinate(mesh) + + p = Constant(5) + u_exact = x*(1-x)*y*(1-y)*(x**2 + y**2 - x*y)*sin(2*pi*x)*exp(cos(pi*y)) + f = -div(inner(grad(u_exact), grad(u_exact))**((p-2)/2) * grad(u_exact)) + + u = Function(V, name="Solution") + u.interpolate(0.9*u_exact) + v = TestFunction(V) + + F = ( + inner(inner(grad(u), grad(u))**((p-2)/2) * grad(u), grad(v))*dx + - inner(f, v)*dx + ) + bcs = DirichletBC(V, 0, "on_boundary") + solver_parameters = {"snes_monitor": None, + "snes_linesearch_monitor": None, + "snes_linesearch_type": "l2", + "snes_linesearch_maxlambda": 1} + +To apply goal-based adaptivity, we need a goal functional. For this we will employ the integral of the normal derivative of the solution on the top boundary: :: + + top = tuple(i + 1 for (i, name) in enumerate(ngmesh.GetRegionNames(codim=1)) if name == "top") + n = FacetNormal(mesh) + J = inner(grad(u), n)*ds(top) + +We now specify options for how the goal-based adaptivity should proceed. We choose to use an expensive/robust approach, +where the adjoint solution is approximated in a higher-degree function space. This tends to give excellent error estimates. +It is possible to employ cheaper approximations by setting the parameters for the :code:`GoalAdaptiveNonlinearVariationalSolver` appropriately. :: + + dwr_parameters = { + "max_iterations": 30, + "output_dir": "output/p-laplace", + "run_name": "p-laplace", + "use_adjoint_residual": True, + "dual_low_method": "solve", + "dorfler_alpha": 0.5, + "dual_extra_degree": 1, + } + +We then solve the problem, passing the goal functional :math:`J` and our specified tolerance. We also pass the exact solution, so that +the DWR automation can compute the effectivity indices (ratio of the estimated error in the goal functional to the true error): :: + + + tolerance = 1e-4 + problem = NonlinearVariationalProblem(F, u, bcs) + GoalAdaptiveNonlinearVariationalSolver(problem, J, tolerance, dwr_parameters, + exact_solution=u_exact, primal_solver_parameters=solver_parameters).solve() + +:demo:`A Python script version of this demo can be found here +`. + +.. rubric:: References + +.. bibliography:: demo_references.bib + :filter: docname in docnames From d942f8fc375709e805e290d14605cfcd930c64b1 Mon Sep 17 00:00:00 2001 From: Patrick Farrell Date: Fri, 27 Feb 2026 17:55:08 +0000 Subject: [PATCH 16/51] Seems to work --- .../goal_based_adaptivity.py.rst | 13 +++++++++---- 1 file changed, 9 insertions(+), 4 deletions(-) diff --git a/demos/goal_based_adaptivity/goal_based_adaptivity.py.rst b/demos/goal_based_adaptivity/goal_based_adaptivity.py.rst index d727feec91..6cadfc68de 100644 --- a/demos/goal_based_adaptivity/goal_based_adaptivity.py.rst +++ b/demos/goal_based_adaptivity/goal_based_adaptivity.py.rst @@ -31,26 +31,30 @@ Since we will be adapting the mesh, :doc:`we must build the domain with Netgen < square = WorkPlane().Rectangle(1, 1).Face().bc("all") square.edges.Max(Y).name = "top" geo = OCCGeometry(square, dim=2) - ngmesh = geo.GenerateMesh(maxh=0.2) + ngmesh = geo.GenerateMesh(maxh=0.1) mesh = Mesh(ngmesh) V = FunctionSpace(mesh, "CG", 3) (x, y) = SpatialCoordinate(mesh) p = Constant(5) - u_exact = x*(1-x)*y*(1-y)*(x**2 + y**2 - x*y)*sin(2*pi*x)*exp(cos(pi*y)) + u_exact = x*(1-x)*y*(1-y)*exp(2*pi*x)*exp(cos(pi*y)) f = -div(inner(grad(u_exact), grad(u_exact))**((p-2)/2) * grad(u_exact)) u = Function(V, name="Solution") - u.interpolate(0.9*u_exact) + u.interpolate(0.99*u_exact) v = TestFunction(V) + dx = dx(degree=20) + ds = ds(degree=20) F = ( inner(inner(grad(u), grad(u))**((p-2)/2) * grad(u), grad(v))*dx - inner(f, v)*dx ) bcs = DirichletBC(V, 0, "on_boundary") solver_parameters = {"snes_monitor": None, + "snes_atol": 1e-6, + "snes_rtol": 1e-12, "snes_linesearch_monitor": None, "snes_linesearch_type": "l2", "snes_linesearch_maxlambda": 1} @@ -62,7 +66,7 @@ To apply goal-based adaptivity, we need a goal functional. For this we will empl J = inner(grad(u), n)*ds(top) We now specify options for how the goal-based adaptivity should proceed. We choose to use an expensive/robust approach, -where the adjoint solution is approximated in a higher-degree function space. This tends to give excellent error estimates. +where the adjoint solution is approximated in a higher-degree function space. This tends to give better error estimates. It is possible to employ cheaper approximations by setting the parameters for the :code:`GoalAdaptiveNonlinearVariationalSolver` appropriately. :: dwr_parameters = { @@ -71,6 +75,7 @@ It is possible to employ cheaper approximations by setting the parameters for th "run_name": "p-laplace", "use_adjoint_residual": True, "dual_low_method": "solve", + "primal_low_method": "solve", "dorfler_alpha": 0.5, "dual_extra_degree": 1, } From f94045da0867e521956873ce7158dee40b4c375b Mon Sep 17 00:00:00 2001 From: Patrick Farrell Date: Sat, 28 Feb 2026 12:36:05 +0000 Subject: [PATCH 17/51] Lint --- firedrake/adaptive_variational_solver.py | 1 - 1 file changed, 1 deletion(-) diff --git a/firedrake/adaptive_variational_solver.py b/firedrake/adaptive_variational_solver.py index 940f0d03d1..0a340cd6d5 100644 --- a/firedrake/adaptive_variational_solver.py +++ b/firedrake/adaptive_variational_solver.py @@ -1,4 +1,3 @@ -from firedrake import dmhooks from firedrake.petsc import PETSc from firedrake.function import Function from firedrake.cofunction import Cofunction From 4ee730e4d67de814d476713c85647ef4d56957f3 Mon Sep 17 00:00:00 2001 From: Patrick Farrell Date: Sat, 28 Feb 2026 12:48:07 +0000 Subject: [PATCH 18/51] Updates to demo --- .../goal_based_adaptivity.py.rst | 34 +++++++++++++++++-- 1 file changed, 31 insertions(+), 3 deletions(-) diff --git a/demos/goal_based_adaptivity/goal_based_adaptivity.py.rst b/demos/goal_based_adaptivity/goal_based_adaptivity.py.rst index 6cadfc68de..3b774ab24c 100644 --- a/demos/goal_based_adaptivity/goal_based_adaptivity.py.rst +++ b/demos/goal_based_adaptivity/goal_based_adaptivity.py.rst @@ -38,7 +38,7 @@ Since we will be adapting the mesh, :doc:`we must build the domain with Netgen < (x, y) = SpatialCoordinate(mesh) p = Constant(5) - u_exact = x*(1-x)*y*(1-y)*exp(2*pi*x)*exp(cos(pi*y)) + u_exact = x*(1-x)*y*(1-y)*exp(2*pi*x)*cos(pi*y) f = -div(inner(grad(u_exact), grad(u_exact))**((p-2)/2) * grad(u_exact)) u = Function(V, name="Solution") @@ -66,7 +66,7 @@ To apply goal-based adaptivity, we need a goal functional. For this we will empl J = inner(grad(u), n)*ds(top) We now specify options for how the goal-based adaptivity should proceed. We choose to use an expensive/robust approach, -where the adjoint solution is approximated in a higher-degree function space. This tends to give better error estimates. +where the adjoint solution is approximated in a higher-degree function space. This tends to give better error estimates. It is possible to employ cheaper approximations by setting the parameters for the :code:`GoalAdaptiveNonlinearVariationalSolver` appropriately. :: dwr_parameters = { @@ -83,12 +83,40 @@ It is possible to employ cheaper approximations by setting the parameters for th We then solve the problem, passing the goal functional :math:`J` and our specified tolerance. We also pass the exact solution, so that the DWR automation can compute the effectivity indices (ratio of the estimated error in the goal functional to the true error): :: - tolerance = 1e-4 problem = NonlinearVariationalProblem(F, u, bcs) GoalAdaptiveNonlinearVariationalSolver(problem, J, tolerance, dwr_parameters, exact_solution=u_exact, primal_solver_parameters=solver_parameters).solve() +The solver terminates after seven refinements. The error estimates :math:`\eta` are very accurate. The effectivity indices + +.. math:: + + I = \frac{\eta}{J(u) - J(u_h)} + +are very close to one throughout: + ++-----------------------+-------------------------------+ +| Number of refinements | Effectivity index :math:`I` | ++=======================+===============================+ +| 0 | 0.9703 | ++-----------------------+-------------------------------+ +| 1 | 1.0283 | ++-----------------------+-------------------------------+ +| 2 | 1.0893 | ++-----------------------+-------------------------------+ +| 3 | 1.0305 | ++-----------------------+-------------------------------+ +| 4 | 1.0794 | ++-----------------------+-------------------------------+ +| 5 | 1.0252 | ++-----------------------+-------------------------------+ +| 6 | 1.0213 | ++-----------------------+-------------------------------+ +| 7 | 1.0213 | ++-----------------------+-------------------------------+ + + :demo:`A Python script version of this demo can be found here `. From 87edf722f7d89e3588ad8c3bee785015089e3a23 Mon Sep 17 00:00:00 2001 From: Patrick Farrell Date: Sat, 28 Feb 2026 13:05:23 +0000 Subject: [PATCH 19/51] Finalise demo --- .../goal_based_adaptivity_bvp.py.rst} | 17 +++++++++++------ demos/goal_based_adaptivity_bvp/mesh_38.png | Bin 0 -> 2353403 bytes docs/source/advanced_tut.rst | 1 + 3 files changed, 12 insertions(+), 6 deletions(-) rename demos/{goal_based_adaptivity/goal_based_adaptivity.py.rst => goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst} (90%) create mode 100644 demos/goal_based_adaptivity_bvp/mesh_38.png diff --git a/demos/goal_based_adaptivity/goal_based_adaptivity.py.rst b/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst similarity index 90% rename from demos/goal_based_adaptivity/goal_based_adaptivity.py.rst rename to demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst index 3b774ab24c..2e6a23b363 100644 --- a/demos/goal_based_adaptivity/goal_based_adaptivity.py.rst +++ b/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst @@ -1,5 +1,5 @@ -Goal-based adaptivity for computing functionals of the solution -=============================================================== +Goal-based adaptivity for stationary boundary value problems +============================================================ .. rst-class:: emphasis @@ -70,7 +70,7 @@ where the adjoint solution is approximated in a higher-degree function space. Th It is possible to employ cheaper approximations by setting the parameters for the :code:`GoalAdaptiveNonlinearVariationalSolver` appropriately. :: dwr_parameters = { - "max_iterations": 30, + "max_iterations": 100, "output_dir": "output/p-laplace", "run_name": "p-laplace", "use_adjoint_residual": True, @@ -88,7 +88,7 @@ the DWR automation can compute the effectivity indices (ratio of the estimated e GoalAdaptiveNonlinearVariationalSolver(problem, J, tolerance, dwr_parameters, exact_solution=u_exact, primal_solver_parameters=solver_parameters).solve() -The solver terminates after seven refinements. The error estimates :math:`\eta` are very accurate. The effectivity indices +The solver terminates with the goal functional computed to :math:`10^{-4}` after 7 refinements. The error estimates :math:`\eta` are very accurate. The effectivity indices .. math:: @@ -97,7 +97,7 @@ The solver terminates after seven refinements. The error estimates :math:`\eta` are very close to one throughout: +-----------------------+-------------------------------+ -| Number of refinements | Effectivity index :math:`I` | +| Number of refinements | Effectivity index :math:`I` | +=======================+===============================+ | 0 | 0.9703 | +-----------------------+-------------------------------+ @@ -116,9 +116,14 @@ are very close to one throughout: | 7 | 1.0213 | +-----------------------+-------------------------------+ +Changing the tolerance to :math:`10^{-8}` takes 38 refinements. The resulting mesh is plotted below. + +.. image:: mesh_38.png + :align: center + :width: 60% :demo:`A Python script version of this demo can be found here -`. +`. .. rubric:: References diff --git a/demos/goal_based_adaptivity_bvp/mesh_38.png b/demos/goal_based_adaptivity_bvp/mesh_38.png new file mode 100644 index 0000000000000000000000000000000000000000..1a4813e9dbda5c15f4bff9b760f6ea9ef1f9661b GIT binary patch literal 2353403 zcmW(-2Rv2pA3nCOnS_i>5|ZqYon(h3du4Ao*;_YBLVmh*vomf&D0`3WkUg)x_ulUP zzx^-e0&-X^^XsJ-am|+kEQK_ja=|T|k|=Z2urHxP6N4u!5jke3hytyw~l)Mp4{L?l-|l>t8>wbD>gg7E)7(rYpC;0T$g z+LOm*YlN(n5?po6pI(DQwAL@QydjAED+G~iLfUzO?r= zF-Q=2?*?%-K%oT0<1(p!?5(?Rw%*UmkE ztij6iIv?=re*G-^kT#CXqvr<4yX2|Zdl?RD`jzWb!c%9B#g)a!7sC?ErhY$4Z(0PN z&Ek*iFR`&xLC!Dzf?PZi)+Q?m$qjGmlk%LLw+b9$_wPS9Fo=ytK+wryMA}qcP=KA? z(pvT_{9a*wUGOFy1hEI5Ez(T+&s*RQM^5Xd1ODS#C@C+`=(D|dubW@$G*i3&OHz{b zy{x)A25_s88y0QUi;x zK#yA*QH^ygpP1jZEH-4N9_jDbH8(eZ`t%`&R{nhNXm787g%{tMy)Tb%IftN{-% 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zaJZa-Y|H<5fuob9owfJ>et{tLeIU4i=l^|!yPczzo4c8#^Z&f&k?8;Z67t`Lq2L;b N5>owXk-RDT{{TQcU047B literal 0 HcmV?d00001 diff --git a/docs/source/advanced_tut.rst b/docs/source/advanced_tut.rst index 5007d12f4b..152649e38e 100644 --- a/docs/source/advanced_tut.rst +++ b/docs/source/advanced_tut.rst @@ -35,3 +35,4 @@ element systems. Steady Boussinesq problem with integral constraints. Steady multicomponent flow -- microfluidic mixing of hydrocarbons. Deflation techniques for computing multiple solutions of nonlinear problems. + Goal-based adaptivity for stationary boundary value problems. From 6ce616d1875c90f8e6eafbf166e98171eb720de4 Mon Sep 17 00:00:00 2001 From: Patrick Farrell Date: Sat, 28 Feb 2026 13:07:25 +0000 Subject: [PATCH 20/51] Minor text edits --- .../goal_based_adaptivity_bvp.py.rst | 5 ++--- 1 file changed, 2 insertions(+), 3 deletions(-) diff --git a/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst b/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst index 2e6a23b363..be2d85b185 100644 --- a/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst +++ b/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst @@ -8,8 +8,7 @@ Goal-based adaptivity for stationary boundary value problems is the solution of a partial differential equation. Deriving the DWR method for a specific problem usually involves substantial expertise, in deriving the appropriate adjoint equation, residual formulation, etc. In this demo we show how the DWR method - can be automatically implemented using the :code:`GoalAdaptiveNonlinearVariationalSolver` - class in Firedrake. + can be automatically implemented in Firedrake for stationary boundary value problems. The demo was contributed by `Patrick Farrell `__, based on the MSc project of Joseph Flood. @@ -116,7 +115,7 @@ are very close to one throughout: | 7 | 1.0213 | +-----------------------+-------------------------------+ -Changing the tolerance to :math:`10^{-8}` takes 38 refinements. The resulting mesh is plotted below. +Changing the tolerance to :math:`10^{-8}` takes 38 refinements. The resulting mesh is plotted below. The mesh resolution is adaptively concentrated at the top boundary, since the goal functional is localised there. .. image:: mesh_38.png :align: center From e20063c5130b16a83144ff0ad172abfa5651f952 Mon Sep 17 00:00:00 2001 From: Patrick Farrell Date: Sat, 28 Feb 2026 14:24:56 +0000 Subject: [PATCH 21/51] Small edits --- .../goal_based_adaptivity_bvp.py.rst | 10 ++++++---- 1 file changed, 6 insertions(+), 4 deletions(-) diff --git a/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst b/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst index be2d85b185..0d84132a28 100644 --- a/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst +++ b/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst @@ -65,8 +65,10 @@ To apply goal-based adaptivity, we need a goal functional. For this we will empl J = inner(grad(u), n)*ds(top) We now specify options for how the goal-based adaptivity should proceed. We choose to use an expensive/robust approach, -where the adjoint solution is approximated in a higher-degree function space. This tends to give better error estimates. -It is possible to employ cheaper approximations by setting the parameters for the :code:`GoalAdaptiveNonlinearVariationalSolver` appropriately. :: +where the adjoint solution is approximated in a higher-degree function space, and where both the adjoint and primal residuals +are employed for the error estimate. This tends to give better error estimates, but requires four solves on every grid (primal +and adjoint solutions with degree :math:`p` and :math:`p+1`). It is possible to employ cheaper approximations by setting +the parameters for the :code:`GoalAdaptiveNonlinearVariationalSolver` appropriately. :: dwr_parameters = { "max_iterations": 100, @@ -80,14 +82,14 @@ It is possible to employ cheaper approximations by setting the parameters for th } We then solve the problem, passing the goal functional :math:`J` and our specified tolerance. We also pass the exact solution, so that -the DWR automation can compute the effectivity indices (ratio of the estimated error in the goal functional to the true error): :: +the DWR automation can compute effectivity indices, but this is not generally required: :: tolerance = 1e-4 problem = NonlinearVariationalProblem(F, u, bcs) GoalAdaptiveNonlinearVariationalSolver(problem, J, tolerance, dwr_parameters, exact_solution=u_exact, primal_solver_parameters=solver_parameters).solve() -The solver terminates with the goal functional computed to :math:`10^{-4}` after 7 refinements. The error estimates :math:`\eta` are very accurate. The effectivity indices +The solver terminates with the goal functional computed to :math:`10^{-4}` after 7 refinements. The error estimates :math:`\eta` are very accurate: their effectivity indices .. math:: From aadff9a74aca2d7c89966e6b53c03ccf1489688c Mon Sep 17 00:00:00 2001 From: Patrick Farrell Date: Sat, 28 Feb 2026 16:04:56 +0000 Subject: [PATCH 22/51] The PDF version doesn't like my unicode math --- .../goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst b/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst index 0d84132a28..e317f2860e 100644 --- a/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst +++ b/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst @@ -15,7 +15,7 @@ Goal-based adaptivity for stationary boundary value problems The dual-weighted residual (DWR) method :cite:`Becker2001` is a technique for designing global and local error estimators for the error in a goal functional :math:`J(u)`. While implementing DWR by hand involves substantial expertise, the high-level symbolic UFL representation of the problem to solve permits the *automation* of DWR :cite:`Rognes2010`. -In this demo we demonstrate how to automatically apply DWR to a nonlinear stationary boundary-value problem, the 𝑝-Laplacian: +In this demo we demonstrate how to automatically apply DWR to a nonlinear stationary boundary-value problem, the :math:`p`-Laplacian: .. math:: :name: eq:plaplace From ccf7b4e30e98e6f3ef87785c1bdc8a03900bd266 Mon Sep 17 00:00:00 2001 From: Pablo Brubeck Date: Sat, 28 Feb 2026 20:48:25 +0000 Subject: [PATCH 23/51] Apply suggestions from code review --- firedrake/mg/ufl_utils.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/firedrake/mg/ufl_utils.py b/firedrake/mg/ufl_utils.py index 7505f19e9c..a421efafd8 100644 --- a/firedrake/mg/ufl_utils.py +++ b/firedrake/mg/ufl_utils.py @@ -159,7 +159,7 @@ def coarsen_function_space(V, self, coefficient_mapping=None): name, prev_level = name.split("_level_") except ValueError: prev_level = 0 - level = prev_level + level_increment + level = int(prev_level) + level_increment name = f"{name}_level_{level}" V_coarse = V_fine.reconstruct(mesh=mesh_coarse, name=name) V_coarse._fine = V_fine From 2a9cdabe8e0a79f9a486d14861f78a2ebc52a081 Mon Sep 17 00:00:00 2001 From: Pablo Brubeck Date: Mon, 2 Mar 2026 13:43:00 +0000 Subject: [PATCH 24/51] Fix test --- .../goal_based_adaptivity_bvp.py.rst | 34 +++++++++++-------- tests/firedrake/demos/test_demos_run.py | 3 +- 2 files changed, 21 insertions(+), 16 deletions(-) diff --git a/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst b/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst index e317f2860e..a5fc485c83 100644 --- a/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst +++ b/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst @@ -33,25 +33,26 @@ Since we will be adapting the mesh, :doc:`we must build the domain with Netgen < ngmesh = geo.GenerateMesh(maxh=0.1) mesh = Mesh(ngmesh) - V = FunctionSpace(mesh, "CG", 3) + degree = 3 + V = FunctionSpace(mesh, "CG", degree) (x, y) = SpatialCoordinate(mesh) p = Constant(5) u_exact = x*(1-x)*y*(1-y)*exp(2*pi*x)*cos(pi*y) f = -div(inner(grad(u_exact), grad(u_exact))**((p-2)/2) * grad(u_exact)) + # Since the problem is highly nonlinear, for the purposes of this demo we will + # cheat and pick our initial guess really close to the exact solution. u = Function(V, name="Solution") u.interpolate(0.99*u_exact) - v = TestFunction(V) - dx = dx(degree=20) - ds = ds(degree=20) - F = ( - inner(inner(grad(u), grad(u))**((p-2)/2) * grad(u), grad(v))*dx - - inner(f, v)*dx - ) - bcs = DirichletBC(V, 0, "on_boundary") - solver_parameters = {"snes_monitor": None, + v = TestFunction(V) + F = (inner(inner(grad(u), grad(u))**((p-2)/2) * grad(u), grad(v)) * dx + - inner(f, v) * dx(degree=degree+10) + ) + bcs = DirichletBC(V, u_exact, "on_boundary") + solver_parameters = { + "snes_monitor": None, "snes_atol": 1e-6, "snes_rtol": 1e-12, "snes_linesearch_monitor": None, @@ -71,14 +72,14 @@ and adjoint solutions with degree :math:`p` and :math:`p+1`). It is possible to the parameters for the :code:`GoalAdaptiveNonlinearVariationalSolver` appropriately. :: dwr_parameters = { - "max_iterations": 100, - "output_dir": "output/p-laplace", - "run_name": "p-laplace", + "max_iterations": 40, "use_adjoint_residual": True, "dual_low_method": "solve", "primal_low_method": "solve", "dorfler_alpha": 0.5, "dual_extra_degree": 1, + "run_name": "p-laplace", + "output_dir": "output/p-laplace", } We then solve the problem, passing the goal functional :math:`J` and our specified tolerance. We also pass the exact solution, so that @@ -86,8 +87,11 @@ the DWR automation can compute effectivity indices, but this is not generally re tolerance = 1e-4 problem = NonlinearVariationalProblem(F, u, bcs) - GoalAdaptiveNonlinearVariationalSolver(problem, J, tolerance, dwr_parameters, - exact_solution=u_exact, primal_solver_parameters=solver_parameters).solve() + + adaptive_solver = GoalAdaptiveNonlinearVariationalSolver(problem, J, tolerance, dwr_parameters, + exact_solution=u_exact, + primal_solver_parameters=solver_parameters) + adaptive_solver.solve() The solver terminates with the goal functional computed to :math:`10^{-4}` after 7 refinements. The error estimates :math:`\eta` are very accurate: their effectivity indices diff --git a/tests/firedrake/demos/test_demos_run.py b/tests/firedrake/demos/test_demos_run.py index 7202ddbc5f..c33e8796ac 100644 --- a/tests/firedrake/demos/test_demos_run.py +++ b/tests/firedrake/demos/test_demos_run.py @@ -52,7 +52,8 @@ Demo(("saddle_point_pc", "saddle_point_systems"), ["hypre", "mumps"]), Demo(("fast_diagonalisation", "fast_diagonalisation_poisson"), ["mumps"]), Demo(('vlasov_poisson_1d', 'vp1d'), []), - Demo(('shape_optimization', 'shape_optimization'), ["adjoint", "vtk"]) + Demo(('shape_optimization', 'shape_optimization'), ["adjoint", "vtk"]), + Demo(('goal_based_adaptivity_bvp', 'goal_based_adaptivity_bvp'), ["netgen"]), ] PARALLEL_DEMOS = [ Demo(("full_waveform_inversion", "full_waveform_inversion"), ["adjoint"]), From a1ce02ecea4942e0ecfb69b129c6f9cbf37f8544 Mon Sep 17 00:00:00 2001 From: Patrick Farrell Date: Mon, 2 Mar 2026 14:53:46 +0000 Subject: [PATCH 25/51] Update effectivity indices following quadrature changes --- .../goal_based_adaptivity_bvp.py.rst | 16 ++++++++-------- 1 file changed, 8 insertions(+), 8 deletions(-) diff --git a/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst b/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst index a5fc485c83..50b2b5ccc1 100644 --- a/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst +++ b/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst @@ -104,21 +104,21 @@ are very close to one throughout: +-----------------------+-------------------------------+ | Number of refinements | Effectivity index :math:`I` | +=======================+===============================+ -| 0 | 0.9703 | +| 0 | 0.9682 | +-----------------------+-------------------------------+ -| 1 | 1.0283 | +| 1 | 1.0262 | +-----------------------+-------------------------------+ -| 2 | 1.0893 | +| 2 | 1.0837 | +-----------------------+-------------------------------+ -| 3 | 1.0305 | +| 3 | 1.0210 | +-----------------------+-------------------------------+ -| 4 | 1.0794 | +| 4 | 1.0805 | +-----------------------+-------------------------------+ -| 5 | 1.0252 | +| 5 | 1.0247 | +-----------------------+-------------------------------+ -| 6 | 1.0213 | +| 6 | 1.0207 | +-----------------------+-------------------------------+ -| 7 | 1.0213 | +| 7 | 1.2108 | +-----------------------+-------------------------------+ Changing the tolerance to :math:`10^{-8}` takes 38 refinements. The resulting mesh is plotted below. The mesh resolution is adaptively concentrated at the top boundary, since the goal functional is localised there. From 459bce3039f237097d502055569d71d655edaaeb Mon Sep 17 00:00:00 2001 From: Patrick Farrell Date: Tue, 3 Mar 2026 10:45:44 +0000 Subject: [PATCH 26/51] We don't need the label --- .../goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst | 2 -- 1 file changed, 2 deletions(-) diff --git a/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst b/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst index 50b2b5ccc1..85a8b9e1e3 100644 --- a/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst +++ b/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst @@ -18,8 +18,6 @@ The dual-weighted residual (DWR) method :cite:`Becker2001` is a technique for de In this demo we demonstrate how to automatically apply DWR to a nonlinear stationary boundary-value problem, the :math:`p`-Laplacian: .. math:: - :name: eq:plaplace - -\nabla \cdot \left( |\nabla u|^{p-2} \nabla u \right) = f \text{ in } \Omega, \quad u = 0 \text{ on } \partial \Omega. We solve the problem on a unit square with known analytical solution, so that we can compute effectivity indices of our error estimates. From 56c7377ea9cc273920f11fc7a4b506ef24eee629 Mon Sep 17 00:00:00 2001 From: Patrick Farrell Date: Tue, 3 Mar 2026 11:41:34 +0000 Subject: [PATCH 27/51] Try to clean up output a little, more to do --- firedrake/adaptive_variational_solver.py | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/firedrake/adaptive_variational_solver.py b/firedrake/adaptive_variational_solver.py index 0a340cd6d5..b88c46f09e 100644 --- a/firedrake/adaptive_variational_solver.py +++ b/firedrake/adaptive_variational_solver.py @@ -398,12 +398,12 @@ def compute_efficiency(self, eta_cell, eta_h, eta): eff2 = eta_cell_total / eta self.eff1_vec.append(eff1) self.eff2_vec.append(eff2) - self.print(f'{"Effectivity index 1":45s}{"eta_h/eta:":8s}{eff1:7.4f}') - self.print(f'{"Effectivity index 2":45s}{"Σeta_K/eta:":8s}{eff2:7.4f}') + self.print(f'{"Effectivity index":45s}{"eta_h/eta:":8s}{eff1:7.4f}') + self.print(f'{"Localisation efficiency":45s}{"Σeta_K/eta:":8s}{eff2:7.4f}') else: eff3 = eta_cell_total / eta_h self.eff3_vec.append(eff3) - self.print(f'{"Effectivity index:":45s}{"Σeta_K/eta_h:":8s}{eff3:7.4f}') + self.print(f'{"Localisation efficiency:":45s}{"Σeta_K/eta_h:":8s}{eff3:7.4f}') def set_adaptive_cell_markers(self, eta_cell): """Mark cells for refinement (Dorfler marking)""" From 6a05c70b5c16f6b6349deeea3c320f0f52a3dcdb Mon Sep 17 00:00:00 2001 From: Patrick Farrell Date: Thu, 12 Mar 2026 10:18:46 +0000 Subject: [PATCH 28/51] Add Joe Flood and reference --- demos/demo_references.bib | 15 +++++++++++++++ .../goal_based_adaptivity_bvp.py.rst | 11 ++++++----- 2 files changed, 21 insertions(+), 5 deletions(-) diff --git a/demos/demo_references.bib b/demos/demo_references.bib index 7179174452..79eca5db62 100644 --- a/demos/demo_references.bib +++ b/demos/demo_references.bib @@ -413,3 +413,18 @@ @article{Rognes2010 doi = {10.1137/10081962X}, } +@inbook{Endtmayer2024, + ISBN={9780443294501}, + DOI={10.1016/bs.aams.2024.08.003}, + booktitle={Error Control, + Adaptive Discretizations, + and Applications, + Part 2}, + title={A posteriori single- and multi-goal error control and adaptivity for partial differential equations}, + author={Bernhard Endtmayer and Ulrich Langer and Thomas Richter and Andreas Schafelner and Thomas Wick}, + series={Advances in Applied Mechanics}, + volume={59}, + publisher={Elsevier}, + year={2024}, + pages={19--108} } + diff --git a/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst b/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst index 85a8b9e1e3..d1513ef600 100644 --- a/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst +++ b/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst @@ -10,8 +10,8 @@ Goal-based adaptivity for stationary boundary value problems adjoint equation, residual formulation, etc. In this demo we show how the DWR method can be automatically implemented in Firedrake for stationary boundary value problems. - The demo was contributed by `Patrick Farrell - `__, based on the MSc project of Joseph Flood. + The demo was contributed by `Patrick Farrell `__, based on the MSc project of + `Joseph Flood `__. The dual-weighted residual (DWR) method :cite:`Becker2001` is a technique for designing global and local error estimators for the error in a goal functional :math:`J(u)`. While implementing DWR by hand involves substantial expertise, the high-level symbolic UFL representation of the problem to solve permits the *automation* of DWR :cite:`Rognes2010`. @@ -65,9 +65,10 @@ To apply goal-based adaptivity, we need a goal functional. For this we will empl We now specify options for how the goal-based adaptivity should proceed. We choose to use an expensive/robust approach, where the adjoint solution is approximated in a higher-degree function space, and where both the adjoint and primal residuals -are employed for the error estimate. This tends to give better error estimates, but requires four solves on every grid (primal -and adjoint solutions with degree :math:`p` and :math:`p+1`). It is possible to employ cheaper approximations by setting -the parameters for the :code:`GoalAdaptiveNonlinearVariationalSolver` appropriately. :: +are employed for the error estimate. This requires four solves on every grid (primal and adjoint solutions with degree :math:`p` +and :math:`p+1`), and gives a provably efficient and reliable error estimator under a saturation assumption up to a term that is cubic in the error :cite:`Endtmayer2024`. +It is possible to employ cheaper approximations by setting the parameters for the :code:`GoalAdaptiveNonlinearVariationalSolver` +appropriately. :: dwr_parameters = { "max_iterations": 40, From 3872c540d888e5deb97eb2e50fb527a9c97bee42 Mon Sep 17 00:00:00 2001 From: Patrick Farrell Date: Thu, 12 Mar 2026 10:19:12 +0000 Subject: [PATCH 29/51] Do the right thing if given a mesh on a MeshHierarchy --- firedrake/adaptive_variational_solver.py | 13 +++++++++---- 1 file changed, 9 insertions(+), 4 deletions(-) diff --git a/firedrake/adaptive_variational_solver.py b/firedrake/adaptive_variational_solver.py index b88c46f09e..c05acccb6b 100644 --- a/firedrake/adaptive_variational_solver.py +++ b/firedrake/adaptive_variational_solver.py @@ -93,11 +93,16 @@ def __init__(self, problem: NonlinearVariationalProblem, goal_functional, tolera self.atm = AdaptiveTransferManager() mesh = V.mesh().unique() - amh, level = utils.get_level(mesh) - if amh is None: + mh, level = utils.get_level(mesh) + if mh is None: amh = AdaptiveMeshHierarchy(mesh) - if not isinstance(amh, AdaptiveMeshHierarchy): - raise ValueError("Problem needs to be defined on an AdaptiveMeshHierarchy") + elif isinstance(mh, AdaptiveMeshHierarchy): + amh = mh + else: + meshes = list(mh) + amh = AdaptiveMeshHierarchy(meshes[0]) + for m in meshes[1:level+1]: + amh.add_mesh(m) # FIXME we should construct a subset of the original hierarchy instead amh, level = utils.get_level(mesh) From ed64c834e191dec9e3604c9ef203006267a042c1 Mon Sep 17 00:00:00 2001 From: Patrick Farrell Date: Thu, 12 Mar 2026 10:24:25 +0000 Subject: [PATCH 30/51] Default to solve primal and dual low-order problems --- firedrake/adaptive_variational_solver.py | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/firedrake/adaptive_variational_solver.py b/firedrake/adaptive_variational_solver.py index c05acccb6b..ac537d8a2f 100644 --- a/firedrake/adaptive_variational_solver.py +++ b/firedrake/adaptive_variational_solver.py @@ -37,8 +37,8 @@ def __init__(self, config: dict): self.use_adjoint_residual = config.get("use_adjoint_residual", False) # For switching between primal and primal + adjoint