def test_HarmonicSmoothing():
# Create some mesh and its boundary
mesh = UnitSquareMesh(10, 10)
boundary = BoundaryMesh(mesh, 'exterior')
# Move boundary
disp = Expression(("0.3*x[0]*x[1]", "0.5*(1.0-x[1])"))
ALE.move(boundary, disp)
# Move mesh according to given boundary
ALE.move(mesh, boundary)
# Check that new boundary topology corresponds to given one
boundary_new = BoundaryMesh(mesh, 'exterior')
assert boundary.topology().hash() == boundary_new.topology().hash()
# Check that coordinates are almost equal
err = sum(sum(abs(boundary.coordinates() \
- boundary_new.coordinates()))) / mesh.num_vertices()
print("Current CG solver produced error in boundary coordinates", err)
assert round(err - 0.0, 5) == 0
# Check mesh quality
magic_number = 0.35
rmin = MeshQuality.radius_ratio_min_max(mesh)[0]
assert rmin > magic_number
def test_compute_collisions_tree_2d(self):
references = [[set([20, 21, 22, 23, 28, 29, 30, 31]),
set([0, 1, 2, 3, 8, 9, 10, 11])],
[set([6, 7]),
set([24, 25])]]
points = [Point(0.52, 0.51), Point(0.9, -0.9)]
for i, point in enumerate(points):
mesh_A = UnitSquareMesh(4, 4)
mesh_B = UnitSquareMesh(4, 4)
mesh_B.translate(point)
tree_A = BoundingBoxTree()
tree_A.build(mesh_A)
tree_B = BoundingBoxTree()
tree_B.build(mesh_B)
entities_A, entities_B = tree_A.compute_collisions(tree_B)
if MPI.size(mesh_A.mpi_comm()) == 1:
self.assertEqual(set(entities_A), references[i][0])
self.assertEqual(set(entities_B), references[i][1])
def test_compute_entity_collisions_tree_2d(self):
references = [[[20, 21, 22, 23, 28, 29, 30, 31],
[0, 1, 2, 3, 8, 9, 10, 11]],
[[6],
[25]]]
points = [Point(0.52, 0.51), Point(0.9, -0.9)]
for i, point in enumerate(points):
mesh_A = UnitSquareMesh(4, 4)
mesh_B = UnitSquareMesh(4, 4)
mesh_B.translate(point)
tree_A = BoundingBoxTree()
tree_A.build(mesh_A)
tree_B = BoundingBoxTree()
tree_B.build(mesh_B)
entities_A, entities_B = tree_A.compute_entity_collisions(tree_B)
if MPI.num_processes() == 1:
self.assertEqual(sorted(entities_A), references[i][0])
self.assertEqual(sorted(entities_B), references[i][1])
def _cooks(cls, **kwargs):
mesh = UnitSquareMesh(10, 5)
def cooks_domain(x, y):
return [48 * x, 44 * (x + y) - 18 * x * y]
mesh.coordinates()[:] = np.array(cooks_domain(mesh.coordinates()[:, 0], mesh.coordinates()[:, 1])).transpose()
# plot(mesh, interactive=True, axes=True)
maxx, minx, maxy, miny = 48, 0, 60, 0
# setup boundary parts
llc, lrc, tlc, trc = compile_subdomains(['near(x[0], 0.) && near(x[1], 0.)',
'near(x[0], 48.) && near(x[1], 0.)',
'near(x[0], 0.) && near(x[1], 60.)',
'near(x[0], 48.) && near(x[1], 60.)'])
