StroemungsRaum: add heat equation examples using FEniCS by Ouardghi · Pull Request #598 · Parallel-in-Time/pySDC

Ouardghi · 2026-02-05T13:48:41Z

This PR introduces the Heat Equation examples using FEniCS for the StroemungsRaum project.
The implementation is self-contained and does not affect existing projects.

Copilot

Pull request overview

This PR adds Heat Equation examples using FEniCS for the StroemungsRaum research project, which focuses on parallel-in-time methods and space-time parallelization for CFD simulations. The implementation introduces problem classes, test files, accuracy analysis scripts, and plotting utilities for solving 2D heat equations with different boundary conditions using the FEniCS finite element framework.

Changes:

Added three problem classes for 2D heat equation solving with varying boundary condition treatments
Implemented test suite with problem class tests, plotting tests, and accuracy convergence tests
Created accuracy analysis scripts for 3rd and 5th order convergence studies
Added environment configuration and project README documentation

Reviewed changes

Copilot reviewed 14 out of 20 changed files in this pull request and generated 55 comments.

Show a summary per file

File	Description
test_problem_class_heat_equation_FEniCS.py	Basic problem class test with incorrect import path
test_plots_heat_equation_FEniCS.py	Tests for visualization output generation
test_accuracy_heat_equations_FEniCS.py	Convergence tests with commented-out 5th order test
run_heat_equation_FEniCS.py	Main simulation runner with data export functionality
run_accuracy_3rd_order_heat_equation_FEniCS.py	3rd order convergence analysis with plotting
run_accuracy_5th_order_heat_equation_FEniCS.py	5th order convergence analysis (not tested)
HeatEquation_2D_FEniCS.py	Three problem classes with comprehensive docstrings
plots_heat_equation_FEniCS.py	Visualization utilities for solutions and cross-sections
environment.yml	Conda environment with FEniCS dependencies
README.rst	Project documentation and funding information
data/.json, .xdmf, *.png	Generated test data and output files

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Copilot · 2026-02-06T10:01:23Z

+import subprocess
+import os
+import warnings


Several imports are not used in this test file: subprocess, os, and warnings. These should be removed to keep the code clean.

Suggested change

import subprocess

import os

import warnings

Copilot · 2026-02-06T10:01:23Z

+import subprocess
+import os
+import warnings


Several imports are not used in this test file: subprocess, os, and warnings. These should be removed to keep the code clean.

Suggested change

import subprocess

import os

import warnings

import os

Copilot · 2026-02-06T10:01:24Z

+from mpl_toolkits.mplot3d import Axes3D
+
+
+def run_simulation(ml=None, mass=None):


The unused parameter 'ml' in the function signature should be removed as it's not used in the function body and is not documented.

Suggested change

def run_simulation(ml=None, mass=None):

def run_simulation(mass=None):

Why don't you call this function from the scripts that compute the order? Why do you have a seemingly same function thrice?

Copilot · 2026-02-06T10:01:24Z

+
+    Args:
+        t0 (float): initial time
+        ml (bool): use single or multiple levels


The 'ml' parameter in the docstring is mentioned but not present in the actual function signature. The docstring should be updated to remove this parameter or the parameter should be added if it's actually needed.

Suggested change

ml (bool): use single or multiple levels

Copilot · 2026-02-06T10:01:24Z

+        # mesh = df.UnitIntervalMesh(c_nvars)
+
+        mesh = df.UnitSquareMesh(c_nvars, c_nvars)
+
+        # for _ in range(refinements):
+        #    mesh = df.refine(mesh)
+


Commented-out code on lines 106-107 should be removed. If mesh refinement is needed in the future, it can be retrieved from version control history.

Suggested change

# mesh = df.UnitIntervalMesh(c_nvars)

mesh = df.UnitSquareMesh(c_nvars, c_nvars)

# for _ in range(refinements):

# mesh = df.refine(mesh)

mesh = df.UnitSquareMesh(c_nvars, c_nvars)

Copilot · 2026-02-06T10:01:36Z

+
+import dolfin as df
+import matplotlib.pyplot as plt
+import matplotlib.tri as mtri


Import of 'mtri' is not used.

Suggested change

import matplotlib.tri as mtri

Copilot · 2026-02-06T10:01:37Z

+import dolfin as df
+import matplotlib.pyplot as plt
+import matplotlib.tri as mtri
+import matplotlib.cm as cm


Import of 'cm' is not used.