residuals self.exact_indicators = config.get("exact_indicators", False) # Maybe remove self.uniform_refinement = config.get("uniform_refinement", False) - self.primal_low_method = config.get("primal_low_method", "interpolate") - self.dual_low_method = config.get("dual_low_method", "interpolate") + self.primal_low_method = config.get("primal_low_method", "solve") + self.dual_low_method = config.get("dual_low_method", "solve") self.write_mesh = config.get("write_mesh", "all") # Default all, options: "first_and_last" "by iteration" "none" self.write_mesh_iteration_vector = config.get("write_iteration_vector", []) self.write_mesh_iteration_interval = config.get("write_iteration_interval", 1) From 95ac11123d4db550b35363915febcf67fd1b5d30 Mon Sep 17 00:00:00 2001 From: Patrick Farrell Date: Fri, 13 Mar 2026 10:36:53 +0000 Subject: [PATCH 31/51] Solve low-order first --- firedrake/adaptive_variational_solver.py | 10 ++++++---- 1 file changed, 6 insertions(+), 4 deletions(-) diff --git a/firedrake/adaptive_variational_solver.py b/firedrake/adaptive_variational_solver.py index ac537d8a2f..8cea11c5e2 100644 --- a/firedrake/adaptive_variational_solver.py +++ b/firedrake/adaptive_variational_solver.py @@ -136,11 +136,15 @@ def solve_uh(): solver.solve() if self.options.use_adjoint_residual: + if self.options.primal_low_method == "solve": + solve_uh() + # Now solve in higher-order space high_degree = self.degree + self.options.dual_extra_degree # Use dual degree high_element = PMGPC.reconstruct_degree(self.element, high_degree) V_high = V.reconstruct(element=high_element) - u_high = Function(V_high).interpolate(u) + u_high = Function(V_high) + u_high.interpolate(u) v_old, = F.arguments() v_high = TestFunction(V_high) @@ -153,9 +157,7 @@ def solve_uh(): solver.set_transfer_manager(self.atm) solver.solve() - if self.options.primal_low_method == "solve": - solve_uh() - elif self.options.primal_low_method == "project": + if self.options.primal_low_method == "project": u.project(u_high) elif self.options.primal_low_method == "interpolate": u.interpolate(u_high) From 69142150fdbe8f2e86b8894b798d9ddbab0c3bee Mon Sep 17 00:00:00 2001 From: Patrick Farrell Date: Fri, 13 Mar 2026 10:58:45 +0000 Subject: [PATCH 32/51] Simplify AdaptiveMeshHierarchy logic --- firedrake/adaptive_variational_solver.py | 7 ------- 1 file changed, 7 deletions(-) diff --git a/firedrake/adaptive_variational_solver.py b/firedrake/adaptive_variational_solver.py index 8cea11c5e2..75a7f084eb 100644 --- a/firedrake/adaptive_variational_solver.py +++ b/firedrake/adaptive_variational_solver.py @@ -96,18 +96,11 @@ def __init__(self, problem: NonlinearVariationalProblem, goal_functional, tolera mh, level = utils.get_level(mesh) if mh is None: amh = AdaptiveMeshHierarchy(mesh) - elif isinstance(mh, AdaptiveMeshHierarchy): - amh = mh else: meshes = list(mh) amh = AdaptiveMeshHierarchy(meshes[0]) for m in meshes[1:level+1]: amh.add_mesh(m) - - # FIXME we should construct a subset of the original hierarchy instead - amh, level = utils.get_level(mesh) - while len(amh) > level+1: - amh.pop_mesh() self.amh = amh # Data storage and writing From 19b46be2dfa4b58b973d887633a4cf5e6a310199 Mon Sep 17 00:00:00 2001 From: Patrick Farrell Date: Fri, 13 Mar 2026 15:47:29 +0000 Subject: [PATCH 33/51] Specify quadrature degree on both integrands --- .../goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst b/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst index d1513ef600..627999b1b3 100644 --- a/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst +++ b/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst @@ -45,7 +45,7 @@ Since we will be adapting the mesh, :doc:`we must build the domain with Netgen < u.interpolate(0.99*u_exact) v = TestFunction(V) - F = (inner(inner(grad(u), grad(u))**((p-2)/2) * grad(u), grad(v)) * dx + F = (inner(inner(grad(u), grad(u))**((p-2)/2) * grad(u), grad(v)) * dx(degree=degree+10) - inner(f, v) * dx(degree=degree+10) ) bcs = DirichletBC(V, u_exact, "on_boundary") From a7a984e243733ff0b1bf65bc824a00dedf0c59ba Mon Sep 17 00:00:00 2001 From: Patrick Farrell Date: Sun, 5 Apr 2026 11:44:13 +0100 Subject: [PATCH 34/51] If we have solved the primal problem with high order, use that in the adjoint --- firedrake/adaptive_variational_solver.py | 9 +++++++++ 1 file changed, 9 insertions(+) diff --git a/firedrake/adaptive_variational_solver.py b/firedrake/adaptive_variational_solver.py index 75a7f084eb..4a2f942d4c 100644 --- a/firedrake/adaptive_variational_solver.py +++ b/firedrake/adaptive_variational_solver.py @@ -115,6 +115,8 @@ def __init__(self, problem: NonlinearVariationalProblem, goal_functional, tolera self.eff2_vec = [] self.eff3_vec = [] + self.u_high = None + def solve_primal(self): F = self.problem.F u = self.problem.u @@ -150,6 +152,8 @@ def solve_uh(): solver.set_transfer_manager(self.atm) solver.solve() + self.u_high = u_high + if self.options.primal_low_method == "project": u.project(u_high) elif self.options.primal_low_method == "interpolate": @@ -177,6 +181,10 @@ def solve_zh(z): dJ = derivative(J, u, TestFunction(Z)) a = adjoint(dF) + if self.u_high is not None: + a = replace(a, {u: self.u_high}) + dJ = replace(dJ, {u: self.u_high}) + bcs_dual = [bc.reconstruct(V=Z, indices=bc._indices, g=0) for bc in bcs] problem = LinearVariationalProblem(a, dJ, z, bcs_dual) solver = LinearVariationalSolver(problem, solver_parameters=self.sp_dual) @@ -445,6 +453,7 @@ def solve(self): self.step() except StopIteration: break + self.u_high = None def step(self): it = len(self.amh) - 1 From 4d611eddb8e48df11dde4845e2cd3d1606927308 Mon Sep 17 00:00:00 2001 From: Patrick Farrell Date: Sun, 5 Apr 2026 12:01:33 +0100 Subject: [PATCH 35/51] Keep valuable sign information about error estimate --- firedrake/adaptive_variational_solver.py | 24 ++++++++++++------------ 1 file changed, 12 insertions(+), 12 deletions(-) diff --git a/firedrake/adaptive_variational_solver.py b/firedrake/adaptive_variational_solver.py index 4a2f942d4c..e40752a2a6 100644 --- a/firedrake/adaptive_variational_solver.py +++ b/firedrake/adaptive_variational_solver.py @@ -220,17 +220,17 @@ def compute_etah(self, u_err, z_err): F = self.problem.F u = self.problem.u - primal_err = abs(assemble(residual(F, z_err))) + primal_err = assemble(residual(F, -z_err)) if self.options.use_adjoint_residual: Z = self.z_lo.function_space() dF = derivative(F, u, TrialFunction(Z)) dJ = derivative(J, u) G = action(adjoint(dF), self.z_lo) - dJ - dual_err = abs(assemble(residual(G, u_err))) - eta_h = 0.5 * abs(primal_err + dual_err) + dual_err = assemble(residual(G, -u_err)) + eta_h = 0.5 * (primal_err + dual_err) else: - eta_h = abs(primal_err) + eta_h = primal_err self.etah_vec.append(eta_h) @@ -245,20 +245,20 @@ def compute_etah(self, u_err, z_err): Ju = assemble(replace(J, {u: self.u_exact}), form_compiler_parameters=fcp) if self.u_exact is not None or self.goal_exact is not None: - eta = abs(Juh - Ju) + eta = Ju - Juh self.eta_vec.append(eta) self.print(f'{"Exact goal":45s}{"J(u):":8s}{Ju:15.12f}') - self.print(f'{"True error, |J(u) - J(u_h)|":45s}{"eta:":8s}{eta:15.12f}') + self.print(f'{"True error, J(u) - J(u_h)":45s}{"eta:":8s}{eta:15.12f}') else: eta = None if self.options.use_adjoint_residual: - self.print(f'{"Primal error, |rho(u_h;z-z_h)|:":45s}{"eta_pri:":8s}{primal_err:15.12f}') - self.print(f'{"Dual error, |rho*(z_h;u-u_h)|:":45s}{"eta_adj:":8s}{dual_err:15.12f}') - self.print(f'{"Difference":35s}{"|eta_pri-eta_adj|:":18s}{abs(primal_err-dual_err):19.12e}') - self.print(f'{"Predicted error, 0.5|rho+rho*|":45s}{"eta_h:":8s}{eta_h:15.12f}') + self.print(f'{"Primal error, rho(u_h;z-z_h):":45s}{"eta_pri:":8s}{primal_err:15.12f}') + self.print(f'{"Dual error, rho*(z_h;u-u_h):":45s}{"eta_adj:":8s}{dual_err:15.12f}') + self.print(f'{"Difference":35s}{"eta_pri-eta_adj:":18s}{abs(primal_err-dual_err):19.12e}') + self.print(f'{"Predicted error, 0.5(rho+rho*)":45s}{"eta_h:":8s}{eta_h:15.12f}') else: - self.print(f'{"Predicted error, |rho(u_h;z-z_h)|":45s}{"eta_h:":8s}{eta_h:15.12f}') + self.print(f'{"Predicted error, rho(u_h;z-z_h)":45s}{"eta_h:":8s}{eta_h:15.12f}') return eta_h, eta def automatic_error_indicators(self, u_err, z_err): @@ -463,7 +463,7 @@ def step(self): z_err = self.solve_dual() self.write_solution(it) eta_h, eta = self.compute_etah(u_err, z_err) - if eta_h < self.tolerance: + if abs(eta_h) < self.tolerance: self.print("Error estimate below tolerance, finished.") raise StopIteration From 33fd77627fb1c3f46fb2cfe4342fb2939fddacfb Mon Sep 17 00:00:00 2001 From: Patrick Farrell Date: Sun, 5 Apr 2026 12:14:47 +0100 Subject: [PATCH 36/51] Clean up printing a little --- firedrake/adaptive_variational_solver.py | 32 ++++++++++++------------ 1 file changed, 16 insertions(+), 16 deletions(-) diff --git a/firedrake/adaptive_variational_solver.py b/firedrake/adaptive_variational_solver.py index e40752a2a6..397435ae70 100644 --- a/firedrake/adaptive_variational_solver.py +++ b/firedrake/adaptive_variational_solver.py @@ -235,7 +235,7 @@ def compute_etah(self, u_err, z_err): self.etah_vec.append(eta_h) Juh = assemble(J) - self.print(f'{"Computed goal":45s}{"J(uh):":8s}{Juh:15.12f}') + self.print(f'{"Computed goal J(uh):":40s}{Juh:15.12f}') self.Juh = Juh if self.goal_exact is not None: @@ -247,18 +247,18 @@ def compute_etah(self, u_err, z_err): if self.u_exact is not None or self.goal_exact is not None: eta = Ju - Juh self.eta_vec.append(eta) - self.print(f'{"Exact goal":45s}{"J(u):":8s}{Ju:15.12f}') - self.print(f'{"True error, J(u) - J(u_h)":45s}{"eta:":8s}{eta:15.12f}') + self.print(f'{"Exact goal J(u):":40s}{Ju:15.12f}') + self.print(f'{"True error, J(u) - J(u_h):":40s}{eta:15.12f}') else: eta = None if self.options.use_adjoint_residual: - self.print(f'{"Primal error, rho(u_h;z-z_h):":45s}{"eta_pri:":8s}{primal_err:15.12f}') - self.print(f'{"Dual error, rho*(z_h;u-u_h):":45s}{"eta_adj:":8s}{dual_err:15.12f}') - self.print(f'{"Difference":35s}{"eta_pri-eta_adj:":18s}{abs(primal_err-dual_err):19.12e}') - self.print(f'{"Predicted error, 0.5(rho+rho*)":45s}{"eta_h:":8s}{eta_h:15.12f}') + self.print(f'{"Primal error, rho(u_h;z-z_h):":40s}{primal_err:15.12f}') + self.print(f'{"Dual error, rho*(z_h;u-u_h):":40s}{dual_err:15.12f}') + self.print(f'{"Difference":40s}{abs(primal_err-dual_err):19.12e}') + self.print(f'{"Discretisation error, 0.5(rho+rho*)":40s}{eta_h:15.12f}') else: - self.print(f'{"Predicted error, rho(u_h;z-z_h)":45s}{"eta_h:":8s}{eta_h:15.12f}') + self.print(f'{"Discretisation error, rho(u_h;z-z_h)":40s}{eta_h:15.12f}') return eta_h, eta def automatic_error_indicators(self, u_err, z_err): @@ -353,8 +353,8 @@ def automatic_error_indicators(self, u_err, z_err): self.eta_primal_total = abs(evec.sum()) with eta_dual.dat.vec as evec: self.eta_dual_total = abs(evec.sum()) - self.print(f'{"Sum of primal refinement indicators":45s}{"Σeta_K:":8s}{self.eta_primal_total:15.12f}') - self.print(f'{"Sum of dual refinement indicators":45s}{"Σeta_K:":8s}{self.eta_dual_total:15.12f}') + self.print(f'{"Sum of primal refinement indicators:":40s}{self.eta_primal_total:15.12f}') + self.print(f'{"Sum of dual refinement indicators:":40s}{self.eta_dual_total:15.12f}') else: eta_cell = eta_primal @@ -398,20 +398,20 @@ def compute_efficiency(self, eta_cell, eta_h, eta): eta_cell_total = abs(evec.sum()) self.eta_cell_sum_vec.append(eta_cell_total) - self.print(f'{"Sum of refinement indicators":45s}{"Σeta_K:":8s}{eta_cell_total:15.12f}') + self.print(f'{"Sum of refinement indicators":40s}{eta_cell_total:15.12f}') if self.u_exact is not None or self.goal_exact is not None: # Compute efficiency indices - eff1 = eta_h / eta - eff2 = eta_cell_total / eta + eff1 = abs(eta_h / eta) + eff2 = abs(eta_cell_total / eta) self.eff1_vec.append(eff1) self.eff2_vec.append(eff2) - self.print(f'{"Effectivity index":45s}{"eta_h/eta:":8s}{eff1:7.4f}') - self.print(f'{"Localisation efficiency":45s}{"Σeta_K/eta:":8s}{eff2:7.4f}') + self.print(f'{"Effectivity index":40s}{eff1:7.4f}') + self.print(f'{"Localisation efficiency":40s}{eff2:7.4f}') else: eff3 = eta_cell_total / eta_h self.eff3_vec.append(eff3) - self.print(f'{"Localisation efficiency:":45s}{"Σeta_K/eta_h:":8s}{eff3:7.4f}') + self.print(f'{"Localisation efficiency:":40s}{eff3:7.4f}') def set_adaptive_cell_markers(self, eta_cell): """Mark cells for refinement (Dorfler marking)""" From dcaa83021a227787396ea3faa24c0a1447299642 Mon Sep 17 00:00:00 2001 From: Patrick Farrell Date: Sun, 5 Apr 2026 12:41:52 +0100 Subject: [PATCH 37/51] Also account for algebraic solver error. Can allow for very coarse nonlinear solves while still retaining excellent error estimates. --- .../goal_based_adaptivity_bvp.py.rst | 7 +-- firedrake/adaptive_variational_solver.py | 48 ++++++++++++------- 2 files changed, 34 insertions(+), 21 deletions(-) diff --git a/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst b/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst index 627999b1b3..3532542e00 100644 --- a/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst +++ b/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst @@ -21,7 +21,8 @@ In this demo we demonstrate how to automatically apply DWR to a nonlinear statio -\nabla \cdot \left( |\nabla u|^{p-2} \nabla u \right) = f \text{ in } \Omega, \quad u = 0 \text{ on } \partial \Omega. We solve the problem on a unit square with known analytical solution, so that we can compute effectivity indices of our error estimates. -Since we will be adapting the mesh, :doc:`we must build the domain with Netgen `: :: +Since we will be adapting the mesh, :doc:`we must build the domain with Netgen `. +Notice that we can set very coarse tolerances on the nonlinear solvers, as DWR also provides an estimate of the algebraic solver error: :: from firedrake import * from netgen.occ import * @@ -52,7 +53,7 @@ Since we will be adapting the mesh, :doc:`we must build the domain with Netgen < solver_parameters = { "snes_monitor": None, "snes_atol": 1e-6, - "snes_rtol": 1e-12, + "snes_rtol": 1e-1, "snes_linesearch_monitor": None, "snes_linesearch_type": "l2", "snes_linesearch_maxlambda": 1} @@ -71,7 +72,7 @@ It is possible to employ cheaper approximations by setting the parameters for th appropriately. :: dwr_parameters = { - "max_iterations": 40, + "max_iterations": 100, "use_adjoint_residual": True, "dual_low_method": "solve", "primal_low_method": "solve", diff --git a/firedrake/adaptive_variational_solver.py b/firedrake/adaptive_variational_solver.py index 397435ae70..bb6c51da36 100644 --- a/firedrake/adaptive_variational_solver.py +++ b/firedrake/adaptive_variational_solver.py @@ -211,16 +211,19 @@ def solve_zh(z): # Default to interpolation self.z_lo.interpolate(self.z) z_err = self.z - self.z_lo - return z_err + return self.z_lo, z_err - def compute_etah(self, u_err, z_err): + def compute_etah(self, u_err, z_lo, z_err): """Compute error estimate""" from firedrake.assemble import assemble J = self.goal_functional F = self.problem.F u = self.problem.u + # Primal contribution to error estimator primal_err = assemble(residual(F, -z_err)) + + # Dual contribution to error estimator if self.options.use_adjoint_residual: Z = self.z_lo.function_space() dF = derivative(F, u, TrialFunction(Z)) @@ -228,10 +231,15 @@ def compute_etah(self, u_err, z_err): G = action(adjoint(dF), self.z_lo) - dJ dual_err = assemble(residual(G, -u_err)) - eta_h = 0.5 * (primal_err + dual_err) + discretisation_error = 0.5 * (primal_err + dual_err) else: - eta_h = primal_err + discretisation_error = primal_err + + # Estimate of solver error + solver_error = assemble(residual(F, -z_lo)) + # Final error estimate + eta_h = discretisation_error + solver_error self.etah_vec.append(eta_h) Juh = assemble(J) @@ -247,18 +255,22 @@ def compute_etah(self, u_err, z_err): if self.u_exact is not None or self.goal_exact is not None: eta = Ju - Juh self.eta_vec.append(eta) - self.print(f'{"Exact goal J(u):":40s}{Ju:15.12f}') - self.print(f'{"True error, J(u) - J(u_h):":40s}{eta:15.12f}') + self.print(f'{"Exact goal J(u):":40s}{Ju: 15.12f}') + self.print(f'{"True error, J(u) - J(u_h):":40s}{eta: 15.12f}') else: eta = None if self.options.use_adjoint_residual: - self.print(f'{"Primal error, rho(u_h;z-z_h):":40s}{primal_err:15.12f}') - self.print(f'{"Dual error, rho*(z_h;u-u_h):":40s}{dual_err:15.12f}') + self.print(f'{"Primal