Refactor

docs/notebooks/10-appendix-convergence-testing.ipynb

@@ -5,7 +5,7 @@
    "id": "23f1215b",
    "metadata": {},
    "source": [
-    "# Appendix: Code testing and verification"
+    "# Appendix: Code testing and verification with Manufactured Solutions"
    ]
   },
   {
@@ -24,16 +24,22 @@
     "\n",
     "This has been included in this project in two ways:\n",
     "- For each ODE class a ``rhs_analytic`` function needs to be defined which can be used for probing the right (i.e. expected) order of convergence for the spatial discretization of the numerical right-hand side.\n",
-    "- The method of manufactured solutions (MMS) can be used to test the order of time integration and compare various discretizations of the same initial-boundary-value problem."
+    "- The method of manufactured solutions (MMS) can also be used to test the order of time integration and compare various discretizations of the same initial-boundary-value problem."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "26409459",
+   "metadata": {},
+   "source": [
+    "## Method of Manufactured Solution (MMS)"
    ]
   },
   {
    "cell_type": "markdown",
    "id": "a1413cf5",
    "metadata": {},
    "source": [
-    "# Method of Manufactured Solution (MMS)\n",
-    "\n",
     "The main idea of this approach is to construct test cases where the solution to a problem is known a-priori. This means for example when testing the discretization of a spatial derivative, one considers functions, where the continuous counterpart can be computed analytically. We make this more precise in the following sections.\n",
     "A detailed introduction to MMS can be found [here](https://www.osti.gov/servlets/purl/759450-wLI4Ux/native/).\n"
    ]
@@ -43,8 +49,6 @@
    "id": "eb058f7c",
    "metadata": {},
    "source": [
-    "## 1. Testing spatial order of convergence\n",
-    "\n",
     "In the following we show some examples which are all part of the CI testing of the codebase. They can be found in the test folder in the files `test_laplace.py` and `test_rhs.py`.\n",
     "\n",
     "In a nutshell, it is as simple as this (for the leading example $-\\Delta u = \\text{rhs}$)\n",
@@ -66,7 +70,7 @@
    "id": "843c121d",
    "metadata": {},
    "source": [
-    "### Combining the Laplacian stencil with various BCs"
+    "## Spatial order of convergence for Laplacian stencils"
    ]
   },
   {
@@ -355,7 +359,7 @@
    "id": "f2a3c20e",
    "metadata": {},
    "source": [
-    "### Testing ODE right-hand sides\n",
+    "## Testing ODE right-hand sides\n",
     "\n",
     "The ODEs are all given in the form $\\partial_t u = \\text{rhs}(t,u)$, e.g. for Allen-Cahn in the form $\\text{rhs}(t,u) = \\Delta u + g(t,u)$.\n",
     "\n",
@@ -432,7 +436,7 @@
    "id": "da5b50fd",
    "metadata": {},
    "source": [
-    "## 2. Time-dependent problems"
+    "## Time-dependent problems"
    ]
   },
   {

evoxels/precompiled_solvers/allen_cahn.py

@@ -23,7 +23,7 @@ def run_allen_cahn_solver(
     plot_bounds = None,
 ):
     """
-    Runs the Cahn-Hilliard solver with a predefined problem and timestepper.
+    Solves time-dependent Allen-Cahn problem with ForwardEuler timestepper.
     """
     solver = TimeDependentSolver(
         voxelfields,

evoxels/precompiled_solvers/cahn_hilliard.py

@@ -20,7 +20,7 @@ def run_cahn_hilliard_solver(
     plot_bounds = None,
 ):
     """
-    Runs the Cahn-Hilliard solver with a predefined problem and timestepper.
+    Solves time-dependent Cahn-Hilliard problem with PseudoSpectralIMEX timestepper.
     """
     solver = TimeDependentSolver(
         voxelfields,

evoxels/problem_definition.py

@@ -186,11 +186,11 @@ def pad_bc(self, u):
         return self.pad_boundary(u, self.bcs[0], self.bcs[1])
 
     def rhs_analytic(self, mask, u, t):
-        grad = spv.gradient(u)
-        norm_grad = sp.sqrt(grad.dot(grad))
+        grad_m = spv.gradient(mask)
+        norm_grad_m = sp.sqrt(grad_m.dot(grad_m))
 
-        divergence = spv.divergence(self.D*(grad - u/mask*spv.gradient(mask)))
-        du = divergence + norm_grad*self.bc_flux + mask*self._eval_f(u/mask, t, sp)
+        divergence = spv.divergence(self.D*(spv.gradient(u) - u/mask*grad_m))
+        du = divergence + norm_grad_m*self.bc_flux + mask*self._eval_f(u/mask, t, sp)
         return du
 
     def rhs(self, u, t):

tests/test_rhs.py

@@ -57,7 +57,7 @@ def test_coupled_reaction_diffusion_rhs():
 def test_reaction_diffusion_smoothed_boundary_rhs():
     _, _, slope, order = rhs_convergence_test(
         ODE_class      = ReactionDiffusionSBM,
-        problem_kwargs = {"D": 1.0, "BC_type": 'dirichlet', "bcs": (0,1),},
+        problem_kwargs = {"D": 1.0, "BC_type": 'dirichlet', "bcs": (0,1), "bc_flux": 1},
         test_function  = test_fun_sbm,
         mask_function  = mask_fun,
         convention     = 'staggered_x',