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"""Unit tests for MultiMesh PDE solvers"""
# Copyright (C) 2017 August Johansson
#
# This file is part of DOLFIN.
#
# DOLFIN is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# DOLFIN is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with DOLFIN. If not, see <http://www.gnu.org/licenses/>.
#
# First added: 2017-07-18
# Last changed: 2017-07-18
import pytest
from dolfin import *
from dolfin_utils.test import skip_in_parallel, fixture
def exactsolution_2d_impl():
return Expression("x[0] + x[1]", degree=1)
def exactsolution_3d_impl():
return Expression("x[0] + x[1] + x[2]", degree=1)
def solve_multimesh_poisson(mesh_0, mesh_1, exactsolution):
# Build multimesh
multimesh = MultiMesh()
multimesh.add(mesh_0)
multimesh.add(mesh_1)
multimesh.build()
# FEM setup
V = MultiMeshFunctionSpace(multimesh, "Lagrange", 1)
u = TrialFunction(V)
v = TestFunction(V)
n = FacetNormal(multimesh)
h = 2.0*Circumradius(multimesh)
h = (h('+') + h('-')) / 2
# Set data
f = Constant(0.0)
# Set parameters
alpha = 4.0
beta = 4.0
# Define bilinear form
a = dot(grad(u), grad(v))*dX \
- dot(avg(grad(u)), jump(v, n))*dI \
- dot(avg(grad(v)), jump(u, n))*dI \
+ alpha/h*jump(u)*jump(v)*dI \
+ beta*dot(jump(grad(u)), jump(grad(v)))*dO
# Define linear form
L = f*v*dX
# Assemble linear system
A = assemble_multimesh(a)
b = assemble_multimesh(L)
# Apply boundary condition
bc = MultiMeshDirichletBC(V, exactsolution, DomainBoundary())
bc.apply(A, b)
# Solve
uh = MultiMeshFunction(V)
solve(A, uh.vector(), b)
return uh
@fixture
def exactsolution_2d():
return exactsolution_2d_impl()
@fixture
def exactsolution_3d():
return exactsolution_3d_impl()
@pytest.mark.slow
@skip_in_parallel
def test_multimesh_poisson_2d(exactsolution_2d):
# This tests solves a Poisson problem on two meshes in 2D with u =
# x+y as exact solution
# FIXME: This test is quite slow.
# Define meshes
mesh_0 = UnitSquareMesh(2, 2)
mesh_1 = RectangleMesh(Point(0.1*DOLFIN_PI, 0.1*DOLFIN_PI),
Point(0.2*DOLFIN_PI, 0.2*DOLFIN_PI),
2, 2)
# Solve multimesh Poisson
uh = solve_multimesh_poisson(mesh_0, mesh_1, exactsolution_2d)
# Check error
assert errornorm(exactsolution_2d, uh, 'L2', degree_rise=1) < 0.005
@pytest.mark.slow
@pytest.mark.skip
@skip_in_parallel
@pytest.mark.skipif(True, reason="3D not fully implemented")
def test_multimesh_poisson_3d(exactsolution_3d):
# This tests solves a Poisson problem on two meshes in 3D with u =
# x+y+z as exact solution
# FIXME: This test is quite slow.
# Define meshes
mesh_0 = UnitCubeMesh(2, 2, 2)
mesh_1 = BoxMesh(Point(0.1*DOLFIN_PI, 0.1*DOLFIN_PI, 0.1*DOLFIN_PI),
Point(0.2*DOLFIN_PI, 0.2*DOLFIN_PI, 0.2*DOLFIN_PI),
2, 2, 2)
# Solve multimesh Poisson
uh = solve_multimesh_poisson(mesh_0, mesh_1, exactsolution_3d)
# Check error
assert errornorm(exactsolution_3d, uh, 'L2', degree_rise=1) < DOLFIN_EPS_LARGE
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