error, rho(u_h; z-z_h):":40s}{primal_err: 15.12e}') + self.print(f'{"Dual error, rho*(z_h; u-u_h):":40s}{dual_err: 15.12e}') self.print(f'{"Difference":40s}{abs(primal_err-dual_err):19.12e}') - self.print(f'{"Discretisation error, 0.5(rho+rho*)":40s}{eta_h:15.12f}') + self.print(f'{"Discretisation error, 0.5(rho + rho*)":40s}{discretisation_error: 15.12e}') + self.print(f'{"Solver error, rho(u_h; z_h):":40s}{solver_error: 15.12e}') + self.print(f'{"Final error estimate:":40s}{eta_h: 15.12e}') else: - self.print(f'{"Discretisation error, rho(u_h;z-z_h)":40s}{eta_h:15.12f}') + self.print(f'{"Solver error, rho(u_h; z_h):":40s}{solver_error: 15.12e}') + self.print(f'{"Discretisation error, rho(u_h; z-z_h)":40s}{discretisation_error: 15.12e}') + self.print(f'{"Final error estimate:":40s}{eta_h: 15.12e}') return eta_h, eta def automatic_error_indicators(self, u_err, z_err): @@ -353,8 +365,8 @@ def automatic_error_indicators(self, u_err, z_err): self.eta_primal_total = abs(evec.sum()) with eta_dual.dat.vec as evec: self.eta_dual_total = abs(evec.sum()) - self.print(f'{"Sum of primal refinement indicators:":40s}{self.eta_primal_total:15.12f}') - self.print(f'{"Sum of dual refinement indicators:":40s}{self.eta_dual_total:15.12f}') + self.print(f'{"Sum of primal refinement indicators:":40s}{self.eta_primal_total: 15.12e}') + self.print(f'{"Sum of dual refinement indicators:":40s}{self.eta_dual_total: 15.12e}') else: eta_cell = eta_primal @@ -398,7 +410,7 @@ def compute_efficiency(self, eta_cell, eta_h, eta): eta_cell_total = abs(evec.sum()) self.eta_cell_sum_vec.append(eta_cell_total) - self.print(f'{"Sum of refinement indicators":40s}{eta_cell_total:15.12f}') + self.print(f'{"Sum of refinement indicators:":40s}{eta_cell_total: 15.12e}') if self.u_exact is not None or self.goal_exact is not None: # Compute efficiency indices @@ -406,12 +418,12 @@ def compute_efficiency(self, eta_cell, eta_h, eta): eff2 = abs(eta_cell_total / eta) self.eff1_vec.append(eff1) self.eff2_vec.append(eff2) - self.print(f'{"Effectivity index":40s}{eff1:7.4f}') - self.print(f'{"Localisation efficiency":40s}{eff2:7.4f}') + self.print(f'{"Effectivity index:":40s}{eff1: 15.12f}') + self.print(f'{"Localisation efficiency:":40s}{eff2: 15.12f}') else: eff3 = eta_cell_total / eta_h self.eff3_vec.append(eff3) - self.print(f'{"Localisation efficiency:":40s}{eff3:7.4f}') + self.print(f'{"Localisation efficiency:":40s}{eff3: 15.12f}') def set_adaptive_cell_markers(self, eta_cell): """Mark cells for refinement (Dorfler marking)""" @@ -460,9 +472,9 @@ def step(self): self.print(f"---------------------------- [MESH LEVEL {it}] ----------------------------") self.write_mesh(it) u_err = self.solve_primal() - z_err = self.solve_dual() + z_lo, z_err = self.solve_dual() self.write_solution(it) - eta_h, eta = self.compute_etah(u_err, z_err) + eta_h, eta = self.compute_etah(u_err, z_lo, z_err) if abs(eta_h) < self.tolerance: self.print("Error estimate below tolerance, finished.") raise StopIteration From 2a2a4dd362ef5fdef7cd3b631acc55653c68d609 Mon Sep 17 00:00:00 2001 From: Patrick Farrell Date: Sun, 5 Apr 2026 12:44:39 +0100 Subject: [PATCH 38/51] Update demo --- .../goal_based_adaptivity_bvp.py.rst | 18 +++++++++--------- 1 file changed, 9 insertions(+), 9 deletions(-) diff --git a/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst b/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst index 3532542e00..77b81d5f23 100644 --- a/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst +++ b/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst @@ -93,7 +93,7 @@ the DWR automation can compute effectivity indices, but this is not generally re primal_solver_parameters=solver_parameters) adaptive_solver.solve() -The solver terminates with the goal functional computed to :math:`10^{-4}` after 7 refinements. The error estimates :math:`\eta` are very accurate: their effectivity indices +The solver terminates with the goal functional computed to :math:`10^{-4}` after 7 refinements. Each nonlinear solve only required one Newton iteration. The error estimates :math:`\eta` are very accurate: their effectivity indices .. math:: @@ -104,21 +104,21 @@ are very close to one throughout: +-----------------------+-------------------------------+ | Number of refinements | Effectivity index :math:`I` | +=======================+===============================+ -| 0 | 0.9682 | +| 0 | 1.0034 | +-----------------------+-------------------------------+ -| 1 | 1.0262 | +| 1 | 1.0354 | +-----------------------+-------------------------------+ -| 2 | 1.0837 | +| 2 | 1.0976 | +-----------------------+-------------------------------+ -| 3 | 1.0210 | +| 3 | 1.0958 | +-----------------------+-------------------------------+ -| 4 | 1.0805 | +| 4 | 1.0024 | +-----------------------+-------------------------------+ -| 5 | 1.0247 | +| 5 | 1.0444 | +-----------------------+-------------------------------+ -| 6 | 1.0207 | +| 6 | 0.9901 | +-----------------------+-------------------------------+ -| 7 | 1.2108 | +| 7 | 1.0352 | +-----------------------+-------------------------------+ Changing the tolerance to :math:`10^{-8}` takes 38 refinements. The resulting mesh is plotted below. The mesh resolution is adaptively concentrated at the top boundary, since the goal functional is localised there. From 45cb0b01b406d79c727cb4ac3fd75d90af2157b1 Mon Sep 17 00:00:00 2001 From: Patrick Farrell Date: Sun, 5 Apr 2026 12:48:49 +0100 Subject: [PATCH 39/51] Small edits --- .../goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst b/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst index 77b81d5f23..a40f0845aa 100644 --- a/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst +++ b/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst @@ -121,7 +121,7 @@ are very close to one throughout: | 7 | 1.0352 | +-----------------------+-------------------------------+ -Changing the tolerance to :math:`10^{-8}` takes 38 refinements. The resulting mesh is plotted below. The mesh resolution is adaptively concentrated at the top boundary, since the goal functional is localised there. +Changing the tolerance to :math:`10^{-8}` takes 37 refinements. The resulting mesh is plotted below. The mesh resolution is adaptively concentrated at the top boundary, since the goal functional is localised there. .. image:: mesh_38.png :align: center From 7677e4525f444ccfea50efff1e307bf69f5769da Mon Sep 17 00:00:00 2001 From: Patrick Farrell Date: Sun, 5 Apr 2026 12:59:56 +0100 Subject: [PATCH 40/51] Comment on more practical variants, set defaults for practical variants --- .../goal_based_adaptivity_bvp.py.rst | 10 ++++++---- firedrake/adaptive_variational_solver.py | 4 ++-- 2 files changed, 8 insertions(+), 6 deletions(-) diff --git a/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst b/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst index a40f0845aa..9090ba71dd 100644 --- a/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst +++ b/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst @@ -53,7 +53,7 @@ Notice that we can set very coarse tolerances on the nonlinear solvers, as DWR a solver_parameters = { "snes_monitor": None, "snes_atol": 1e-6, - "snes_rtol": 1e-1, + "snes_rtol": 1e-1, # very coarse! "snes_linesearch_monitor": None, "snes_linesearch_type": "l2", "snes_linesearch_maxlambda": 1} @@ -68,8 +68,8 @@ We now specify options for how the goal-based adaptivity should proceed. We choo where the adjoint solution is approximated in a higher-degree function space, and where both the adjoint and primal residuals are employed for the error estimate. This requires four solves on every grid (primal and adjoint solutions with degree :math:`p` and :math:`p+1`), and gives a provably efficient and reliable error estimator under a saturation assumption up to a term that is cubic in the error :cite:`Endtmayer2024`. -It is possible to employ cheaper approximations by setting the parameters for the :code:`GoalAdaptiveNonlinearVariationalSolver` -appropriately. :: +It is possible to employ cheaper and more practical approximations by setting the parameters for the :code:`GoalAdaptiveNonlinearVariationalSolver` +appropriately, as discussed below. :: dwr_parameters = { "max_iterations": 100, @@ -118,7 +118,7 @@ are very close to one throughout: +-----------------------+-------------------------------+ | 6 | 0.9901 | +-----------------------+-------------------------------+ -| 7 | 1.0352 | +| 7 | 0.9659 | +-----------------------+-------------------------------+ Changing the tolerance to :math:`10^{-8}` takes 37 refinements. The resulting mesh is plotted below. The mesh resolution is adaptively concentrated at the top boundary, since the goal functional is localised there. @@ -127,6 +127,8 @@ Changing the tolerance to :math:`10^{-8}` takes 37 refinements. The resulting me :align: center :width: 60% +We now discuss more practical variants. The configuration above solves four PDEs per adaptive step (primal and adjoint, degree :math:`p` and :math:`p+1`). Changing the DWR parameters to `{"use_adjoint_residual": False, "dual_low_method": "interpolate"}` instead only solves two PDEs per adaptive step (primal at degree :math:`p`, and adjoint at degree :math:`p+1`), and is thus much faster. For this problem with tolerance :math:`10^{-4}` this barely makes a difference to the effectivity indices: most are around 1, with only one step where :math:`I \approx 1.25`. We therefore recommend this as the default settings for production use. + :demo:`A Python script version of this demo can be found here `. diff --git a/firedrake/adaptive_variational_solver.py b/firedrake/adaptive_variational_solver.py index bb6c51da36..15ff83b255 100644 --- a/firedrake/adaptive_variational_solver.py +++ b/firedrake/adaptive_variational_solver.py @@ -37,8 +37,8 @@ def __init__(self, config: dict): self.use_adjoint_residual = config.get("use_adjoint_residual", False) # For switching between primal and primal + adjoint residuals self.exact_indicators = config.get("exact_indicators", False) # Maybe remove self.uniform_refinement = config.get("uniform_refinement", False) - self.primal_low_method = config.get("primal_low_method", "solve") - self.dual_low_method = config.get("dual_low_method", "solve") + self.primal_low_method = config.get("primal_low_method", "interpolate") + self.dual_low_method = config.get("dual_low_method", "interpolate") self.write_mesh = config.get("write_mesh", "all") # Default all, options: "first_and_last" "by iteration" "none" self.write_mesh_iteration_vector = config.get("write_iteration_vector", []) self.write_mesh_iteration_interval = config.get("write_iteration_interval", 1) From 7d6c8aff299ad42411d0f03a72036e8a56f71e43 Mon Sep 17 00:00:00 2001 From: Patrick Farrell Date: Sun, 5 Apr 2026 22:06:31 +0100 Subject: [PATCH 41/51] Start cleaning up --- firedrake/adaptive_variational_solver.py | 27 +----------------------- 1 file changed, 1 insertion(+), 26 deletions(-) diff --git a/firedrake/adaptive_variational_solver.py b/firedrake/adaptive_variational_solver.py index 15ff83b255..1bec0037ce 100644 --- a/firedrake/adaptive_variational_solver.py +++ b/firedrake/adaptive_variational_solver.py @@ -26,7 +26,6 @@ class GoalAdaptiveOptions: def __init__(self, config: dict): - self.manual_indicators = config.get("manual_indicators", False) # Used for manual indicators (only implemented for Poisson but could be overriden) self.dorfler_alpha = config.get("dorfler_alpha", 0.5) # Dorfler marking parameter, default 0.5 self.max_iterations = config.get("max_iterations", 10) self.output_dir = config.get("output_dir", "./output") @@ -384,27 +383,6 @@ def automatic_error_indicators(self, u_err, z_err): self.print("L2 error in (dual) refinement indicators: ", unorm) return eta_cell - def manual_error_indicators(self, u_err, z_err): - """ Currently only implemented for Poisson, but can be overriden. To adapt to other PDEs, replace the form of - eta_cell = assemble() to the symbolic form of the error indicators. This form is usually obtained by integrating - the weak form by parts (to recover the strong form) and redistributing facet fluxes. - """ - from firedrake.assemble import assemble - u = self.problem.u - mesh = u.function_space().mesh().unique() - n = FacetNormal(mesh) - f = self.source_term - DG0 = FunctionSpace(mesh, "DG", degree=0) - test = TestFunction(DG0) - eta_cell = assemble( - inner(f + div(grad(u)), z_err * test) * dx - - inner(jump(grad(u), n), z_err * avg(test)) * dS - - inner(dot(grad(u), n), z_err * test) * ds - ) - with eta_cell.dat.vec as evec: - evec.abs() - return eta_cell - def compute_efficiency(self, eta_cell, eta_h, eta): with eta_cell.dat.vec as evec: eta_cell_total = abs(evec.sum()) @@ -488,10 +466,7 @@ def step(self): markers = self.set_uniform_cell_markers() else: self.print("Computing local refinement indicators eta_K ...") - if self.options.manual_indicators: - eta_cell = self.manual_error_indicators(u_err, z_err) - else: - eta_cell = self.automatic_error_indicators(u_err, z_err) + eta_cell = self.automatic_error_indicators(u_err, z_err) self.compute_efficiency(eta_cell, eta_h, eta) markers = self.set_adaptive_cell_markers(eta_cell) From 46725a8b20219ea49c8ab5f1b5e8cb37d2539ab5 Mon Sep 17 00:00:00 2001 From: Patrick Farrell Date: Sun, 5 Apr 2026 22:31:18 +0100 Subject: [PATCH 42/51] Code cleanups, default to extra cell/facet degree 1 --- .../goal_based_adaptivity_bvp.py.rst | 18 +++++------- firedrake/adaptive_variational_solver.py | 28 ++++++------------- 2 files changed, 15 insertions(+), 31 deletions(-) diff --git a/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst b/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst index 9090ba71dd..9a1e66c3fb 100644 --- a/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst +++ b/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst @@ -93,13 +93,13 @@ the DWR automation can compute effectivity indices, but this is not generally re primal_solver_parameters=solver_parameters) adaptive_solver.solve() -The solver terminates with the goal functional computed to :math:`10^{-4}` after 7 refinements. Each nonlinear solve only required one Newton iteration. The error estimates :math:`\eta` are very accurate: their effectivity indices +The initial error in the goal functional is :math:`-3.5 \times 10^{-2}`. The solver terminates with the goal functional computed to :math:`10^{-4}` after 4 refinements. Each nonlinear solve only required one Newton iteration. The error estimates :math:`\eta` are very accurate: their effectivity indices .. math:: I = \frac{\eta}{J(u) - J(u_h)} -are very close to one throughout: +are very close to one throughout, except in the final step: +-----------------------+-------------------------------+ | Number of refinements | Effectivity index :math:`I` | @@ -108,19 +108,15 @@ are very close to one throughout: +-----------------------+-------------------------------+ | 1 | 1.0354 | +-----------------------+-------------------------------+ -| 2 | 1.0976 | +| 2 | 1.0749 | +-----------------------+-------------------------------+ -| 3 | 1.0958 | +| 3 | 1.0406 | +-----------------------+-------------------------------+ -| 4 | 1.0024 | -+-----------------------+-------------------------------+ -| 5 | 1.0444 | -+-----------------------+-------------------------------+ -| 6 | 0.9901 | -+-----------------------+-------------------------------+ -| 7 | 0.9659 | +| 4 | 4.1940 | +-----------------------+-------------------------------+ +The effectivity index in the final step is larger than one because the solver error is larger than the discretisation error. (The code prints a warning to refine the solver tolerances if this happens.) + Changing the tolerance to :math:`10^{-8}` takes 37 refinements. The resulting mesh is plotted below. The mesh resolution is adaptively concentrated at the top boundary, since the goal functional is localised there. .. image:: mesh_38.png diff --git a/firedrake/adaptive_variational_solver.py b/firedrake/adaptive_variational_solver.py index 1bec0037ce..61e0bf8604 100644 --- a/firedrake/adaptive_variational_solver.py +++ b/firedrake/adaptive_variational_solver.py @@ -6,6 +6,7 @@ from firedrake.variational_solver import (NonlinearVariationalProblem, NonlinearVariationalSolver, LinearVariationalProblem, LinearVariationalSolver) from firedrake.solving import