top, bottom, left, right = compile_subdomains([ 'x[0] >= 0. && x[0] <= 48. && x[1] >= 44. && on_boundary',
'x[0] >= 0. && x[0] <= 48. && x[1] <= 44. && on_boundary',
'near(x[0], 0.) && on_boundary',
'near(x[0], 48.) && on_boundary'])
# the corners
llc.minx = minx
llc.miny = miny
lrc.maxx = maxx
lrc.miny = miny
tlc.minx = minx
tlc.maxy = maxy
trc.maxx = maxx
trc.maxy = maxy
# the edges
top.minx = minx
top.maxx = maxx
bottom.minx = minx
bottom.maxx = maxx
left.minx = minx
right.maxx = maxx
return mesh, {'top':top, 'bottom':bottom, 'left':left, 'right':right, 'llc':llc, 'lrc':lrc, 'tlc':tlc, 'trc':trc, 'all': DomainBoundary()}, 2
def test_HarmonicSmoothing(self):
print ""
print "Testing HarmonicSmoothing::move(Mesh& mesh, " \
"const BoundaryMesh& new_boundary)"
# Create some mesh and its boundary
mesh = UnitSquareMesh(10, 10)
boundary = BoundaryMesh(mesh, 'exterior')
# Move boundary
disp = Expression(("0.3*x[0]*x[1]", "0.5*(1.0-x[1])"))
boundary.move(disp)
# Move mesh according to given boundary
mesh.move(boundary)
# Check that new boundary topology corresponds to given one
boundary_new = BoundaryMesh(mesh, 'exterior')
self.assertEqual(boundary.topology().hash(),
boundary_new.topology().hash())
# Check that coordinates are almost equal
err = sum(sum(abs(boundary.coordinates() \
- boundary_new.coordinates()))) / mesh.num_vertices()
print "Current CG solver produced error in boundary coordinates", err
self.assertAlmostEqual(err, 0.0, places=5)
# Check mesh quality
magic_number = 0.35
self.assertTrue(mesh.radius_ratio_min()>magic_number)
def test_compute_entity_collisions_tree_2d():
references = [[set([20, 21, 22, 23, 28, 29, 30, 31]),
set([0, 1, 2, 3, 8, 9, 10, 11])],
[set([6]),
set([25])]]
points = [Point(0.52, 0.51), Point(0.9, -0.9)]
for i, point in enumerate(points):
mesh_A = UnitSquareMesh(4, 4)
mesh_B = UnitSquareMesh(4, 4)
mesh_B.translate(point)
tree_A = BoundingBoxTree()
tree_A.build(mesh_A)
tree_B = BoundingBoxTree()
tree_B.build(mesh_B)
entities_A, entities_B = tree_A.compute_entity_collisions(tree_B)
assert set(entities_A) == references[i][0]
assert set(entities_B) == references[i][1]
def neumann_elasticity_data():
'''
Return:
a bilinear form in the neumann elasticity problem
L linear form in therein
V function space, where a, L are defined
bc homog. dirichlet conditions for case where we want pos. def problem
z list of orthonormal vectors in the nullspace of A that form basis
of ker(A)
'''
mesh = UnitSquareMesh(40, 40)
V = VectorFunctionSpace(mesh, 'CG', 1)
u = TrialFunction(V)
v = TestFunction(V)
f = Expression(('sin(pi*x[0])', 'cos(pi*x[1])'))
epsilon = lambda u: sym(grad(u))
# Material properties
E, nu = 10.0, 0.3
mu, lmbda = Constant(E/(2*(1 + nu))), Constant(E*nu/((1 + nu)*(1 - 2*nu)))
sigma = lambda u: 2*mu*epsilon(u) + lmbda*tr(epsilon(u))*Identity(2)
a = inner(sigma(u), epsilon(v))*dx
L = inner(f, v)*dx # Zero stress
bc = DirichletBC(V, Constant((0, 0)), DomainBoundary())
z0 = interpolate(Constant((1, 0)), V).vector()
normalize(z0, 'l2')
z1 = interpolate(Constant((0, 1)), V).vector()
normalize(z1, 'l2')
