Fixing the error computation in the partitioned-heat-equation tutorial (

#14)

* working on a fix for the partitioned-heat-equation tutorial

* working on a fix for the partitioned-heat-equation tutorial

* Trying out solutions for L2 error computation from the Discourse

* Error computation in working state

* Formatting

* Calculate relative error instead of absolute error and clean up script

* Formatting

Co-authored-by: Ishaan Desai <ishaandesai@gmail.com>

fenicsxprecice/expression_core.py

@@ -134,7 +134,7 @@ class SegregatedRBFInterpolationExpression(CouplingExpression):
     """
 
     def segregated_interpolant_2d(self, coords_x, coords_y, data):
-        assert(coords_x.shape == coords_y.shape)
+        assert (coords_x.shape == coords_y.shape)
         # create least squares system to approximate a * x ** 2 + b * x + c ~= y
 
         def lstsq_interp(x, y, w): return w[0] * x ** 2 + w[1] * y ** 2 + w[2] * x * y + w[3] * x + w[4] * y + w[5]

tutorials/partitioned-heat-conduction/fenicsx/errorcomputation.py

@@ -1,15 +1,17 @@
-from fenics import inner, assemble, dx, project, sqrt
+from ufl import dx
+from dolfinx.fem import assemble_scalar, form
+import numpy as np
+from mpi4py import MPI
 
 
-def compute_errors(u_approx, u_ref, v, total_error_tol=10 ** -4):
-    # compute pointwise L2 error
-    error_normalized = (u_ref - u_approx) / u_ref
-    # project onto function space
-    error_pointwise = project(abs(error_normalized), v)
-    # determine L2 norm to estimate total error
-    error_total = sqrt(assemble(inner(error_pointwise, error_pointwise) * dx))
-    error_pointwise.rename("error", " ")
+def compute_errors(u_approx, u_ref, total_error_tol=10 ** -4):
+    mesh = u_ref.function_space.mesh
+
+    # compute total L2 error between reference and calculated solution
+    error_pointwise = form(((u_approx - u_ref) / u_ref) ** 2 * dx)
+    error_total = np.sqrt(mesh.comm.allreduce(assemble_scalar(error_pointwise), MPI.SUM))
 
     assert (error_total < total_error_tol)
 
-    return error_total, error_pointwise
+    # return error_total, error_pointwise
+    return error_total

tutorials/partitioned-heat-conduction/fenicsx/heat.py

@@ -31,7 +31,7 @@
 from dolfinx.io import XDMFFile
 from ufl import TrialFunction, TestFunction, dx, ds, dot, grad, inner, lhs, rhs, FiniteElement, VectorElement
 from fenicsxprecice import Adapter
-# from errorcomputation import compute_errors  # TODO update do dolfinx
+from errorcomputation import compute_errors  # TODO update do dolfinx
 from my_enums import ProblemType, DomainPart
 import argparse
 import numpy as np
@@ -120,7 +120,6 @@ def eval(self, x):
 # Define initial value
 u_n = Function(V, name="Temperature")
 u_n.interpolate(u_D.eval)
-# u_n.rename("Temperature", "")
 
 precice, precice_dt, initial_data = None, 0.0, None
 
@@ -182,6 +181,7 @@ def eval(self, x):
 # reference solution at t=0
 u_ref = Function(V, name="reference")
 u_ref.interpolate(u_D_function)
+
 '''
 # TODO
 # mark mesh w.r.t ranks
@@ -207,8 +207,9 @@ def eval(self, x):
     '''
 
     # error_total, error_pointwise = compute_errors(u_n, u_ref, V) # TODO
-    '''
+    ''
     # TODO
+    '''
     error_out << error_pointwise
     '''
     u_D.t = t + dt.value
@@ -263,18 +264,17 @@ def eval(self, x):
 
         if precice.is_time_window_complete():
             u_ref.interpolate(u_D_function)
-            # TODO
-            # error, error_pointwise = compute_errors(u_n, u_ref, V, total_error_tol=error_tol)
-            # print('n = %d, t = %.2f: L2 error on domain = %.3g' % (n, t, error))
+            # error, error_pointwise = compute_errors(mesh, u_n, u_ref, total_error_tol=error_tol)
+            error = compute_errors(u_n, u_ref, total_error_tol=error_tol)
+            print('n = %d, t = %.2f: L2 error on domain = %.3g' % (n, t, error))
             print('output u^%d and u_ref^%d' % (n, n))
+
             xdmf.write_function(u_n, t)
-            '''
-            # TODO
+
             # output solution and reference solution at t_n+1
-            temperature_out << u_n
-            ref_out << u_ref
-            error_out << error_pointwise
-            '''
+            # temperature_out << u_n
+            # ref_out << u_ref
+            # error_out << error_pointwise
 
         # Update Dirichlet BC
         u_D.t = t + dt.value

tutorials/partitioned-heat-conduction/fenicsx/problem_setup.py

@@ -1,7 +1,6 @@
 """
 Problem setup for partitioned-heat-conduction/fenics-fenics tutorial
 """
-# from dolfinx.fem import Function, VectorFunctionSpace, Expression
 from dolfinx.mesh import DiagonalType, create_rectangle
 from my_enums import DomainPart
 import numpy as np