solve +from firedrake.logging import RED from firedrake.preconditioners.pmg import PMGPC from firedrake.mg import utils @@ -30,11 +31,10 @@ def __init__(self, config: dict): self.max_iterations = config.get("max_iterations", 10) self.output_dir = config.get("output_dir", "./output") self.dual_extra_degree = config.get("dual_extra_degree", 1) - self.cell_residual_extra_degree = config.get("cell_residual_extra_degree", 0) - self.facet_residual_extra_degree = config.get("facet_residual_extra_degree", 0) + self.cell_residual_extra_degree = config.get("cell_residual_extra_degree", 1) + self.facet_residual_extra_degree = config.get("facet_residual_extra_degree", 1) self.write_at_iteration = config.get("write_at_iteration", True) self.use_adjoint_residual = config.get("use_adjoint_residual", False) # For switching between primal and primal + adjoint residuals - self.exact_indicators = config.get("exact_indicators", False) # Maybe remove self.uniform_refinement = config.get("uniform_refinement", False) self.primal_low_method = config.get("primal_low_method", "interpolate") self.dual_low_method = config.get("dual_low_method", "interpolate") @@ -45,9 +45,7 @@ def __init__(self, config: dict): self.write_solution_iteration_vector = config.get("write_iteration_vector", []) self.write_solution_iteration_interval = config.get("write_solution", "all") # Default all, options: "first_and_last" "by iteration" "none" self.results_file_name = config.get("results_file_name", None) - self.nev = config.get("nev", 5) self.run_name = config.get("run_name", None) - self.form_compiler_parameters = config.get("form_compiler_parameters", None) # Solver parameters sp_cell = { @@ -237,6 +235,9 @@ def compute_etah(self, u_err, z_lo, z_err): # Estimate of solver error solver_error = assemble(residual(F, -z_lo)) + if abs(solver_error) > abs(discretisation_error): + self.print(RED % 'Warning: solver error estimate greater than discretisation error estimate, refine solver tolerances') + # Final error estimate eta_h = discretisation_error + solver_error self.etah_vec.append(eta_h) @@ -248,14 +249,13 @@ def compute_etah(self, u_err, z_lo, z_err): if self.goal_exact is not None: Ju = self.goal_exact elif self.u_exact is not None: - fcp = self.options.form_compiler_parameters - Ju = assemble(replace(J, {u: self.u_exact}), form_compiler_parameters=fcp) + Ju = assemble(replace(J, {u: self.u_exact})) if self.u_exact is not None or self.goal_exact is not None: eta = Ju - Juh self.eta_vec.append(eta) self.print(f'{"Exact goal J(u):":40s}{Ju: 15.12f}') - self.print(f'{"True error, J(u) - J(u_h):":40s}{eta: 15.12f}') + self.print(f'{"True error, J(u) - J(u_h):":40s}{eta: 15.12e}') else: eta = None @@ -369,18 +369,6 @@ def automatic_error_indicators(self, u_err, z_err): else: eta_cell = eta_primal - # XXX Exact error indicators (experimental - ignore) - if self.options.exact_indicators: - u_err_exact = self.u_exact - u - eta_dual_exact = assemble( - inner(inner(Rcell_star, u_err_exact), test)*dx - + inner(avg(inner(Rfacet_star, u_err_exact)), both(test))*dS - + inner(inner(Rfacet_star, u_err_exact), test)*ds - ) - udiff = assemble(eta_dual_exact - eta_dual) - with udiff.dat.vec as uvec: - unorm = uvec.norm() - self.print("L2 error in (dual) refinement indicators: ", unorm) return eta_cell def compute_efficiency(self, eta_cell, eta_h, eta): From a08b6a14cafa6edd6f07b6d39e15ebfb6c80ed50 Mon Sep 17 00:00:00 2001 From: Patrick Farrell Date: Sun, 5 Apr 2026 22:42:34 +0100 Subject: [PATCH 43/51] More tweaks --- .../goal_based_adaptivity_bvp.py.rst | 6 +++--- demos/goal_based_adaptivity_bvp/mesh_38.png | Bin 2353403 -> 0 bytes demos/goal_based_adaptivity_bvp/mesh_40.png | Bin 0 -> 2359703 bytes 3 files changed, 3 insertions(+), 3 deletions(-) delete mode 100644 demos/goal_based_adaptivity_bvp/mesh_38.png create mode 100644 demos/goal_based_adaptivity_bvp/mesh_40.png diff --git a/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst b/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst index 9a1e66c3fb..74c8b1652d 100644 --- a/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst +++ b/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst @@ -115,11 +115,11 @@ are very close to one throughout, except in the final step: | 4 | 4.1940 | +-----------------------+-------------------------------+ -The effectivity index in the final step is larger than one because the solver error is larger than the discretisation error. (The code prints a warning to refine the solver tolerances if this happens.) +The effectivity index in the final step is larger than one because the solver error is larger than the discretisation error. (The code prints a warning to refine the solver tolerances if this happens, which in this case we can safely ignore.) -Changing the tolerance to :math:`10^{-8}` takes 37 refinements. The resulting mesh is plotted below. The mesh resolution is adaptively concentrated at the top boundary, since the goal functional is localised there. +Changing the tolerance to :math:`10^{-8}` takes 40 refinements. The resulting mesh is plotted below. The mesh resolution is adaptively concentrated at the top boundary, since the goal functional is localised there. -.. image:: mesh_38.png +.. image:: mesh_40.png :align: center :width: 60% diff --git a/demos/goal_based_adaptivity_bvp/mesh_38.png b/demos/goal_based_adaptivity_bvp/mesh_38.png deleted file mode 100644 index 1a4813e9dbda5c15f4bff9b760f6ea9ef1f9661b..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 2353403 zcmW(-2Rv2pA3nCOnS_i>5|ZqYon(h3du4Ao*;_YBLVmh*vomf&D0`3WkUg)x_ulUP zzx^-e0&-X^^XsJ-am|+kEQK_ja=|T|k|=Z2urHxP6N4u!5jke3hytyw~l)Mp4{L?l-|l>t8>wbD>gg7E)7(rYpC;0T$g z+LOm*YlN(n5?po6pI(DQwAL@QydjAED+G~iLfUzO?r= zF-Q=2?*?%-K%oT0<1(p!?5(?Rw%*UmkE ztij6iIv?=re*G-^kT#CXqvr<4yX2|Zdl?RD`jzWb!c%9B#g)a!7sC?ErhY$4Z(0PN z&Ek*iFR`&xLC!Dzf?PZi)+Q?m$qjGmlk%LLw+b9$_wPS9Fo=ytK+wryMA}qcP=KA? z(pvT_{9a*wUGOFy1hEI5Ez(T+&s*RQM^5Xd1ODS#C@C+`=(D|dubW@$G*i3&OHz{b zy{x)A25_s88y0QUi;x zK#yA*QH^ygpP1jZEH-4N9_jDbH8(eZ`t%`&R{nhNXm787g%{tMy)Tb%IftN{-% 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z+6F{#r}Q;}QGKm4-BLFJ&L!BaK!O#BwfiVRO@I{%3WW*q^fd^1-`erzc!_qg_RuS( ziX>YI#5I)H7aIteD=m) zxEmb|f!a(XAO^pw*01xv_o)2P`ojeR0Z#$|9;1b`8?hjjz@KmuQ558^2zqav&YUEl z>h-B%pdy}NS~>PL4ad8U(zVj``?IL{9?Q4|K9nJ2tdwTT+P9?DyiDYP+ZVG#+x6q1OIQ03J7yIzGK-^tf<;3t?5byyjsAwEC_L!@BkxC%BMuv99v&lXRtO{J|tinb{ zjyxrkJ7D87PLdY-{nGFFqX3b*wr&dW2`fDx@6pQ~KGmyu2g>#VUMA_)9czz+MB4mm zU5%;)KaKi}RA`p^i)0(K6LUDae^6j0TK?(AS?;qBn&3em9ew9s|1@k>FZ=z!Os|M$AJg}056m8T8(0pa50;$!3FVdLc0 z=6Wf_^HPXQfQ6G&h?Dc)=QF55{9hNixLG^c2K@goNMIzX0~av Date: Tue, 7 Apr 2026 10:57:53 +0100 Subject: [PATCH 44/51] Cleanup --- .../goal_based_adaptivity_bvp.py.rst | 15 +- firedrake/adaptive_variational_solver.py | 370 +++++++----------- firedrake/mg/ufl_utils.py | 38 ++ 3 files changed, 185 insertions(+), 238 deletions(-) diff --git a/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst b/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst index 74c8b1652d..c6fb608581 100644 --- a/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst +++ b/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst @@ -68,10 +68,10 @@ We now specify options for how the goal-based adaptivity should proceed. We choo where the adjoint solution is approximated in a higher-degree function space, and where both the adjoint and primal residuals are employed for the error estimate. This requires four solves on every grid (primal and adjoint solutions with degree :math:`p` and :math:`p+1`), and gives a provably efficient and reliable error estimator under a saturation assumption up to a term that is cubic in the error :cite:`Endtmayer2024`. -It is possible to employ cheaper and more practical approximations by setting the parameters for the :code:`GoalAdaptiveNonlinearVariationalSolver` +It is possible to employ cheaper and more practical approximations by setting the options for the :code:`GoalAdaptiveNonlinearVariationalSolver` appropriately, as discussed below. :: - dwr_parameters = { + goal_adaptive_options = { "max_iterations": 100, "use_adjoint_residual": True, "dual_low_method": "solve", @@ -79,7 +79,7 @@ appropriately, as discussed below. :: "dorfler_alpha": 0.5, "dual_extra_degree": 1, "run_name": "p-laplace", - "output_dir": "output/p-laplace", + "output_dir": "./output", } We then solve the problem, passing the goal functional :math:`J` and our specified tolerance. We also pass the exact solution, so that @@ -88,9 +88,10 @@ the DWR automation can compute effectivity indices, but this is not generally re tolerance = 1e-4 problem = NonlinearVariationalProblem(F, u, bcs) - adaptive_solver = GoalAdaptiveNonlinearVariationalSolver(problem, J, tolerance, dwr_parameters, - exact_solution=u_exact, - primal_solver_parameters=solver_parameters) + adaptive_solver = GoalAdaptiveNonlinearVariationalSolver(problem, J, tolerance, + goal_adaptive_options=goal_adaptive_options, + primal_solver_parameters=solver_parameters, + exact_solution=u_exact) adaptive_solver.solve() The initial error in the goal functional is :math:`-3.5 \times 10^{-2}`. The solver terminates with the goal functional computed to :math:`10^{-4}` after 4 refinements. Each nonlinear solve only required one Newton iteration. The error estimates :math:`\eta` are very accurate: their effectivity indices @@ -123,7 +124,7 @@ Changing the tolerance to :math:`10^{-8}` takes 40 refinements. The resulting me :align: center :width: 60% -We now discuss more practical variants. The configuration above solves four PDEs per adaptive step (primal and adjoint, degree :math:`p` and :math:`p+1`). Changing the DWR parameters to `{"use_adjoint_residual": False, "dual_low_method": "interpolate"}` instead only solves two PDEs per adaptive step (primal at degree :math:`p`, and adjoint at degree :math:`p+1`), and is thus much faster. For this problem with tolerance :math:`10^{-4}` this barely makes a difference to the effectivity indices: most are around 1, with only one step where :math:`I \approx 1.25`. We therefore recommend this as the default settings for production use. +We now discuss more practical variants. The configuration above solves four PDEs per adaptive step (primal and adjoint, degree :math:`p` and :math:`p+1`). Changing `goal_adaptive_options` to `{"use_adjoint_residual": False, "dual_low_method": "interpolate"}` instead only solves two PDEs per adaptive step (primal at degree :math:`p`, and adjoint at degree :math:`p+1`), and is thus much faster. For this problem with tolerance :math:`10^{-4}` this barely makes a difference to the effectivity indices: most are around 1, with only one step where :math:`I \approx 1.25`. We therefore recommend this as the default settings for production use. :demo:`A Python script version of this demo can be found here `. diff --git a/firedrake/adaptive_variational_solver.py b/firedrake/adaptive_variational_solver.py index 61e0bf8604..909c1830eb 100644 --- a/firedrake/adaptive_variational_solver.py +++ b/firedrake/adaptive_variational_solver.py @@ -1,51 +1,65 @@ +from typing import Sequence from firedrake.petsc import PETSc from firedrake.function import Function -from firedrake.cofunction import Cofunction from firedrake.functionspace import FunctionSpace, TensorFunctionSpace from firedrake.ufl_expr import TestFunction, TrialFunction, derivative, action, adjoint from firedrake.variational_solver import (NonlinearVariationalProblem, NonlinearVariationalSolver, LinearVariationalProblem, LinearVariationalSolver) +from firedrake.nullspace import VectorSpaceBasis from firedrake.solving import solve +from firedrake.output import VTKFile from firedrake.logging import RED from firedrake.preconditioners.pmg import PMGPC -from firedrake.mg import utils -from firedrake.mg.ufl_utils import coarsen, CoarseningError +from firedrake.mg.utils import get_level +from firedrake.mg.ufl_utils import refine from firedrake.mg.adaptive_hierarchy import AdaptiveMeshHierarchy from firedrake.mg.adaptive_transfer_manager import AdaptiveTransferManager -from firedrake.output import VTKFile from finat.ufl import BrokenElement, FiniteElement -from ufl import avg, dot, div, grad, dx, ds, dS, inner, jump, as_vector, replace, FacetNormal +from ufl import avg, dx, ds, dS, inner, as_vector, replace import ufl - -from functools import singledispatch -from pathlib import Path import numpy as np -import csv + + +__all__ = ["GoalAdaptiveNonlinearVariationalSolver"] class GoalAdaptiveOptions: - def __init__(self, config: dict): - self.dorfler_alpha = config.get("dorfler_alpha", 0.5) # Dorfler marking parameter, default 0.5 - self.max_iterations = config.get("max_iterations", 10) - self.output_dir = config.get("output_dir", "./output") - self.dual_extra_degree = config.get("dual_extra_degree", 1) - self.cell_residual_extra_degree = config.get("cell_residual_extra_degree", 1) - self.facet_residual_extra_degree = config.get("facet_residual_extra_degree", 1) - self.write_at_iteration = config.get("write_at_iteration", True) - self.use_adjoint_residual = config.get("use_adjoint_residual", False) # For switching between primal and primal + adjoint residuals - self.uniform_refinement = config.get("uniform_refinement", False) - self.primal_low_method = config.get("primal_low_method", "interpolate") - self.dual_low_method = config.get("dual_low_method", "interpolate") - self.write_mesh = config.get("write_mesh", "all") # Default all, options: "first_and_last" "by iteration" "none" - self.write_mesh_iteration_vector = config.get("write_iteration_vector", []) - self.write_mesh_iteration_interval = config.get("write_iteration_interval", 1) - self.write_solution = config.get("write_solution", "all") # Default all, options: "first_and_last" "by iteration" "none" - self.write_solution_iteration_vector = config.get("write_iteration_vector", []) - self.write_solution_iteration_interval = config.get("write_solution", "all") # Default all, options: "first_and_last" "by iteration" "none" - self.results_file_name = config.get("results_file_name", None) - self.run_name = config.get("run_name", None) + def __init__(self, + dorfler_alpha: float = 0.5, + max_iterations: int = 10, + output_dir: str = "./output", + run_name: str = "default", + primal_extra_degree: int = 1, + dual_extra_degree: int = 1, + cell_residual_extra_degree: int = 1, + facet_residual_extra_degree: int = 1, + use_adjoint_residual: bool = False, + uniform_refinement: bool = False, + primal_low_method: str = "interpolate", + dual_low_method: str = "interpolate", + write_solution: str = "all", + write_iteration_vector: Sequence | None = None, + write_solution_frequency: int | None = None, + verbose: bool = True, + ): + self.dorfler_alpha = dorfler_alpha # Dorfler marking threshold + self.max_iterations = max_iterations + self.output_dir = output_dir + self.run_name = run_name + self.primal_extra_degree = primal_extra_degree + self.dual_extra_degree = dual_extra_degree + self.cell_residual_extra_degree = cell_residual_extra_degree + self.facet_residual_extra_degree = facet_residual_extra_degree + self.use_adjoint_residual = use_adjoint_residual # For switching between primal and primal + adjoint residuals + self.uniform_refinement = uniform_refinement + self.primal_low_method = primal_low_method + self.dual_low_method = dual_low_method + self.write_solution = write_solution # options: "all", "first_and_last", "by iteration", None + self.write_solution_iteration_vector = write_iteration_vector + self.write_solution_frequency = write_solution_frequency + self.verbose = verbose # Solver parameters sp_cell = { @@ -61,36 +75,62 @@ def __init__(self, config: dict): } -class GoalAdaptiveNonlinearVariationalSolver(): +class GoalAdaptiveNonlinearVariationalSolver: """Solves a nonlinear variational problem to minimise the error in a user-specified goal functional. We do this by adaptively refining the mesh based on the solution to a dual problem - which links the goal functional to the PDE. + + Parameters + ---------- + problem + The varitional formulation of the PDE defined on the coarse mesh + goal_functional + The goal functional defined in terms of the solution to the PDE + goal_adaptive_options + An options dictionary to construct a :class:`GoalAdaptiveOptions` + primal_solver_parameters + A dictionary of solver parameters for the primal problem + dual_solver_parameters + A dictionary of solver parameters for the dual problem + nullspace + The nullspace of the problem + exact_solution + The exact solution to the problem (optional). + It is used to verify the efficiency of the error estimate + exact_goal + The exact value for the goal functional (optional). + It is used to verify the efficiency of the error estimate. """ - def __init__(self, problem: NonlinearVariationalProblem, goal_functional, tolerance: float, solver_parameters: dict, - *, primal_solver_parameters=None, dual_solver_parameters=None, exact_solution=None, exact_goal=None, source_term=None, verbose=True, - nullspace=None): - # User input vars + def __init__(self, + problem: NonlinearVariationalProblem, + goal_functional: ufl.BaseForm, + tolerance: float, + goal_adaptive_options: dict | None = None, + primal_solver_parameters: dict | None = None, + dual_solver_parameters: dict | None = None, + nullspace: VectorSpaceBasis | None = None, + exact_solution: ufl.classes.Expr | None = None, + exact_goal: ufl.classes.Expr | None = None, + ): + if goal_adaptive_options is None: + goal_adaptive_options = {} self.problem = problem + if not (isinstance(goal_functional, ufl.BaseForm) and len(goal_functional.arguments()) == 0): + raise ValueError("goal_functional must be a 0-form") self.goal_functional = goal_functional self.tolerance = tolerance + self.options = GoalAdaptiveOptions(**goal_adaptive_options) self.sp_primal = primal_solver_parameters self.sp_dual = dual_solver_parameters + self.nullspace = nullspace self.u_exact = as_mixed(exact_solution) if isinstance(exact_solution, (tuple, list)) else exact_solution self.goal_exact = exact_goal - self.options = GoalAdaptiveOptions(solver_parameters) - self.source_term = source_term - # Derived vars - self.verbose = verbose + # Set up an AdaptiveMeshHierarchy V = problem.u.function_space() - self.element = V.ufl_element() - self.degree = self.element.degree() - self.nullspace = nullspace - self.atm = AdaptiveTransferManager() - mesh = V.mesh().unique() - mh, level = utils.get_level(mesh) + mh, level = get_level(mesh) if mh is None: amh = AdaptiveMeshHierarchy(mesh) else: @@ -99,19 +139,16 @@ def __init__(self, problem: NonlinearVariationalProblem, goal_functional, tolera for m in meshes[1:level+1]: amh.add_mesh(m) self.amh = amh + self.atm = AdaptiveTransferManager() - # Data storage and writing - self.output_dir = Path(self.options.output_dir) - self.output_dir.mkdir(parents=True, exist_ok=True) # ensures folder exists - self.N_vec = [] - self.Ndual_vec = [] + # Data storage + self.Ndofs_vec = [] self.eta_vec = [] self.etah_vec = [] self.eta_cell_sum_vec = [] self.eff1_vec = [] self.eff2_vec = [] self.eff3_vec = [] - self.u_high = None def solve_primal(self): @@ -119,10 +156,10 @@ def solve_primal(self): u = self.problem.u bcs = self.problem.bcs V = self.problem.u.function_space() - self.N_vec.append(V.dim()) + self.Ndofs_vec.append(V.dim()) def solve_uh(): - self.print(f'Solving primal (degree: {self.degree}, dofs: {V.dim()}) ...') + self.print(f'Solving primal (degree: {V.ufl_element().degree()}, dofs: {V.dim()}) ...') solver = NonlinearVariationalSolver(self.problem, solver_parameters=self.sp_primal) solver.set_transfer_manager(self.atm) solver.solve() @@ -132,9 +169,8 @@ def solve_uh(): solve_uh() # Now solve in higher-order space - high_degree = self.degree + self.options.dual_extra_degree # Use dual degree - high_element = PMGPC.reconstruct_degree(self.element, high_degree) - V_high = V.reconstruct(element=high_element) + high_degree = V.ufl_element().degree() + self.options.primal_extra_degree + V_high = reconstruct_degree(V, high_degree) u_high = Function(V_high) u_high.interpolate(u) @@ -144,7 +180,7 @@ def solve_uh(): bcs_high = [bc.reconstruct(V=V_high, indices=bc._indices) for bc in bcs] problem_high = NonlinearVariationalProblem(F_high, u_high, bcs_high) - self.print(f"Solving primal in higher space for error estimate (degree: {high_degree}, dofs: {V_high.dim()}) ...") + self.print(f"Solving primal with higher order for error estimate (degree: {high_degree}, dofs: {V_high.dim()}) ...") solver = NonlinearVariationalSolver(problem_high, solver_parameters=self.sp_primal) solver.set_transfer_manager(self.atm) solver.solve() @@ -162,7 +198,6 @@ def solve_uh(): return u_err def solve_dual(self): - V = self.problem.u.function_space() def solve_zh(z): bcs = self.problem.bcs @@ -188,16 +223,15 @@ def solve_zh(z): solver.set_transfer_manager(self.atm) solver.solve() - # Higher-order dual soluton - dual_degree = self.degree + self.options.dual_extra_degree - dual_element = PMGPC.reconstruct_degree(self.element, dual_degree) - V_dual = V.reconstruct(element=dual_element) + # Higher-order dual solution + V = self.problem.u.function_space() + dual_degree = V.ufl_element().degree() + self.options.dual_extra_degree + V_dual = reconstruct_degree(V, dual_degree) self.z = Function(V_dual) - self.Ndual_vec.append(V_dual.dim()) solve_zh(self.z) - # Lower-order dual soluton + # Lower-order dual solution self.z_lo = Function(V) if self.options.dual_low_method == "solve": self.z_lo.interpolate(self.z) @@ -210,7 +244,7 @@ def solve_zh(z): z_err = self.z - self.z_lo return self.z_lo, z_err - def compute_etah(self, u_err, z_lo, z_err): + def estimate_error(self, u_err, z_lo, z_err): """Compute error estimate""" from firedrake.assemble import assemble J = self.goal_functional @@ -272,7 +306,7 @@ def compute_etah(self, u_err, z_lo, z_err): self.print(f'{"Final error estimate:":40s}{eta_h: 15.12e}') return eta_h, eta - def automatic_error_indicators(self, u_err, z_err): + def compute_error_indicators(self, u_err, z_err): """Compute cell and facet residuals R_cell, R_facet""" from firedrake.assemble import assemble J = self.goal_functional @@ -284,8 +318,9 @@ def automatic_error_indicators(self, u_err, z_err): dim = mesh.topological_dimension cell = mesh.ufl_cell() variant = "integral" - cell_residual_degree = self.degree + self.options.cell_residual_extra_degree - facet_residual_degree = self.degree + self.options.facet_residual_extra_degree + degree = V.ufl_element().degree() + cell_residual_degree = degree + self.options.cell_residual_extra_degree + facet_residual_degree = degree + self.options.facet_residual_extra_degree # ------------------------------- Primal residual ------------------------------- # Cell bubbles B = FunctionSpace(mesh, "B", dim+1, variant=variant) # Bubble function space @@ -335,7 +370,7 @@ def automatic_error_indicators(self, u_err, z_err): # ------------------------------- Adjoint residual ------------------------------- if self.options.use_adjoint_residual: - # r*(v) = J"(u)[v] - A"_u(u)[v, z] since F = A(u;v) - L(v) + # r*(v) = J'(u)[v] - A'_u(u)[v, z] since F = A(u;v) - L(v) dF = derivative(F, u, TrialFunction(V)) dJ = derivative(J, u, TestFunction(V)) rstar = action(adjoint(dF), self.z_lo) - dJ @@ -357,7 +392,6 @@ def automatic_error_indicators(self, u_err, z_err): ) with eta_dual.dat.vec as evec: evec.abs() - # indicators: 0.5 * (primal + dual) eta_cell = assemble(0.5*(eta_primal + eta_dual)) with eta_primal.dat.vec as evec: @@ -371,7 +405,8 @@ def automatic_error_indicators(self, u_err, z_err): return eta_cell - def compute_efficiency(self, eta_cell, eta_h, eta): + def compute_efficiency_indices(self, eta_cell, eta_h, eta): + """Compute efficiency indices""" with eta_cell.dat.vec as evec: eta_cell_total = abs(evec.sum()) @@ -379,7 +414,6 @@ def compute_efficiency(self, eta_cell, eta_h, eta): self.print(f'{"Sum of refinement indicators:":40s}{eta_cell_total: 15.12e}') if self.u_exact is not None or self.goal_exact is not None: - # Compute efficiency indices eff1 = abs(eta_h / eta) eff2 = abs(eta_cell_total / eta) self.eff1_vec.append(eff1) @@ -413,6 +447,7 @@ def set_uniform_cell_markers(self): return markers def refine_problem(self, markers): + """Rediscretise the problem on the finest mesh""" mesh = self.amh[-1] new_mesh = mesh.refine_marked_elements(markers) self.amh.add_mesh(new_mesh) @@ -422,10 +457,9 @@ def refine_problem(self, markers): self.goal_functional = refine(self.goal_functional, refine, coefficient_mapping=coef_map) if self.u_exact is not None: self.u_exact = refine(self.u_exact, refine, coefficient_mapping=coef_map) - if self.source_term is not None: - self.source_term = refine(self.source_term, refine, coefficient_mapping=coef_map) def solve(self): + """Run the adaptive refinement loop: SOLVE -> ESTIMATE -> MARK -> REFINE""" for it in range(self.options.max_iterations): try: self.step() @@ -434,13 +468,15 @@ def solve(self): self.u_high = None def step(self): + """Compute one step of SOLVE -> ESTIMATE -> MARK -> REFINE""" it = len(self.amh) - 1 self.print(f"---------------------------- [MESH LEVEL {it}] ----------------------------") - self.write_mesh(it) + # SOLVE u_err = self.solve_primal() z_lo, z_err = self.solve_dual() self.write_solution(it) - eta_h, eta = self.compute_etah(u_err, z_lo, z_err) + # ESTIMATE + eta_h, eta = self.estimate_error(u_err, z_lo, z_err) if abs(eta_h) < self.tolerance: self.print("Error estimate below tolerance, finished.") raise StopIteration @@ -448,201 +484,73 @@ def step(self): if it == self.options.max_iterations - 1: self.print(f"Maximum iteration ({self.options.max_iterations}) reached. Exiting.") raise StopIteration - + # MARK if self.options.uniform_refinement: self.print("Refining uniformly") markers = self.set_uniform_cell_markers() else: self.print("Computing local refinement indicators eta_K ...") - eta_cell = self.automatic_error_indicators(u_err, z_err) - self.compute_efficiency(eta_cell, eta_h, eta) + eta_cell = self.compute_error_indicators(u_err, z_err) + self.compute_efficiency_indices(eta_cell, eta_h, eta) markers = self.set_adaptive_cell_markers(eta_cell) - - if self.options.write_at_iteration: - self.print("Appending data ...") - self.append_data() + # REFINE self.print("Transferring problem to new mesh ...") self.refine_problem(markers) - if not self.options.write_at_iteration: - self.print("Writing data ...") - self.write_data() - - # Writing functions: -------------------------------------- def print(self, *args, **kwargs): - if self.verbose: + if self.options.verbose: PETSc.Sys.Print(*args, **kwargs) - def write_data(self): - # Write to file - if self.options.results_file_name is None: - file_path = self.output_dir / "results.csv" - else: - file_path = self.output_dir / self.options.results_file_name - rows = list(zip(self.N_vec, self.Ndual_vec, self.eta_vec, self.etah_vec, self.eta_cell_sum_vec, self.eff1_vec, self.eff2_vec)) - headers = ("N", "Ndual", "eta", "eta_h", "sum_eta_T", "eff1", "eff2") - with open(file_path, "w", newline="") as file: - w = csv.writer(file) - w.writerow(headers) - w.writerows(rows) - - def append_data(self): - it = len(self.amh) - 1 - Juh = self.Juh - run_name = self.options.run_name - if run_name is None: - file_path = self.output_dir / "results.csv" - else: - file_path = self.output_dir / f"{run_name}/{run_name}_results.csv" - if self.u_exact is None and self.goal_exact is None and not self.options.uniform_refinement: - headers = ("iteration", "N", "Ndual", "Juh", "eta_h", "sum_eta_T") - row = ( - it, - self.N_vec[-1], self.Ndual_vec[-1], Juh, self.etah_vec[-1], self.eta_cell_sum_vec[-1] - ) - elif self.options.uniform_refinement: - headers = ("iteration", "N", "Ndual", "Juh", "eta", "eta_h") - row = ( - it, - self.N_vec[-1], self.Ndual_vec[-1], Juh, self.eta_vec[-1], self.etah_vec[-1] - ) - else: - headers = ("iteration", "N", "Ndual", "Juh", "eta", "eta_h", "sum_eta_T", "eff1", "eff2") - row = ( - it, - self.N_vec[-1], self.Ndual_vec[-1], Juh, self.eta_vec[-1], self.etah_vec[-1], self.eta_cell_sum_vec[-1], self.eff1_vec[-1], self.eff2_vec[-1] - ) - - file_path.parent.mkdir(parents=True, exist_ok=True) # create directories if missing - if it == 0: - with open(file_path, "w", newline="") as file: - writer = csv.writer(file) - writer.writerow(headers) - writer.writerow(row) - else: - with open(file_path, "a", newline="") as file: - writer = csv.writer(file) - writer.writerow(row) - def write_solution(self, it): should_write = False - write_solution = self.options.write_mesh + write_solution = self.options.write_solution if write_solution == "all": should_write = True elif write_solution == "first_and_last": if it == 0 or it == self.options.max_iterations: should_write = True elif write_solution == "by_iteration": - # Case A: user gave specific iterations (list/tuple/set) - if getattr(self.options, "write_solution_iteration_vector", None) is not None: - # allow any iterable; convert to set for O(1) lookup - targets = set(self.options.write_iteration_vector) - should_write = it in targets - # Case B: otherwise use interval (positive int) - elif getattr(self.options, "write_solution_iteration_interval", None) is not None: - interval = int(self.options.write_iteration_interval) - if interval <= 0: - raise ValueError("write_solution_iteration_interval must be a positive integer") - should_write = (it % interval == 0) # includes it=0 + # Case A: user gave specific iterations + if self.options.write_solution_iteration_vector is not None: + should_write = it in self.options.write_iteration_vector + # Case B: otherwise use frequency (positive int) + elif self.options.write_solution_frequency is not None: + freq = int(self.options.write_solution_frequency) + if freq <= 0: + raise ValueError("write_solution_frequency must be a positive integer") + should_write = (it % freq == 0) if should_write: + output_dir = self.options.output_dir run_name = self.options.run_name + prefix = f"{output_dir}/{run_name}/{run_name}" self.print("Writing (primal) solution ...") - u = self.problem.u - VTKFile(self.output_dir / f"{run_name}/{run_name}_solution_{it}.pvd").write(*u.subfunctions) + VTKFile(f"{prefix}_solution_{it}.pvd").write(*self.problem.u.subfunctions) self.print("Writing (dual) solution ...") - VTKFile(self.output_dir / f"{run_name}/{run_name}_dual_solution_{it}.pvd").write(*self.z.subfunctions) + VTKFile(f"{prefix}_dual_solution_{it}.pvd").write(*self.z.subfunctions) - def write_mesh(self, it): - mesh = self.problem.u.function_space().mesh() - should_write = False - write_mesh = self.options.write_mesh - if write_mesh == "all": - should_write = True - elif write_mesh == "first_and_last": - if it == 0 or it == self.options.max_iterations: - should_write = True - elif write_mesh == "by_iteration": - # Case A: user gave specific iterations (list/tuple/set) - if getattr(self.options, "write_mesh_iteration_vector", None) is not None: - # allow any iterable; convert to set for O(1) lookup - targets = set(self.options.write_iteration_vector) - should_write = it in targets - # Case B: otherwise use interval (positive int) - elif getattr(self.options, "write_mesh_iteration_interval", None) is not None: - interval = int(self.options.write_iteration_interval) - if interval <= 0: - raise ValueError("write_mesh_iteration_interval must be a positive integer") - should_write = (it % interval == 0) # includes it=0 - if should_write: - self.print("Writing mesh ...") - run_name = self.options.run_name - VTKFile(self.output_dir / f"{run_name}/{run_name}_mesh_{it}.pvd").write(mesh) - - -# Utility functions def residual(F, test): + """Replace the argument of a linear Form""" v, = F.arguments() return replace(F, {v: test}) def both(u): + """Add u on both sides of a facet""" return u("+") + u("-") def as_mixed(exprs): + """Flatten a list of ufl.Expr objects into a vector""" return as_vector([e[idx] for e in exprs for idx in np.ndindex(e.ufl_shape)]) +def reconstruct_degree(V, degree): + """Reconstruct a FunctionSpace with a different degree""" + return V.reconstruct(element=PMGPC.reconstruct_degree(V.ufl_element(), degree)) + + def reconstruct_bcs(bcs, V): - """Reconstruct a list of bcs""" + """Reconstruct a list of bcs on a different FunctionSpace""" bcs = [bc.reconstruct(V=V, indices=bc._indices) for bc in bcs] return bcs - - -@singledispatch -def refine(expr, self, coefficient_mapping=None): - return coarsen(expr, self, coefficient_mapping=coefficient_mapping) # fallback to original - - -@refine.register(ufl.Mesh) -@refine.register(ufl.MeshSequence) -def refine_mesh(mesh, self, coefficient_mapping=None): - hierarchy, level = utils.get_level(mesh) - if hierarchy is None: - raise CoarseningError("No mesh