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"""Unit tests for the fem interface"""
# Copyright (C) 2016 Chris Richardson
#
# 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/>.
import pytest
import numpy as np
from dolfin import *
from dolfin_utils.test import *
def test_scalar_p1():
meshc = UnitCubeMesh(2, 2, 2)
meshf = UnitCubeMesh(3, 4, 5)
Vc = FunctionSpace(meshc, "CG", 1)
Vf = FunctionSpace(meshf, "CG", 1)
u = Expression("x[0] + 2*x[1] + 3*x[2]", degree=1)
uc = interpolate(u, Vc)
uf = interpolate(u, Vf)
mat = PETScDMCollection.create_transfer_matrix(Vc, Vf)
Vuc = Function(Vf)
mat.mult(uc.vector(), Vuc.vector())
as_backend_type(Vuc.vector()).update_ghost_values()
diff = Function(Vf)
diff.assign(Vuc - uf)
assert diff.vector().norm("l2") < 1.0e-12
def test_scalar_p1_scaled_mesh():
# Make coarse mesh smaller than fine mesh
meshc = UnitCubeMesh(2, 2, 2)
for x in meshc.coordinates():
x *= 0.9
meshf = UnitCubeMesh(3, 4, 5)
Vc = FunctionSpace(meshc, "CG", 1)
Vf = FunctionSpace(meshf, "CG", 1)
u = Expression("x[0] + 2*x[1] + 3*x[2]", degree=1)
uc = interpolate(u, Vc)
uf = interpolate(u, Vf)
mat = PETScDMCollection.create_transfer_matrix(Vc, Vf)
Vuc = Function(Vf)
mat.mult(uc.vector(), Vuc.vector())
as_backend_type(Vuc.vector()).update_ghost_values()
diff = Function(Vf)
diff.assign(Vuc - uf)
print(diff.vector().norm("l2"))
assert diff.vector().norm("l2") < 1.0e-12
# Now make coarse mesh larger than fine mesh
for x in meshc.coordinates():
x *= 1.5
uc = interpolate(u, Vc)
mat = PETScDMCollection.create_transfer_matrix(Vc, Vf)
mat.mult(uc.vector(), Vuc.vector())
as_backend_type(Vuc.vector()).update_ghost_values()
diff.assign(Vuc - uf)
assert diff.vector().norm("l2") < 1.0e-12
def test_scalar_p2():
meshc = UnitCubeMesh(2, 2, 2)
meshf = UnitCubeMesh(3, 4, 5)
Vc = FunctionSpace(meshc, "CG", 2)
Vf = FunctionSpace(meshf, "CG", 2)
u = Expression("x[0]*x[2] + 2*x[1]*x[0] + 3*x[2]", degree=2)
uc = interpolate(u, Vc)
uf = interpolate(u, Vf)
mat = PETScDMCollection.create_transfer_matrix(Vc, Vf)
Vuc = Function(Vf)
mat.mult(uc.vector(), Vuc.vector())
as_backend_type(Vuc.vector()).update_ghost_values()
diff = Function(Vf)
diff.assign(Vuc - uf)
assert diff.vector().norm("l2") < 1.0e-12
def test_vector_p1_2d():
meshc = UnitSquareMesh(3, 3)
meshf = UnitSquareMesh(5, 5)
Vc = VectorFunctionSpace(meshc, "CG", 1)
Vf = VectorFunctionSpace(meshf, "CG", 1)
u = Expression(("x[0] + 2*x[1]", "4*x[0]"), degree=1)
uc = interpolate(u, Vc)
uf = interpolate(u, Vf)
mat = PETScDMCollection.create_transfer_matrix(Vc, Vf)
Vuc = Function(Vf)
mat.mult(uc.vector(), Vuc.vector())
as_backend_type(Vuc.vector()).update_ghost_values()
diff = Function(Vf)
diff.assign(Vuc - uf)
assert diff.vector().norm("l2") < 1.0e-12
def test_vector_p2_2d():
meshc = UnitSquareMesh(5, 4)
meshf = UnitSquareMesh(5, 8)
Vc = VectorFunctionSpace(meshc, "CG", 2)
Vf = VectorFunctionSpace(meshf, "CG", 2)
u = Expression(("x[0] + 2*x[1]*x[0]", "4*x[0]*x[1]"), degree=2)
uc = interpolate(u, Vc)
uf = interpolate(u, Vf)
mat = PETScDMCollection.create_transfer_matrix(Vc, Vf)
Vuc = Function(Vf)
mat.mult(uc.vector(), Vuc.vector())
as_backend_type(Vuc.vector()).update_ghost_values()
diff = Function(Vf)
diff.assign(Vuc - uf)
assert diff.vector().norm("l2") < 1.0e-12
def test_vector_p1_3d():
meshc = UnitCubeMesh(2, 3, 4)
meshf = UnitCubeMesh(3, 4, 5)
Vc = VectorFunctionSpace(meshc, "CG", 1)
Vf = VectorFunctionSpace(meshf, "CG", 1)
u = Expression(("x[0] + 2*x[1]", "4*x[0]", "3*x[2] + x[0]"), degree=1)
uc = interpolate(u, Vc)
uf = interpolate(u, Vf)
mat = PETScDMCollection.create_transfer_matrix(Vc, Vf)
Vuc = Function(Vf)
mat.mult(uc.vector(), Vuc.vector())
as_backend_type(Vuc.vector()).update_ghost_values()
diff = Function(Vf)
diff.assign(Vuc - uf)
assert diff.vector().norm("l2") < 1.0e-12
def test_taylor_hood_cube():
pytest.xfail("Problem with Mixed Function Spaces")
meshc = UnitCubeMesh(2, 2, 2)
meshf = UnitCubeMesh(3, 4, 5)
Ve = VectorElement("CG", meshc.ufl_cell(), 2)
Qe = FiniteElement("CG", meshc.ufl_cell(), 1)
Ze = MixedElement([Ve, Qe])
Zc = FunctionSpace(meshc, Ze)
Zf = FunctionSpace(meshf, Ze)
z = Expression(("x[0]*x[1]", "x[1]*x[2]", "x[2]*x[0]", "x[0] + 3*x[1] + x[2]"), degree=2)
zc = interpolate(z, Zc)
zf = interpolate(z, Zf)
mat = PETScDMCollection.create_transfer_matrix(Zc, Zf)
Zuc = Function(Zf)
mat.mult(zc.vector(), Zuc.vector())
as_backend_type(Zuc.vector()).update_ghost_values()
diff = Function(Zf)
diff.assign(Zuc - zf)
assert diff.vector().norm("l2") < 1.0e-12
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