X = mesh.coordinates().reshape((-1, 2))
c0, c1 = np.sum(X, axis=0)/len(X)
z2 = interpolate(Expression(('x[1]-c1',
'-(x[0]-c0)'), c0=c0, c1=c1), V).vector()
normalize(z2, 'l2')
z = [z0, z1, z2]
# Check that this is orthonormal basis
I = np.zeros((3, 3))
for i, zi in enumerate(z):
for j, zj in enumerate(z):
I[i, j] = zi.inner(zj)
print I
print la.norm(I-np.eye(3))
assert la.norm(I-np.eye(3)) < 1E-13
return a, L, V, bc, z
def test_mesh_point_2d(self):
"Test mesh-point intersection in 2D"
point = Point(0.1, 0.2)
mesh = UnitSquareMesh(16, 16)
intersection = intersect(mesh, point)
if MPI.size(mesh.mpi_comm()) == 1:
self.assertEqual(intersection.intersected_cells(), [98])
def test_compute_collisions_point_2d(self):
reference = {1: set([226]),
2: set([136, 137])}
p = Point(0.3, 0.3)
mesh = UnitSquareMesh(16, 16)
for dim in range(1, 3):
tree = BoundingBoxTree()
tree.build(mesh, dim)
entities = tree.compute_collisions(p)
if MPI.size(mesh.mpi_comm()) == 1:
self.assertEqual(set(entities), reference[dim])
def test_compute_first_entity_collision_2d():
reference = [136, 137]
p = Point(0.3, 0.3)
mesh = UnitSquareMesh(16, 16)
tree = BoundingBoxTree()
tree.build(mesh)
first = tree.compute_first_entity_collision(p)
assert first in reference
tree = mesh.bounding_box_tree()
first = tree.compute_first_entity_collision(p)
assert first in reference
def square_with_obstacle():
# Create classes for defining parts of the boundaries and the interior
# of the domain
class Left(SubDomain):
def inside(self, x, on_boundary):
return near(x[0], 0.0)
class Right(SubDomain):
def inside(self, x, on_boundary):
return near(x[0], 1.0)
class Bottom(SubDomain):
def inside(self, x, on_boundary):
return near(x[1], 0.0)
class Top(SubDomain):
def inside(self, x, on_boundary):
return near(x[1], 1.0)
class Obstacle(SubDomain):
def inside(self, x, on_boundary):
return between(x[1], (0.5, 0.7)) and between(x[0], (0.2, 1.0))
# Initialize sub-domain instances
left = Left()
top = Top()
right = Right()
bottom = Bottom()
obstacle = Obstacle()
# Define mesh
mesh = UnitSquareMesh(100, 100, "crossed")
# Initialize mesh function for interior domains
domains = CellFunction("size_t", mesh)
domains.set_all(0)
obstacle.mark(domains, 1)
# Initialize mesh function for boundary domains
boundaries = MeshFunction("size_t", mesh, mesh.topology().dim() - 1)
boundaries.set_all(0)
left.mark(boundaries, 1)
top.mark(boundaries, 2)
right.mark(boundaries, 3)
bottom.mark(boundaries, 4)
boundary_indices = {"left": 1, "top": 2, "right": 3, "bottom": 4}
f = Constant(0.0)
theta0 = Constant(293.0)
return mesh, f, boundaries, boundary_indices, theta0
def test_compute_entity_collisions_2d():
reference = set([136, 137])
p = Point(0.3, 0.3)
mesh = UnitSquareMesh(16, 16)
tree = BoundingBoxTree()
tree.build(mesh)
entities = tree.compute_entity_collisions(p)
assert set(entities) == reference
tree = mesh.bounding_box_tree()
entities = tree.compute_entity_collisions(p)
assert set(entities) == reference
def test_compute_first_collision_2d():
reference = {1: [226],
2: [136, 137]}
p = Point(0.3, 0.3)
mesh = UnitSquareMesh(16, 16)