hierarchy available") - return hierarchy[level + 1] - - -@refine.register(Cofunction) -@refine.register(Function) -def refine_function(expr, self, coefficient_mapping=None): - if coefficient_mapping is None: - coefficient_mapping = {} - new = coefficient_mapping.get(expr) - if new is None: - Vf = expr.function_space() - Vc = self(Vf, self) - name = expr.name() - if name is not None: - level_increment = -1 if self == coarsen else 1 - try: - name, prev_level = name.split("_level_") - except ValueError: - prev_level = 0 - level = int(prev_level) + level_increment - name = f"{name}_level_{level}" - new = Function(Vc, name=name) - new.interpolate(expr) - coefficient_mapping[expr] = new - return new - - -# Only required for my examples: -def getlabels(mesh, codim): - ngmesh = mesh.netgen_mesh - names = ngmesh.GetRegionNames(codim=codim) - names_to_labels = {} - for l in names: - names_to_labels[l] = tuple(i+1 for i, name in enumerate(names) if name == l) - return names_to_labels diff --git a/firedrake/mg/ufl_utils.py b/firedrake/mg/ufl_utils.py index a421efafd8..235ac6259d 100644 --- a/firedrake/mg/ufl_utils.py +++ b/firedrake/mg/ufl_utils.py @@ -404,6 +404,44 @@ def coarsen_slate_tensor_op(tensor, self, coefficient_mapping=None): return type(tensor)(*children) +@singledispatch +def refine(expr, self, coefficient_mapping=None): + return coarsen(expr, self, coefficient_mapping=coefficient_mapping) # fallback to original + + +@refine.register(ufl.Mesh) +@refine.register(ufl.MeshSequence) +def refine_mesh(mesh, self, coefficient_mapping=None): + hierarchy, level = utils.get_level(mesh) + if hierarchy is None: + raise CoarseningError("No mesh hierarchy available") + return hierarchy[level + 1] + + +@refine.register(firedrake.Cofunction) +@refine.register(firedrake.Function) +def refine_function(expr, self, coefficient_mapping=None): + if coefficient_mapping is None: + coefficient_mapping = {} + new = coefficient_mapping.get(expr) + if new is None: + Vf = expr.function_space() + Vc = self(Vf, self) + name = expr.name() + if name is not None: + level_increment = -1 if self == coarsen else 1 + try: + name, prev_level = name.split("_level_") + except ValueError: + prev_level = 0 + level = int(prev_level) + level_increment + name = f"{name}_level_{level}" + new = firedrake.Function(Vc, name=name) + new.interpolate(expr) + coefficient_mapping[expr] = new + return new + + class Interpolation(object): def __init__(self, Vcoarse, Vfine, manager, cbcs=None, fbcs=None): self.cprimal = firedrake.Function(Vcoarse) From 8b222a440cf14b6a3fa436ec6a72c44642a4bcd3 Mon Sep 17 00:00:00 2001 From: Pablo Brubeck Date: Tue, 7 Apr 2026 13:00:26 +0100 Subject: [PATCH 45/51] Cleanup --- .../goal_based_adaptivity_bvp.py.rst | 2 +- firedrake/adaptive_variational_solver.py | 108 +++++++++++------- 2 files changed, 69 insertions(+), 41 deletions(-) diff --git a/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst b/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst index c6fb608581..c5be1b012d 100644 --- a/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst +++ b/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst @@ -92,7 +92,7 @@ the DWR automation can compute effectivity indices, but this is not generally re goal_adaptive_options=goal_adaptive_options, primal_solver_parameters=solver_parameters, exact_solution=u_exact) - adaptive_solver.solve() + adaptive_solution = adaptive_solver.solve() The initial error in the goal functional is :math:`-3.5 \times 10^{-2}`. The solver terminates with the goal functional computed to :math:`10^{-4}` after 4 refinements. Each nonlinear solve only required one Newton iteration. The error estimates :math:`\eta` are very accurate: their effectivity indices diff --git a/firedrake/adaptive_variational_solver.py b/firedrake/adaptive_variational_solver.py index 909c1830eb..a8d506cee7 100644 --- a/firedrake/adaptive_variational_solver.py +++ b/firedrake/adaptive_variational_solver.py @@ -5,7 +5,6 @@ from firedrake.ufl_expr import TestFunction, TrialFunction, derivative, action, adjoint from firedrake.variational_solver import (NonlinearVariationalProblem, NonlinearVariationalSolver, LinearVariationalProblem, LinearVariationalSolver) -from firedrake.nullspace import VectorSpaceBasis from firedrake.solving import solve from firedrake.output import VTKFile from firedrake.logging import RED @@ -92,9 +91,12 @@ class GoalAdaptiveNonlinearVariationalSolver: primal_solver_parameters A dictionary of solver parameters for the primal problem dual_solver_parameters - A dictionary of solver parameters for the dual problem - nullspace - The nullspace of the problem + A dictionary of solver parameters for the dual problem. + Defaults to `primal_solver_parameters`. + primal_solver_kwargs + Keyword arguments for the primal :class:`~.NonlinearVariationalSolver` + dual_solver_kwargs + Keyword arguments for the primal :class:`~.LinearVariationalSolver` exact_solution The exact solution to the problem (optional). It is used to verify the efficiency of the error estimate @@ -109,21 +111,24 @@ def __init__(self, goal_adaptive_options: dict | None = None, primal_solver_parameters: dict | None = None, dual_solver_parameters: dict | None = None, - nullspace: VectorSpaceBasis | None = None, + primal_solver_kwargs: dict | None = None, + dual_solver_kwargs: dict | None = None, exact_solution: ufl.classes.Expr | None = None, exact_goal: ufl.classes.Expr | None = None, ): if goal_adaptive_options is None: goal_adaptive_options = {} - self.problem = problem + if not (isinstance(goal_functional, ufl.BaseForm) and len(goal_functional.arguments()) == 0): raise ValueError("goal_functional must be a 0-form") + self.problem = problem self.goal_functional = goal_functional self.tolerance = tolerance self.options = GoalAdaptiveOptions(**goal_adaptive_options) self.sp_primal = primal_solver_parameters - self.sp_dual = dual_solver_parameters - self.nullspace = nullspace + self.sp_dual = dual_solver_parameters if dual_solver_parameters is not None else primal_solver_parameters + self.primal_solver_kwargs = primal_solver_kwargs if primal_solver_kwargs is not None else {} + self.dual_solver_kwargs = dual_solver_kwargs if dual_solver_kwargs is not None else {} self.u_exact = as_mixed(exact_solution) if isinstance(exact_solution, (tuple, list)) else exact_solution self.goal_exact = exact_goal @@ -140,6 +145,7 @@ def __init__(self, amh.add_mesh(m) self.amh = amh self.atm = AdaptiveTransferManager() + self.base_levels = len(amh) # Data storage self.Ndofs_vec = [] @@ -160,7 +166,8 @@ def solve_primal(self): def solve_uh(): self.print(f'Solving primal (degree: {V.ufl_element().degree()}, dofs: {V.dim()}) ...') - solver = NonlinearVariationalSolver(self.problem, solver_parameters=self.sp_primal) + solver = NonlinearVariationalSolver(self.problem, solver_parameters=self.sp_primal, + **self.primal_solver_kwargs) solver.set_transfer_manager(self.atm) solver.solve() @@ -171,7 +178,7 @@ def solve_uh(): # Now solve in higher-order space high_degree = V.ufl_element().degree() + self.options.primal_extra_degree V_high = reconstruct_degree(V, high_degree) - u_high = Function(V_high) + u_high = Function(V_high, name="high_order_solution") u_high.interpolate(u) v_old, = F.arguments() @@ -187,10 +194,14 @@ def solve_uh(): self.u_high = u_high - if self.options.primal_low_method == "project": + if self.options.primal_low_method == "solve": + pass + elif self.options.primal_low_method == "project": u.project(u_high) elif self.options.primal_low_method == "interpolate": u.interpolate(u_high) + else: + raise ValueError(f"Unrecognised primal_low_method {self.options.primal_low_method}") u_err = u_high - u else: solve_uh() @@ -219,7 +230,7 @@ def solve_zh(z): bcs_dual = [bc.reconstruct(V=Z, indices=bc._indices, g=0) for bc in bcs] problem = LinearVariationalProblem(a, dJ, z, bcs_dual) - solver = LinearVariationalSolver(problem, solver_parameters=self.sp_dual) + solver = LinearVariationalSolver(problem, solver_parameters=self.sp_dual, **self.dual_solver_kwargs) solver.set_transfer_manager(self.atm) solver.solve() @@ -227,22 +238,23 @@ def solve_zh(z): V = self.problem.u.function_space() dual_degree = V.ufl_element().degree() + self.options.dual_extra_degree V_dual = reconstruct_degree(V, dual_degree) - self.z = Function(V_dual) + self.z = Function(V_dual, name="dual_high_order_solution") solve_zh(self.z) # Lower-order dual solution - self.z_lo = Function(V) + z_lo = Function(V, name="dual_low_order_solution") if self.options.dual_low_method == "solve": - self.z_lo.interpolate(self.z) - solve_zh(self.z_lo) + z_lo.interpolate(self.z) + solve_zh(z_lo) elif self.options.dual_low_method == "project": - self.z_lo.project(self.z) + z_lo.project(self.z) + elif self.options.dual_low_method == "interpolate": + z_lo.interpolate(self.z) else: - # Default to interpolation - self.z_lo.interpolate(self.z) - z_err = self.z - self.z_lo - return self.z_lo, z_err + raise ValueError(f"Unrecognised dual_low_method {self.options.dual_low_method}") + z_err = self.z - z_lo + return z_lo, z_err def estimate_error(self, u_err, z_lo, z_err): """Compute error estimate""" @@ -256,10 +268,10 @@ def estimate_error(self, u_err, z_lo, z_err): # Dual contribution to error estimator if self.options.use_adjoint_residual: - Z = self.z_lo.function_space() + Z = z_lo.function_space() dF = derivative(F, u, TrialFunction(Z)) dJ = derivative(J, u) - G = action(adjoint(dF), self.z_lo) - dJ + G = action(adjoint(dF), z_lo) - dJ dual_err = assemble(residual(G, -u_err)) discretisation_error = 0.5 * (primal_err + dual_err) @@ -279,13 +291,14 @@ def estimate_error(self, u_err, z_lo, z_err): Juh = assemble(J) self.print(f'{"Computed goal J(uh):":40s}{Juh:15.12f}') self.Juh = Juh - if self.goal_exact is not None: - Ju = self.goal_exact + Ju = assemble(self.goal_exact) elif self.u_exact is not None: Ju = assemble(replace(J, {u: self.u_exact})) + else: + Ju = None - if self.u_exact is not None or self.goal_exact is not None: + if Ju is not None: eta = Ju - Juh self.eta_vec.append(eta) self.print(f'{"Exact goal J(u):":40s}{Ju: 15.12f}') @@ -298,15 +311,13 @@ def estimate_error(self, u_err, z_lo, z_err): self.print(f'{"Dual error, rho*(z_h; u-u_h):":40s}{dual_err: 15.12e}') self.print(f'{"Difference":40s}{abs(primal_err-dual_err):19.12e}') self.print(f'{"Discretisation error, 0.5(rho + rho*)":40s}{discretisation_error: 15.12e}') - self.print(f'{"Solver error, rho(u_h; z_h):":40s}{solver_error: 15.12e}') - self.print(f'{"Final error estimate:":40s}{eta_h: 15.12e}') else: - self.print(f'{"Solver error, rho(u_h; z_h):":40s}{solver_error: 15.12e}') self.print(f'{"Discretisation error, rho(u_h; z-z_h)":40s}{discretisation_error: 15.12e}') - self.print(f'{"Final error estimate:":40s}{eta_h: 15.12e}') + self.print(f'{"Solver error, rho(u_h; z_h):":40s}{solver_error: 15.12e}') + self.print(f'{"Final error estimate:":40s}{eta_h: 15.12e}') return eta_h, eta - def compute_error_indicators(self, u_err, z_err): + def compute_error_indicators(self, u_err, z_lo, z_err): """Compute cell and facet residuals R_cell, R_facet""" from firedrake.assemble import assemble J = self.goal_functional @@ -373,7 +384,7 @@ def compute_error_indicators(self, u_err, z_err): # r*(v) = J'(u)[v] - A'_u(u)[v, z] since F = A(u;v) - L(v) dF = derivative(F, u, TrialFunction(V)) dJ = derivative(J, u, TestFunction(V)) - rstar = action(adjoint(dF), self.z_lo) - dJ + rstar = action(adjoint(dF), z_lo) - dJ # dual: project r* -> Rcell*, Rfacet* Lc_star = residual(rstar, bubbles*vc) @@ -459,17 +470,34 @@ def refine_problem(self, markers): self.u_exact = refine(self.u_exact, refine, coefficient_mapping=coef_map) def solve(self): - """Run the adaptive refinement loop: SOLVE -> ESTIMATE -> MARK -> REFINE""" + """Run the adaptive refinement loop: SOLVE -> ESTIMATE -> MARK -> REFINE. + + Returns + ------- + Function + The higher-order solution on the finest level of the hierarchy + + """ for it in range(self.options.max_iterations): try: - self.step() + self.step(it=it) except StopIteration: break + u_high = self.u_high self.u_high = None + return u_high - def step(self): - """Compute one step of SOLVE -> ESTIMATE -> MARK -> REFINE""" - it = len(self.amh) - 1 + def step(self, it=None): + """Compute one step of SOLVE -> ESTIMATE -> MARK -> REFINE + + Returns + ------- + Function + The higher-order solution on the finest level of the hierarchy + + """ + if it is None: + it = len(self.amh) - 1 self.print(f"---------------------------- [MESH LEVEL {it}] ----------------------------") # SOLVE u_err = self.solve_primal() @@ -480,8 +508,7 @@ def step(self): if abs(eta_h) < self.tolerance: self.print("Error estimate below tolerance, finished.") raise StopIteration - - if it == self.options.max_iterations - 1: + elif it == self.options.max_iterations - 1: self.print(f"Maximum iteration ({self.options.max_iterations}) reached. Exiting.") raise StopIteration # MARK @@ -490,12 +517,13 @@ def step(self): markers = self.set_uniform_cell_markers() else: self.print("Computing local refinement indicators eta_K ...") - eta_cell = self.compute_error_indicators(u_err, z_err) + eta_cell = self.compute_error_indicators(u_err, z_lo, z_err) self.compute_efficiency_indices(eta_cell, eta_h, eta) markers = self.set_adaptive_cell_markers(eta_cell) # REFINE self.print("Transferring problem to new mesh ...") self.refine_problem(markers) + return self.u_high def print(self, *args, **kwargs): if self.options.verbose: From fe9026c4e2e5f5e0f3d7d56822c0387660e4daf2 Mon Sep 17 00:00:00 2001 From: Patrick Farrell Date: Tue, 7 Apr 2026 15:34:06 +0200 Subject: [PATCH 46/51] Minor edits to comments --- firedrake/adaptive_variational_solver.py | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/firedrake/adaptive_variational_solver.py b/firedrake/adaptive_variational_solver.py index a8d506cee7..170b10a631 100644 --- a/firedrake/adaptive_variational_solver.py +++ b/firedrake/adaptive_variational_solver.py @@ -83,7 +83,7 @@ class GoalAdaptiveNonlinearVariationalSolver: Parameters ---------- problem - The varitional formulation of the PDE defined on the coarse mesh + The variational formulation of the PDE defined on the coarse mesh goal_functional The goal functional defined in terms of the solution to the PDE goal_adaptive_options @@ -99,10 +99,10 @@ class GoalAdaptiveNonlinearVariationalSolver: Keyword arguments for the primal :class:`~.LinearVariationalSolver` exact_solution The exact solution to the problem (optional). - It is used to verify the efficiency of the error estimate + If supplied, it is used to calculate the efficiency of the error estimate exact_goal The exact value for the goal functional (optional). - It is used to verify the efficiency of the error estimate. + If supplied, it is used to calculate the efficiency of the error estimate. """ def __init__(self, problem: NonlinearVariationalProblem, From 25a857946e3098924b6ac136cf33692ede98984e Mon Sep 17 00:00:00 2001 From: Pablo Brubeck Date: Tue, 7 Apr 2026 15:00:25 +0100 Subject: [PATCH 47/51] Also return eta_h and remove write_iteration_vector option --- .../goal_based_adaptivity_bvp.py.rst | 2 +- firedrake/adaptive_variational_solver.py | 35 +++++++++---------- 2 files changed, 17 insertions(+), 20 deletions(-) diff --git a/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst b/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst index c5be1b012d..8e099b26d0 100644 --- a/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst +++ b/demos/goal_based_adaptivity_bvp/goal_based_adaptivity_bvp.py.rst @@ -92,7 +92,7 @@ the DWR automation can compute effectivity indices, but this is not generally re goal_adaptive_options=goal_adaptive_options, primal_solver_parameters=solver_parameters, exact_solution=u_exact) - adaptive_solution = adaptive_solver.solve() + adaptive_solution, error_estimate = adaptive_solver.solve() The initial error in the goal functional is :math:`-3.5 \times 10^{-2}`. The solver terminates with the goal functional computed to :math:`10^{-4}` after 4 refinements. Each nonlinear solve only required one Newton iteration. The error estimates :math:`\eta` are very accurate: their effectivity indices diff --git a/firedrake/adaptive_variational_solver.py b/firedrake/adaptive_variational_solver.py index 170b10a631..593f2f0a3f 100644 --- a/firedrake/adaptive_variational_solver.py +++ b/firedrake/adaptive_variational_solver.py @@ -39,7 +39,6 @@ def __init__(self, primal_low_method: str = "interpolate", dual_low_method: str = "interpolate", write_solution: str = "all", - write_iteration_vector: Sequence | None = None, write_solution_frequency: int | None = None, verbose: bool = True, ): @@ -56,7 +55,6 @@ def __init__(self, self.primal_low_method = primal_low_method self.dual_low_method = dual_low_method self.write_solution = write_solution # options: "all", "first_and_last", "by iteration", None - self.write_solution_iteration_vector = write_iteration_vector self.write_solution_frequency = write_solution_frequency self.verbose = verbose @@ -474,8 +472,9 @@ def solve(self): Returns ------- - Function - The higher-order solution on the finest level of the hierarchy + Tuple[Function, float] + A tuple with the solution on the finest level of the hierarchy + and the error estimate. """ for it in range(self.options.max_iterations): @@ -483,17 +482,19 @@ def solve(self): self.step(it=it) except StopIteration: break - u_high = self.u_high + u_out = self.u_high if self.u_high is not None else self.problem.u + error_estimate = self.etah_vec[-1] self.u_high = None - return u_high + return u_out, error_estimate def step(self, it=None): """Compute one step of SOLVE -> ESTIMATE -> MARK -> REFINE Returns ------- - Function - The higher-order solution on the finest level of the hierarchy + Tuple[Function, float] + A tuple with the solution on the finest level of the hierarchy + and the error estimate. """ if it is None: @@ -501,6 +502,7 @@ def step(self, it=None): self.print(f"---------------------------- [MESH LEVEL {it}] ----------------------------") # SOLVE u_err = self.solve_primal() + u_out = self.u_high if self.u_high is not None else self.problem.u z_lo, z_err = self.solve_dual() self.write_solution(it) # ESTIMATE @@ -523,7 +525,7 @@ def step(self, it=None): # REFINE self.print("Transferring problem to new mesh ...") self.refine_problem(markers) - return self.u_high + return u_out, eta_h def print(self, *args, **kwargs): if self.options.verbose: @@ -537,16 +539,11 @@ def write_solution(self, it): elif write_solution == "first_and_last": if it == 0 or it == self.options.max_iterations: should_write = True - elif write_solution == "by_iteration": - # Case A: user gave specific iterations - if self.options.write_solution_iteration_vector is not None: - should_write = it in self.options.write_iteration_vector - # Case B: otherwise use frequency (positive int) - elif self.options.write_solution_frequency is not None: - freq = int(self.options.write_solution_frequency) - if freq <= 0: - raise ValueError("write_solution_frequency must be a positive integer") - should_write = (it % freq == 0) + elif self.options.write_solution_frequency is not None: + freq = int(self.options.write_solution_frequency) + if freq <= 0: + raise ValueError("write_solution_frequency must be a positive integer") + should_write = (it % freq == 0) if should_write: output_dir = self.options.output_dir run_name = self.options.run_name From dc39f8dbd3d2393b63a81f54254e93179b0b6d6e Mon Sep 17 00:00:00 2001 From: Pablo Brubeck Date: Tue, 7 Apr 2026 15:20:12 +0100 Subject: [PATCH 48/51] attach the inner solver --- firedrake/adaptive_variational_solver.py | 5 ++++- 1 file changed, 4 insertions(+), 1 deletion(-) diff --git a/firedrake/adaptive_variational_solver.py b/firedrake/adaptive_variational_solver.py index 593f2f0a3f..d7de7633d1 100644 --- a/firedrake/adaptive_variational_solver.py +++ b/firedrake/adaptive_variational_solver.py @@ -168,6 +168,7 @@ def solve_uh(): **self.primal_solver_kwargs) solver.set_transfer_manager(self.atm) solver.solve() + self.primal_solver = solver if self.options.use_adjoint_residual: if self.options.primal_low_method == "solve": @@ -186,9 +187,11 @@ def solve_uh(): problem_high = NonlinearVariationalProblem(F_high, u_high, bcs_high) self.print(f"Solving primal with higher order for error estimate (degree: {high_degree}, dofs: {V_high.dim()}) ...") - solver = NonlinearVariationalSolver(problem_high, solver_parameters=self.sp_primal) + solver = NonlinearVariationalSolver(problem_high, solver_parameters=self.sp_primal, + **self.primal_solver_kwargs) solver.set_transfer_manager(self.atm) solver.solve() + self.primal_solver = solver self.u_high = u_high From b920833a464822df8df9fd1b179a63b2b18a7f40 Mon Sep 17 00:00:00 2001 From: Pablo Brubeck Date: Tue, 7 Apr 2026 17:25:28 +0100 Subject: [PATCH 49/51] Multidomain fixes --- firedrake/adaptive_variational_solver.py | 65 ++++++++++++++---------- firedrake/mg/adaptive_hierarchy.py | 6 --- firedrake/mg/ufl_utils.py | 26 ++++++---- 3 files changed, 53 insertions(+), 44 deletions(-) diff --git a/firedrake/adaptive_variational_solver.py b/firedrake/adaptive_variational_solver.py index d7de7633d1..512465d4c8 100644 --- a/firedrake/adaptive_variational_solver.py +++ b/firedrake/adaptive_variational_solver.py @@ -1,4 +1,3 @@ -from typing import Sequence from firedrake.petsc import PETSc from firedrake.function import Function from firedrake.functionspace import FunctionSpace, TensorFunctionSpace @@ -132,16 +131,21 @@ def __init__(self, # Set up an AdaptiveMeshHierarchy V = problem.u.function_space() - mesh = V.mesh().unique() - mh, level = get_level(mesh) - if mh is None: - amh = AdaptiveMeshHierarchy(mesh) - else: - meshes = list(mh) - amh = AdaptiveMeshHierarchy(meshes[0]) - for m in meshes[1:level+1]: - amh.add_mesh(m) - self.amh = amh + meshes = set(V.mesh()) + meshes.add(V.mesh()) + hierarchy = {} + for mesh in meshes: + mh, level = get_level(mesh) + if mh is None: + amh = AdaptiveMeshHierarchy(mesh) + else: + meshes = list(mh) + amh = AdaptiveMeshHierarchy(meshes[0]) + for m in meshes[1:level+1]: + amh.add_mesh(m) + hierarchy[mesh] = amh + + self.amh = hierarchy[V.mesh()] self.atm = AdaptiveTransferManager() self.base_levels = len(amh) @@ -239,22 +243,22 @@ def solve_zh(z): V = self.problem.u.function_space() dual_degree = V.ufl_element().degree() + self.options.dual_extra_degree V_dual = reconstruct_degree(V, dual_degree) - self.z = Function(V_dual, name="dual_high_order_solution") - - solve_zh(self.z) + z = Function(V_dual, name="dual_high_order_solution") + solve_zh(z) # Lower-order dual solution z_lo = Function(V, name="dual_low_order_solution") if self.options.dual_low_method == "solve": - z_lo.interpolate(self.z) + z_lo.interpolate(z) solve_zh(z_lo) elif self.options.dual_low_method == "project": - z_lo.project(self.z) + z_lo.project(z) elif self.options.dual_low_method == "interpolate": - z_lo.interpolate(self.z) + z_lo.interpolate(z) else: raise ValueError(f"Unrecognised dual_low_method {self.options.dual_low_method}") - z_err = self.z - z_lo + z_err = z - z_lo + self.z = z return z_lo, z_err def estimate_error(self, u_err, z_lo, z_err): @@ -441,13 +445,12 @@ def set_adaptive_cell_markers(self, eta_cell): """Mark cells for refinement (Dorfler marking)""" # NOTE this is not quite Dorfler marking # For Dorfler marking we need to implement a parallel sort - with eta_cell.dat.vec_ro as evec: - _, eta_max = evec.max() - threshold = self.options.dorfler_alpha * eta_max - marked_cells = eta_cell.dat.data_ro > threshold - markers = Function(eta_cell.function_space()) - markers.dat.data_wo[marked_cells] = 1 + for m, e in zip(markers.subfunctions, eta_cell.subfunctions): + with e.dat.vec_ro as evec: + _, emax = evec.max() + threshold = self.options.dorfler_alpha * emax + m.dat.data_wo[e.dat.data_ro > threshold] = 1 return markers def set_uniform_cell_markers(self): @@ -460,9 +463,17 @@ def set_uniform_cell_markers(self): def refine_problem(self, markers): """Rediscretise the problem on the finest mesh""" - mesh = self.amh[-1] - new_mesh = mesh.refine_marked_elements(markers) - self.amh.add_mesh(new_mesh) + domain_markers = {m.function_space().mesh(): m for m in markers.subfunctions} + hierarchy = {} + for mesh in domain_markers: + amh, _ = get_level(mesh) + new_mesh = mesh.refine_marked_elements(domain_markers[mesh]) + amh.add_mesh(new_mesh) + hierarchy[mesh] = amh + + if self.amh not in hierarchy.values(): + mesh = self.amh[-1] + self.amh.add_mesh(type(mesh)([hierarchy[m][-1] for m in mesh])) coef_map = {} self.problem = refine(self.problem, refine, coefficient_mapping=coef_map) diff --git a/firedrake/mg/adaptive_hierarchy.py b/firedrake/mg/adaptive_hierarchy.py index c0e37414db..5c8ea2dc96 100644 --- a/firedrake/mg/adaptive_hierarchy.py +++ b/firedrake/mg/adaptive_hierarchy.py @@ -38,12 +38,6 @@ def add_mesh(self, mesh: MeshGeometry): self.meshes.append(mesh) set_level(mesh, self, level) - def pop_mesh(self): - """ - Removes the finest mesh from the hierarchy. - """ - self.meshes.pop() - def adapt(self, eta: Function | Cofunction, theta: float): """ Adds a new mesh to the hierarchy by locally refining the finest mesh diff --git a/firedrake/mg/ufl_utils.py b/firedrake/mg/ufl_utils.py index 235ac6259d..ed46e3919d 100644 --- a/firedrake/mg/ufl_utils.py +++ b/firedrake/mg/ufl_utils.py @@ -145,13 +145,13 @@ def coarsen_equation_bc(ebc, self, coefficient_mapping=None): @coarsen.register(firedrake.functionspaceimpl.WithGeometryBase) def coarsen_function_space(V, self, coefficient_mapping=None): - # FIXME support multiple hierarchies - # if hasattr(V, "_coarse") and self == coarsen: - # return V._coarse - V_fine = V - # Handle MixedFunctionSpace : V_fine.reconstruct requires MeshSequence. - fine_mesh = V_fine.mesh() if V_fine.index is None else V_fine.parent.mesh() - mesh_coarse = self(fine_mesh, self) + if hasattr(V, "_coarse") and self == coarsen: + return V._coarse + elif hasattr(V, "_fine") and self == refine: + return V._fine + # Handle MixedFunctionSpace : V.reconstruct requires MeshSequence. + mesh = V.mesh() if V.index is None else V.parent.mesh() + new_mesh = self(mesh, self) name = V.name if name is not None: level_increment = -1 if self == coarsen else 1 @@ -161,10 +161,14 @@ def coarsen_function_space(V, self, coefficient_mapping=None): prev_level = 0 level = int(prev_level) + level_increment name = f"{name}_level_{level}" - V_coarse = V_fine.reconstruct(mesh=mesh_coarse, name=name) - V_coarse._fine = V_fine - V_fine._coarse = V_coarse - return V_coarse + V_new = V.reconstruct(mesh=new_mesh, name=name) + if self == coarsen: + V_new._fine = V + V._coarse = V_new + elif self == refine: + V_new._coarse = V + V._fine = V_new + return V_new @coarsen.register(firedrake.Cofunction) From 37ab7d9a51e4ddad230c6994ada252192f929870 Mon Sep 17 00:00:00 2001 From: Pablo Brubeck Date: Tue, 7 Apr 2026 18:25:54 +0100 Subject: [PATCH 50/51] Fixes for multiple hierarchies --- firedrake/mg/ufl_utils.py | 30 +++++++++++++++++++----------- 1 file changed, 19 insertions(+), 11 deletions(-) diff --git a/firedrake/mg/ufl_utils.py b/firedrake/mg/ufl_utils.py index ed46e3919d..4b997d07b4 100644 --- a/firedrake/mg/ufl_utils.py +++ b/firedrake/mg/ufl_utils.py @@ -145,13 +145,13 @@ def coarsen_equation_bc(ebc, self, coefficient_mapping=None): @coarsen.register(firedrake.functionspaceimpl.WithGeometryBase) def coarsen_function_space(V, self, coefficient_mapping=None): - if hasattr(V, "_coarse") and self == coarsen: - return V._coarse - elif hasattr(V, "_fine") and self == refine: - return V._fine # Handle MixedFunctionSpace : V.reconstruct requires MeshSequence. mesh = V.mesh() if V.index is None else V.parent.mesh() new_mesh = self(mesh, self) + if self == coarsen and hasattr(V, "_coarse") and V._coarse.mesh() == new_mesh: + return V._coarse + elif self == refine and hasattr(V, "_fine") and V._fine.mesh() == new_mesh: + return V._fine name = V.name if name is not None: level_increment = -1 if self == coarsen else 1 @@ -201,8 +201,14 @@ def coarsen_function(expr, self, coefficient_mapping=None): @coarsen.register(firedrake.NonlinearVariationalProblem) def coarsen_nlvp(problem, self, coefficient_mapping=None): - if hasattr(problem, "_coarse") and self == coarsen: - return problem._coarse + # Have we done this already? + mh, _ = utils.get_level(problem.u.function_space().mesh()) + if self == coarsen and hasattr(problem, "_coarse"): + if mh is utils.get_level(problem._coarse.u.function_space().mesh())[0]: + return problem._coarse + elif self == refine and hasattr(problem, "_fine"): + if mh is utils.get_level(problem._fine.u.function_space().mesh())[0]: + return problem._fine def inject_on_restrict(fine, restriction, rscale, injection, coarse): manager = get_transfer_manager(fine) @@ -243,10 +249,13 @@ def inject_on_restrict(fine, restriction, rscale, injection, coarse): Jp = self(problem.Jp, self, coefficient_mapping=coefficient_mapping) u = coefficient_mapping[problem.u_restrict] - fine = problem + orig = problem problem = firedrake.NonlinearVariationalProblem(F, u, bcs=bcs, J=J, Jp=Jp, is_linear=problem.is_linear, form_compiler_parameters=problem.form_compiler_parameters) - fine._coarse = problem + if self == coarsen: + orig._coarse = problem + elif self == refine: + orig._fine = problem return problem @@ -282,9 +291,8 @@ def coarsen_snescontext(context, self, coefficient_mapping=None): coefficient_mapping = {} # Have we already done this? - coarse = context._coarse - if coarse is not None: - return coarse + if self == coarsen and context._coarse is not None: + return context._coarse problem = self(context._problem, self, coefficient_mapping=coefficient_mapping) appctx = context.appctx From b241c80f8f98d2b544aa68dbb8f84697b7bac8fb Mon Sep 17 00:00:00 2001 From: Pablo Brubeck Date: Tue, 7 Apr 2026 21:48:38 +0100 Subject: [PATCH 51/51] cleanup --- firedrake/adaptive_variational_solver.py | 36 +++++++++++------------- 1 file changed, 17 insertions(+), 19 deletions(-) diff --git a/firedrake/adaptive_variational_solver.py b/firedrake/adaptive_variational_solver.py index 512465d4c8..d418c13015 100644 --- a/firedrake/adaptive_variational_solver.py +++ b/firedrake/adaptive_variational_solver.py @@ -129,23 +129,19 @@ def __init__(self, self.u_exact = as_mixed(exact_solution) if isinstance(exact_solution, (tuple, list)) else exact_solution self.goal_exact = exact_goal - # Set up an AdaptiveMeshHierarchy + # Set up an AdaptiveMeshHierarchy for every mesh of the problem V = problem.u.function_space() meshes = set(V.mesh()) meshes.add(V.mesh()) - hierarchy = {} for mesh in meshes: mh, level = get_level(mesh) if mh is None: amh = AdaptiveMeshHierarchy(mesh) else: - meshes = list(mh) - amh = AdaptiveMeshHierarchy(meshes[0]) - for m in meshes[1:level+1]: + amh = AdaptiveMeshHierarchy(mh[0]) + for m in mh[1:level+1]: amh.add_mesh(m) - hierarchy[mesh] = amh - self.amh = hierarchy[V.mesh()] self.atm = AdaptiveTransferManager() self.base_levels = len(amh) @@ -455,25 +451,26 @@ def set_adaptive_cell_markers(self, eta_cell): def set_uniform_cell_markers(self): """Uniform marking for comparison tests""" - mesh = self.amh[-1] + V = self.problem.u.function_space() + mesh = V.mesh().unique() markers_space = FunctionSpace(mesh, "DG", 0) markers = Function(markers_space) markers.assign(1) return markers def refine_problem(self, markers): - """Rediscretise the problem on the finest mesh""" - domain_markers = {m.function_space().mesh(): m for m in markers.subfunctions} - hierarchy = {} - for mesh in domain_markers: + """Adaptively refine the mesh and rediscretise the problem on the refined mesh""" + for marker in markers.subfunctions: + mesh = marker.function_space().mesh() + new_mesh = mesh.refine_marked_elements(marker) + amh, _ = get_level(mesh) + amh.add_mesh(new_mesh) + # Reconstruct MeshSequence with the refined meshes + mesh = self.problem.u.function_space().mesh() + if len(mesh) > 1: + new_mesh = type(mesh)([get_level(m)[0][-1] for m in mesh]) amh, _ = get_level(mesh) - new_mesh = mesh.refine_marked_elements(domain_markers[mesh]) amh.add_mesh(new_mesh) - hierarchy[mesh] = amh - - if self.amh not in hierarchy.values(): - mesh = self.amh[-1] - self.amh.add_mesh(type(mesh)([hierarchy[m][-1] for m in mesh])) coef_map = {} self.problem = refine(self.problem, refine, coefficient_mapping=coef_map) @@ -512,7 +509,8 @@ def step(self, it=None): """ if it is None: - it = len(self.amh) - 1 + V = self.problem.u.function_space() + _, it = get_level(V.mesh()) self.print(f"---------------------------- [MESH LEVEL {it}] ----------------------------") # SOLVE u_err = self.solve_primal()

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