Suggested change

import matplotlib.cm as cm

Copilot · 2026-02-06T10:01:37Z

+import matplotlib.pyplot as plt
+import matplotlib.tri as mtri
+import matplotlib.cm as cm
+from mpl_toolkits.mplot3d import Axes3D


Import of 'Axes3D' is not used.

Suggested change

from mpl_toolkits.mplot3d import Axes3D

Copilot · 2026-02-06T10:01:37Z

+    xdmffile_u = df.XDMFFile(path + 'heat_equation_FEniCS_Temperature.xdmf')
+
+    # load parameters
+    parameters = json.load(open(path + "heat_equation_FEniCS_parameters.json", 'r'))


File is opened but is not closed.

Suggested change

parameters = json.load(open(path + "heat_equation_FEniCS_parameters.json", 'r'))

with open(path + "heat_equation_FEniCS_parameters.json", 'r') as f:

parameters = json.load(f)

Copilot · 2026-02-06T10:01:37Z

+    parameters = description['problem_params']
+    parameters.update(description['level_params'])
+    parameters['Tend'] = Tend
+    json.dump(parameters, open(path + "heat_equation_FEniCS_parameters.json", 'w'))


File is opened but is not closed.

Suggested change

json.dump(parameters, open(path + "heat_equation_FEniCS_parameters.json", 'w'))

with open(path + "heat_equation_FEniCS_parameters.json", 'w') as f:

json.dump(parameters, f)

brownbaerchen

Thanks for the PR! The long awaited Stroemungsraum stuff is finally here!

Big PR, big number of comments. In the future, please separate your PRs into small chunks.
For instance, merge the heat equation implementation that the others derive from with a test and then do the others. This way, when you copy paste, you copy paste a version that is ready to be merged and you don't get the same comments every time.
This makes it easier for people to review your PR and improves quality of the review because the reviewers only have so much time. Also, it makes it easier for you because you can build on what you have. Getting something merged is like checking it off your todo list. It's done and doesn't get lost somewhere on your laptop.

Otherwise, please try to keep code duplication to a minimum, write more meaningful tests and only check in code.

brownbaerchen · 2026-02-06T09:42:54Z

We don't usually check in plots to the repository. Please remove.

brownbaerchen · 2026-02-06T10:55:39Z

We also don't check in output files like this. Especially because the size is quite large at 6MB. Please remove.

brownbaerchen · 2026-02-06T10:58:47Z

+    .. math::
+        u(x, y, t) = \sin(\pi x)\sin(\pi y)\cos(t) + c.
+
+    In this class the problem is implemented in the way that the spatial part is solved using ``FEniCS`` [1]_. Hence, the problem


Suggested change

In this class the problem is implemented in the way that the spatial part is solved using ``FEniCS`` [1]_. Hence, the problem

In this class the spatial part is solved using ``FEniCS`` [1]_. Hence, the problem

brownbaerchen · 2026-02-06T11:00:12Z

+        C. Richardson, J. Ring, M. E. Rognes, G. N. Wells. Archive of Numerical Software (2015).
+    .. [2] Automated Solution of Differential Equations by the Finite Element Method. A. Logg, K.-A. Mardal, G. N.
+        Wells and others. Springer (2012).
+    """


Since I see the docstring was originally copy-pasted, is it still up to date?

brownbaerchen · 2026-02-06T11:00:26Z

+    dtype_f = rhs_fenics_mesh
+
+    def __init__(self, c_nvars=64, t0=0.0, family='CG', order=2, refinements=1, nu=0.1, c=0.0):
+        """Initialization routine"""


Suggested change

"""Initialization routine"""

brownbaerchen · 2026-02-06T11:30:53Z

+@pytest.mark.fenics
+@pytest.mark.mpi4py
+@pytest.mark.parametrize('mass', [True])
+def test_plot(mass):


We have decided not to test plotting. Please add # pragma: no cover to tell coverage to exclude your plotting function from the report. In particular, you do:

def plot_stuff(): # pragma: no cover ...

BUT: only exclude pure plotting functions! Do not exclude functions that do analysis or run a simulation. That is our current convention of coverage rules.

brownbaerchen · 2026-02-06T11:37:25Z

+    assert os.path.isfile('data/heat_equation_FEniCS_Temperature.xdmf'), 'ERROR: Temperature.xdmf does not exist'
+    assert os.path.isfile('data/heat_equation_FEniCS_Temperature.h5'), 'ERROR: Temperature.h5 does not exist'
+
+    from pySDC.projects.StroemungsRaum.plotting.plots_heat_equation_FEniCS import plot_solutions


Also remove / change this test.

brownbaerchen · 2026-02-06T11:41:03Z

+def test_problem_class(mass):
+    from pySDC.projects.FluidFlow.run_heat_equation_FEniCS import run_simulation
+
+    run_simulation(mass=mass)


Again, please don't just do a smoke test. You know the exact solution, so here you can even just compare the two.