for dim in range(1, 3):
tree = BoundingBoxTree()
tree.build(mesh, dim)
first = tree.compute_first_collision(p)
assert first in reference[dim]
tree = mesh.bounding_box_tree()
first = tree.compute_first_collision(p)
assert first in reference[mesh.topology().dim()]
def test_compute_entity_collisions_2d(self):
reference = [136, 137]
p = Point(0.3, 0.3)
mesh = UnitSquareMesh(16, 16)
tree = BoundingBoxTree()
tree.build(mesh)
entities = tree.compute_entity_collisions(p, mesh)
if MPI.num_processes() == 1:
self.assertEqual(sorted(entities), reference)
tree = mesh.bounding_box_tree()
entities = tree.compute_entity_collisions(p, mesh)
if MPI.num_processes() == 1:
self.assertEqual(sorted(entities), reference)
def test_compute_closest_entity_2d():
reference = (1, 1.0)
p = Point(-1.0, 0.01)
mesh = UnitSquareMesh(16, 16)
tree = BoundingBoxTree()
tree.build(mesh)
entity, distance = tree.compute_closest_entity(p)
assert entity == reference[0]
assert round(distance - reference[1], 7) == 0
tree = mesh.bounding_box_tree()
entity, distance = tree.compute_closest_entity(p)
assert entity == reference[0]
assert round(distance - reference[1], 7) == 0
def test_compute_first_entity_collision_2d(self):
reference = [136, 137]
p = Point(0.3, 0.3)
mesh = UnitSquareMesh(16, 16)
tree = BoundingBoxTree()
tree.build(mesh)
first = tree.compute_first_entity_collision(p)
if MPI.size(mesh.mpi_comm()) == 1:
self.assertIn(first, reference)
tree = mesh.bounding_box_tree()
first = tree.compute_first_entity_collision(p)
if MPI.size(mesh.mpi_comm()) == 1:
self.assertIn(first, reference)
def test_compute_entity_collisions_2d(self):
reference = set([136, 137])
p = Point(0.3, 0.3)
mesh = UnitSquareMesh(16, 16)
tree = BoundingBoxTree()
tree.build(mesh)
entities = tree.compute_entity_collisions(p)
if MPI.size(mesh.mpi_comm()) == 1:
self.assertEqual(set(entities), reference)
tree = mesh.bounding_box_tree()
entities = tree.compute_entity_collisions(p)
if MPI.size(mesh.mpi_comm()) == 1:
self.assertEqual(set(entities), reference)
def test_compute_collisions_2d(self):
reference = {1: [226],
2: [136, 137]}
p = Point(0.3, 0.3)
mesh = UnitSquareMesh(16, 16)
for dim in range(1, 3):
tree = BoundingBoxTree()
tree.build(mesh, dim)
entities = tree.compute_collisions(p)
if MPI.num_processes() == 1:
self.assertEqual(sorted(entities), reference[dim])
tree = mesh.bounding_box_tree()
entities = tree.compute_collisions(p)
if MPI.num_processes() == 1:
self.assertEqual(sorted(entities), reference[mesh.topology().dim()])
def test_mesh_point_2d_quadrilateral():
"Test mesh-point intersection in 2D for quadrilateral mesh"
point = Point(0.1, 0.2)
mesh = UnitSquareMesh.create(16, 16, CellType.Type.quadrilateral)
intersection = intersect(mesh, point)
assert intersection.intersected_cells() == [49]
def test_compute_first_collision_2d(self):
reference = {1: [226],
2: [136, 137]}
p = Point(0.3, 0.3)
mesh = UnitSquareMesh(16, 16)
for dim in range(1, 3):
tree = BoundingBoxTree()
tree.build(mesh, dim)
first = tree.compute_first_collision(p)
if MPI.size(mesh.mpi_comm()) == 1:
self.assertIn(first, reference[dim])
