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"Unit tests for nullspace test"
# Copyright (C) 2014 Garth N. Wells
#
# 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/>.
from dolfin import *
import pytest
from dolfin_utils.test import *
backends = ["PETSc", pytest.param(("Eigen"), marks=skip_in_parallel)]
def build_elastic_nullspace(V, x):
"""Function to build nullspace for 2D/3D elasticity"""
# Get geometric dim
gdim = V.mesh().geometry().dim()
assert gdim == 2 or gdim == 3
# Set dimension of nullspace
dim = 3 if gdim == 2 else 6
# Create list of vectors for null space
nullspace_basis = [x.copy() for i in range(dim)]
# Build translational null space basis
for i in range(gdim):
V.sub(i).dofmap().set(nullspace_basis[i], 1.0);
# Build rotational null space basis
if gdim == 2:
V.sub(0).set_x(nullspace_basis[2], -1.0, 1);
V.sub(1).set_x(nullspace_basis[2], 1.0, 0);
elif gdim == 3:
V.sub(0).set_x(nullspace_basis[3], -1.0, 1);
V.sub(1).set_x(nullspace_basis[3], 1.0, 0);
V.sub(0).set_x(nullspace_basis[4], 1.0, 2);
V.sub(2).set_x(nullspace_basis[4], -1.0, 0);
V.sub(2).set_x(nullspace_basis[5], 1.0, 1);
V.sub(1).set_x(nullspace_basis[5], -1.0, 2);
for x in nullspace_basis:
x.apply("insert")
return VectorSpaceBasis(nullspace_basis)
def build_broken_elastic_nullspace(V, x):
"""Function to build incorrect null space for 2D elasticity"""
# Create list of vectors for null space
nullspace_basis = [x.copy() for i in range(4)]
# Build translational null space basis
V.sub(0).dofmap().set(nullspace_basis[0], 1.0);
V.sub(1).dofmap().set(nullspace_basis[1], 1.0);
# Build rotational null space basis
V.sub(0).set_x(nullspace_basis[2], -1.0, 1);
V.sub(1).set_x(nullspace_basis[2], 1.0, 0);
# Add vector that is not in nullspace
V.sub(1).set_x(nullspace_basis[3], 1.0, 1);
for x in nullspace_basis:
x.apply("insert")
return VectorSpaceBasis(nullspace_basis)
def test_nullspace_orthogonal():
"""Test that null spaces orthogonalisation"""
meshes = [UnitSquareMesh(12, 12), UnitCubeMesh(4, 4, 4)]
for mesh in meshes:
for p in range(1, 4):
V = VectorFunctionSpace(mesh, 'CG', p)
zero = Constant([0.0]*mesh.geometry().dim())
L = dot(TestFunction(V), zero)*dx
x = assemble(L)
# Build nullspace
null_space = build_elastic_nullspace(V, x)
assert not null_space.is_orthogonal()
assert not null_space.is_orthonormal()
# Orthogonalise nullspace
null_space.orthonormalize()
# Checl that null space basis is orthonormal
assert null_space.is_orthogonal()
assert null_space.is_orthonormal()
@pytest.mark.parametrize('backend', backends)
def test_nullspace_check(backend):
# Check whether backend is available
if not has_linear_algebra_backend(backend):
pytest.skip('Need %s as backend to run this test' % backend)
# Set linear algebra backend
prev_backend = parameters["linear_algebra_backend"]
parameters["linear_algebra_backend"] = backend
# Mesh
mesh = UnitSquareMesh(12, 12)
# Elasticity form
V = VectorFunctionSpace(mesh, 'CG', 1)
u, v = TrialFunction(V), TestFunction(V)
a = inner(sym(grad(u)), grad(v))*dx
# Assemble matrix and create compatible vector
A = assemble(a)
x = Vector()
A.init_vector(x, 1)
# Create null space basis and test
null_space = build_elastic_nullspace(V, x)
assert in_nullspace(A, null_space)
assert in_nullspace(A, null_space, "right")
assert in_nullspace(A, null_space, "left")
# Create incorect null space basis and test
null_space = build_broken_elastic_nullspace(V, x)
assert not in_nullspace(A, null_space)
assert not in_nullspace(A, null_space, "right")
assert not in_nullspace(A, null_space, "left")
# Reset backend
parameters["linear_algebra_backend"] = prev_backend
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