What I like to do is define an input where I know the output and call the right hand side evaluation and solve functions on that. For instance, the second derivative of a sine wave is again a sine wave. Maybe this is difficult with the way dirichlet boundary conditions are handled in FEM, I don't know. But please try to come up with some simple tests.

brownbaerchen · 2026-02-06T11:42:03Z

+-------
+Funded by the **German Federal Ministry of Education and Research (BMBF)** under
+grant number **16ME0708**.
+


Maybe you want to add how to reproduce the results in your paper here?

brownbaerchen · 2026-02-06T11:43:03Z

+from mpl_toolkits.mplot3d import Axes3D
+
+
+def run_simulation(ml=None, mass=None):


Why don't you call this function from the scripts that compute the order? Why do you have a seemingly same function thrice?

…ve tests

Ouardghi · 2026-02-09T10:32:12Z

The review comments have been addressed by splitting the code and keeping only the heat equation implementation in this PR. A simple but more meaningful test was added, where the relative error is checked instead of only verifying file creation or execution. This should make the PR easier to review and provide a cleaner base for adding the other examples in follow-up PRs.

brownbaerchen

Thanks a lot! Much easier to review!

It's a lot of comments, but most of it is tiny things that you can just commit right here.

brownbaerchen · 2026-02-09T12:11:22Z

+        logging.getLogger('FFC').setLevel(logging.WARNING)
+        logging.getLogger('UFL').setLevel(logging.WARNING)


why is this needed? Do they log a lot on info level? Or too much on debug level?

This was mainly used during debugging to reduce verbose output from FFC and UFL. It is not essential and can be removed if preferred.

I leave it up to you

brownbaerchen · 2026-02-09T12:25:48Z

+
+    return P, stats, rel_err
+
+def run_postprocessing(description, problem, stats, Tend):


This function is not tested, right?

This function is not tested, as it only performs postprocessing by writing files and does not contain computational logic.

…FEniCS.py Co-authored-by: Thomas Saupe <39156931+brownbaerchen@users.noreply.github.com>

Co-authored-by: Thomas Saupe <39156931+brownbaerchen@users.noreply.github.com>

Removed logging level settings for FFC and UFL.

brownbaerchen

Thanks a lot! If the tests pass, we can merge like this.

brownbaerchen · 2026-02-09T13:13:39Z

What's wrong with the tests why are they stuck in the queue? Did copilot trigger too many tests @pancetta?

pancetta · 2026-02-09T13:15:49Z

No, but @Ouardghi did, see https://github.com/Parallel-in-Time/pySDC/actions

brownbaerchen · 2026-02-09T13:19:04Z

No, but @Ouardghi did, see https://github.com/Parallel-in-Time/pySDC/actions

Not sure that this is true. This PR was tested at 11:30, but none of the workflows triggered by later pushes ran. If Abdel had overwhelmed the CI, wouldn't the first action in the series of commits have run?

brownbaerchen · 2026-02-09T13:20:40Z

Never mind! The workflows are working and flowing again!

pancetta · 2026-02-10T07:34:00Z

Please fix linting. I'm not sure I understand what the matter is with the fenics tests, though

pancetta · 2026-02-10T07:37:51Z

Copilot suggests to add setuptools explicitly to the etc/environment-fenics.yml, but there is no explanation why this popped up now.

brownbaerchen · 2026-02-10T08:24:16Z

It now fails on master as well, see here.

pancetta · 2026-02-10T09:38:55Z

See PR #616

StroemungsRaum: add heat equation examples using FEniCS

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pancetta assigned brownbaerchen Feb 6, 2026

brownbaerchen requested a review from Copilot February 6, 2026 09:47

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Ouardghi and others added 2 commits February 9, 2026 11:19

Address PR review comments: split examples, reduce duplication, impro…

18165fc

…ve tests

Merge branch 'Parallel-in-Time:master' into pr-stroemungsraum-heat

7ee0727

Ouardghi requested a review from brownbaerchen February 9, 2026 11:25

brownbaerchen requested changes Feb 9, 2026

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Ouardghi and others added 17 commits February 9, 2026 13:34