tree = mesh.bounding_box_tree()
first = tree.compute_first_collision(p)
if MPI.size(mesh.mpi_comm()) == 1:
self.assertIn(first, reference[mesh.topology().dim()])
def test_compute_closest_entity_2d(self):
reference = (0, numpy.sqrt(2.0))
p = Point(-1.0, -1.0)
mesh = UnitSquareMesh(16, 16)
tree = BoundingBoxTree()
tree.build(mesh)
entity, distance = tree.compute_closest_entity(p, mesh)
if MPI.num_processes() == 1:
self.assertEqual(entity, reference[0])
self.assertAlmostEqual(distance, reference[1])
tree = mesh.bounding_box_tree()
entity, distance = tree.compute_closest_entity(p, mesh)
if MPI.num_processes() == 1:
self.assertEqual(entity, reference[0])
self.assertAlmostEqual(distance, reference[1])
def test_compute_closest_entity_2d(self):
reference = (1, 1.0)
p = Point(-1.0, 0.01)
mesh = UnitSquareMesh(16, 16)
tree = BoundingBoxTree()
tree.build(mesh)
entity, distance = tree.compute_closest_entity(p)
if MPI.size(mesh.mpi_comm()) == 1:
self.assertEqual(entity, reference[0])
self.assertAlmostEqual(distance, reference[1])
tree = mesh.bounding_box_tree()
entity, distance = tree.compute_closest_entity(p)
if MPI.size(mesh.mpi_comm()) == 1:
self.assertEqual(entity, reference[0])
self.assertAlmostEqual(distance, reference[1])
def test_ale(self):
print ""
print "Testing ALE::move(Mesh& mesh0, const Mesh& mesh1)"
# Create some mesh
mesh = UnitSquareMesh(4, 5)
# Make some cell function
# FIXME: Initialization by array indexing is probably
# not a good way for parallel test
cellfunc = CellFunction('size_t', mesh)
cellfunc.array()[0:4] = 0
cellfunc.array()[4:] = 1
# Create submeshes - this does not work in parallel
submesh0 = SubMesh(mesh, cellfunc, 0)
submesh1 = SubMesh(mesh, cellfunc, 1)
# Move submesh0
disp = Constant(("0.1", "-0.1"))
submesh0.move(disp)
# Move and smooth submesh1 accordignly
submesh1.move(submesh0)
# Move mesh accordingly
parent_vertex_indices_0 = \
submesh0.data().array('parent_vertex_indices', 0)
parent_vertex_indices_1 = \
submesh1.data().array('parent_vertex_indices', 0)
mesh.coordinates()[parent_vertex_indices_0[:]] = \
submesh0.coordinates()[:]
mesh.coordinates()[parent_vertex_indices_1[:]] = \
submesh1.coordinates()[:]
# If test passes here then it is probably working
# Check for cell quality for sure
magic_number = 0.28
rmin = MeshQuality.radius_ratio_min_max(mesh)[0]
self.assertTrue(rmin > magic_number)
def test_compute_first_collision_2d():
# FIXME: This test should not use facet indices as there are no guarantees
# on how DOLFIN numbers facets
reference = {1: [226],
2: [136, 137]}
p = Point(0.3, 0.3)
mesh = UnitSquareMesh(16, 16)
for dim in range(1, 3):
tree = BoundingBoxTree()
tree.build(mesh, dim)
first = tree.compute_first_collision(p)
# FIXME: Facet test is excluded because it mistakingly relies in the
# facet indices
if dim != mesh.topology().dim() - 1:
assert first in reference[dim]
tree = mesh.bounding_box_tree()
first = tree.compute_first_collision(p)
assert first in reference[mesh.topology().dim()]
def test_lu_cholesky():
"""Test that PETScLUSolver selects LU or Cholesky solver based on
symmetry of matrix operator.
