Add a bit more information

Author: brownbaerchen

pySDC/playgrounds/time_dep_BCs/heat_eq_time_dep_BCs.py

@@ -195,6 +195,8 @@ def put_time_dep_BCs_in_rhs(self, rhs_hat, t):
         """
         Put the time dependent BCs in the right hand side.
 
+        See Section 2.5.10 in https://doi.org/10.15480/882.16360 for details on the implementation of the boundary conditions.
+
         In this simple 1D case the BCs are simply in the last two lines of the problem, so we can put there whatever we want.
         Note that in 2D you essentially do the same, but you need to unflatten the RHS, put the BCs in the last lines, and then reflatten.
         """

pySDC/playgrounds/time_dep_BCs/run_time_dep_heat.py

@@ -8,7 +8,7 @@
 from pySDC.implementations.hooks.plotting import PlotPostStep
 
 
-def run_heat(dt=1e-1, Tend=4):
+def run_heat(dt=1e-1, Tend=4, plotting=False):
     level_params = {}
     level_params['dt'] = dt
 
@@ -24,7 +24,8 @@ def run_heat(dt=1e-1, Tend=4):
 
     controller_params = {}
     controller_params['logger_level'] = 15
-    controller_params['hook_class'] = PlotPostStep
+    if plotting:
+        controller_params['hook_class'] = PlotPostStep
 
     description = {}
     description['problem_class'] = Heat1DTimeDependentBCs
@@ -47,5 +48,5 @@ def run_heat(dt=1e-1, Tend=4):
 
 
 if __name__ == '__main__':
-    run_heat()
+    run_heat(plotting=True)
     plt.show()

pySDC/playgrounds/time_dep_BCs/tests.py

@@ -19,6 +19,8 @@ def test_time_dep_heat_eq(a, b, t):
     expect_boundary = np.empty((2, 2))
     expect_boundary = problem.put_time_dep_BCs_in_rhs(expect_boundary, t)
 
+    # we use T_n(1) = 1 and T_n(-1) = (1)^n, to compute the values at the boundaries from the spectral representation
+    # see Wikipedia for more details: https://en.wikipedia.org/wiki/Chebyshev_polynomials#Roots_and_extrema
     right_boundary = u.sum()
     expect_right_boundary = expect_boundary[0, -2]
     assert np.isclose(