Update pySDC/projects/StroemungsRaum/problem_classes/HeatEquation_2D_…

b70e1fc

…FEniCS.py Co-authored-by: Thomas Saupe <39156931+brownbaerchen@users.noreply.github.com>

Update pySDC/projects/StroemungsRaum/run_heat_equation_FEniCS.py

5fe340e

Co-authored-by: Thomas Saupe <39156931+brownbaerchen@users.noreply.github.com>

Update pySDC/projects/StroemungsRaum/run_heat_equation_FEniCS.py

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Co-authored-by: Thomas Saupe <39156931+brownbaerchen@users.noreply.github.com>

Update pySDC/projects/StroemungsRaum/run_heat_equation_FEniCS.py

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Co-authored-by: Thomas Saupe <39156931+brownbaerchen@users.noreply.github.com>

Update pySDC/projects/StroemungsRaum/tests/test_heat_equation_FEniCS.py

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Co-authored-by: Thomas Saupe <39156931+brownbaerchen@users.noreply.github.com>

Update pySDC/projects/StroemungsRaum/tests/test_heat_equation_FEniCS.py

8651981

Co-authored-by: Thomas Saupe <39156931+brownbaerchen@users.noreply.github.com>

Update pySDC/projects/StroemungsRaum/tests/test_heat_equation_FEniCS.py

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Co-authored-by: Thomas Saupe <39156931+brownbaerchen@users.noreply.github.com>

Update pySDC/projects/StroemungsRaum/run_heat_equation_FEniCS.py

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Co-authored-by: Thomas Saupe <39156931+brownbaerchen@users.noreply.github.com>

Update pySDC/projects/StroemungsRaum/run_heat_equation_FEniCS.py

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Co-authored-by: Thomas Saupe <39156931+brownbaerchen@users.noreply.github.com>

Update pySDC/projects/StroemungsRaum/run_heat_equation_FEniCS.py

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Co-authored-by: Thomas Saupe <39156931+brownbaerchen@users.noreply.github.com>

Update pySDC/projects/StroemungsRaum/run_heat_equation_FEniCS.py

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Update pySDC/projects/StroemungsRaum/run_heat_equation_FEniCS.py

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Update pySDC/projects/StroemungsRaum/run_heat_equation_FEniCS.py

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Update pySDC/projects/StroemungsRaum/run_heat_equation_FEniCS.py

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Update pySDC/projects/StroemungsRaum/run_heat_equation_FEniCS.py

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Update pySDC/projects/StroemungsRaum/run_heat_equation_FEniCS.py

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Update file paths for parameter and XDMF output

758708b

Ouardghi requested a review from brownbaerchen February 9, 2026 12:57

Remove logging level settings in HeatEquation_2D_FEniCS

eb9815a

Removed logging level settings for FFC and UFL.

brownbaerchen approved these changes Feb 9, 2026

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pancetta assigned Copilot Feb 10, 2026

Ouardghi and others added 2 commits February 10, 2026 10:56

Fix linting

3eae722

Merge branch 'Parallel-in-Time:master' into pr-stroemungsraum-heat

e5e5124

pancetta merged commit a1e6338 into Parallel-in-Time:master Feb 10, 2026
79 of 80 checks passed

Ouardghi deleted the pr-stroemungsraum-heat branch February 10, 2026 12:16

		from mpl_toolkits.mplot3d import Axes3D


		def run_simulation(ml=None, mass=None):

	def run_simulation(ml=None, mass=None):
	def run_simulation(mass=None):

	parameters = json.load(open(path + "heat_equation_FEniCS_parameters.json", 'r'))
	with open(path + "heat_equation_FEniCS_parameters.json", 'r') as f:
	parameters = json.load(f)

	json.dump(parameters, open(path + "heat_equation_FEniCS_parameters.json", 'w'))
	with open(path + "heat_equation_FEniCS_parameters.json", 'w') as f:
	json.dump(parameters, f)

	In this class the problem is implemented in the way that the spatial part is solved using ``FEniCS`` [1]_. Hence, the problem
	In this class the spatial part is solved using ``FEniCS`` [1]_. Hence, the problem

		logging.getLogger('FFC').setLevel(logging.WARNING)
		logging.getLogger('UFL').setLevel(logging.WARNING)


		return P, stats, rel_err

		def run_postprocessing(description, problem, stats, Tend):

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Ouardghi commented Feb 9, 2026

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