"""
from petsc4py import PETSc
mesh = UnitSquareMesh(MPI.comm_world, 12, 12)
V = FunctionSpace(mesh, "Lagrange", 1)
u, v = TrialFunction(V), TestFunction(V)
A = PETScMatrix(mesh.mpi_comm())
assemble(Constant(1.0)*u*v*dx, tensor=A)
# Check that solver type is LU
solver = PETScLUSolver(mesh.mpi_comm(), A, "petsc")
pc_type = solver.ksp().getPC().getType()
assert pc_type == "lu"
# Set symmetry flag
A.mat().setOption(PETSc.Mat.Option.SYMMETRIC, True)
# Check symmetry flags
symm = A.mat().isSymmetricKnown()
assert symm[0] == True
assert symm[1] == True
# Check that solver type is Cholesky since matrix has now been
# marked as symmetric
solver = PETScLUSolver(mesh.mpi_comm(), A, "petsc")
pc_type = solver.ksp().getPC().getType()
assert pc_type == "cholesky"
# Re-assemble, which resets symmetry flag
assemble(Constant(1.0)*u*v*dx, tensor=A)
solver = PETScLUSolver(mesh.mpi_comm(), A, "petsc")
pc_type = solver.ksp().getPC().getType()
assert pc_type == "lu"
def mesh(Nx=50, Ny=50, **params):
m = UnitSquareMesh(Nx, Ny)
x = m.coordinates()
# x[:] = (x - 0.5) * 2
# x[:] = 0.5*(cos(pi*(x-1.) / 2.) + 1.)
return m
def __init__(self):
n = 40
self.mesh = UnitSquareMesh(n, n, "crossed")
# Define mesh and boundaries.
class LeftBoundary(SubDomain):
def inside(self, x, on_boundary):
return on_boundary and x[0] < DOLFIN_EPS
class RightBoundary(SubDomain):
def inside(self, x, on_boundary):
return on_boundary and x[0] > 1.0 - DOLFIN_EPS
class LowerBoundary(SubDomain):
def inside(self, x, on_boundary):
return on_boundary and x[1] < DOLFIN_EPS
class UpperBoundary(SubDomain):
def inside(self, x, on_boundary):
return on_boundary and x[1] > 1.0 - DOLFIN_EPS
class RestrictedUpperBoundary(SubDomain):
def inside(self, x, on_boundary):
return (
on_boundary
and x[1] > 1.0 - DOLFIN_EPS
and DOLFIN_EPS < x[0]
and x[0] < 0.5 - DOLFIN_EPS
)
left = LeftBoundary()
right = RightBoundary()
lower = LowerBoundary()
upper = UpperBoundary()
# restricted_upper = RestrictedUpperBoundary()
# Be particularly careful with the boundary conditions.
# The main problem here is that the PPE system is consistent if and
# only if
#
# \int_\Omega div(u) = \int_\Gamma n.u = 0.
#
# This is exactly and even pointwise fulfilled for the continuous
# problem. In the discrete case, we can have to make sure that n.u is
# 0 all along the boundary.
# In the lid-driven cavity problem, of particular interest are the
# corner points at the lid. One has to assert that the z-component of u
# is 0 all across the lid, and the x-component of u is 0 everywhere but
# the lid. Since u is L2-"continuous", the lid condition on u_x must
# not be enforced in the corner points. The u_y component must be
# enforced all over the lid, including the end points.
V_element = FiniteElement("CG", self.mesh.ufl_cell(), 2)
self.W = FunctionSpace(self.mesh, V_element * V_element)
self.u_bcs = [
DirichletBC(self.W, (0.0, 0.0), left),
DirichletBC(self.W, (0.0, 0.0), right),
# DirichletBC(self.W.sub(0), Expression('x[0]'), restricted_upper),
DirichletBC(self.W, (0.0, 0.0), lower),
DirichletBC(self.W.sub(0), Constant("1.0"), upper),
DirichletBC(self.W.sub(1), 0.0, upper),
# DirichletBC(self.W.sub(0), Constant('-1.0'), lower),
# DirichletBC(self.W.sub(1), 0.0, lower),
# DirichletBC(self.W.sub(1), Constant('1.0'), left),
# DirichletBC(self.W.sub(0), 0.0, left),
# DirichletBC(self.W.sub(1), Constant('-1.0'), right),
# DirichletBC(self.W.sub(0), 0.0, right),
]
self.P = FunctionSpace(self.mesh, "CG", 1)
self.p_bcs = []
return
