def build_broken_elastic_nullspace(V):
"""Function to build incorrect null space for 2D elasticity"""
# Create list of vectors for null space
nullspace_basis = [
cpp.la.create_vector(V.dofmap.index_map, V.dofmap.index_map_bs)
for i in range(4)
]
with ExitStack() as stack:
vec_local = [
stack.enter_context(x.localForm()) for x in nullspace_basis
]
basis = [np.asarray(x) for x in vec_local]
dofs = [V.sub(i).dofmap.list.array for i in range(2)]
basis[0][dofs[0]] = 1.0
basis[1][dofs[1]] = 1.0
# Build rotational null space basis
x = V.tabulate_dof_coordinates()
dofs_block = V.dofmap.list.array
x0, x1 = x[dofs_block, 0], x[dofs_block, 1]
basis[2][dofs[0]] = -x1
basis[2][dofs[1]] = x0
# Add vector that is not in nullspace
basis[3][dofs[1]] = x1
return la.VectorSpaceBasis(nullspace_basis)
def build_broken_elastic_nullspace(V):
"""Function to build incorrect null space for 2D elasticity"""
# Create list of vectors for null space
nullspace_basis = [
cpp.la.create_vector(V.dofmap.index_map) for i in range(4)
]
with ExitStack() as stack:
vec_local = [
stack.enter_context(x.localForm()) for x in nullspace_basis
]
basis = [np.asarray(x) for x in vec_local]
# Build translational null space basis
V.sub(0).dofmap.set(basis[0], 1.0)
V.sub(1).dofmap.set(basis[1], 1.0)
# Build rotational null space basis
V.sub(0).set_x(basis[2], -1.0, 1)
V.sub(1).set_x(basis[2], 1.0, 0)
# Add vector that is not in nullspace
V.sub(1).set_x(basis[3], 1.0, 1)
return la.VectorSpaceBasis(nullspace_basis)
def build_elastic_nullspace(V):
"""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 = [
cpp.la.create_vector(V.dofmap.index_map, V.dofmap.index_map_bs)
for i in range(dim)
]
with ExitStack() as stack:
vec_local = [
stack.enter_context(x.localForm()) for x in nullspace_basis
]
basis = [np.asarray(x) for x in vec_local]
dofs = [V.sub(i).dofmap.list.array for i in range(gdim)]
# Build translational null space basis
for i in range(gdim):
basis[i][dofs[i]] = 1.0
# Build rotational null space basis
x = V.tabulate_dof_coordinates()
dofs_block = V.dofmap.list.array
x0, x1, x2 = x[dofs_block, 0], x[dofs_block, 1], x[dofs_block, 2]
if gdim == 2:
basis[2][dofs[0]] = -x1
basis[2][dofs[1]] = x0
elif gdim == 3:
basis[3][dofs[0]] = -x1
basis[3][dofs[1]] = x0
basis[4][dofs[0]] = x2
basis[4][dofs[2]] = -x0
basis[5][dofs[2]] = x1
basis[5][dofs[1]] = -x2
return la.VectorSpaceBasis(nullspace_basis)
def build_elastic_nullspace(V):
"""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 = [
cpp.la.create_vector(V.dofmap.index_map) for i in range(dim)
]
with ExitStack() as stack:
vec_local = [
stack.enter_context(x.localForm()) for x in nullspace_basis
]
basis = [np.asarray(x) for x in vec_local]
# Build translational null space basis
for i in range(gdim):
V.sub(i).dofmap.set(basis[i], 1.0)
# Build rotational null space basis
if gdim == 2:
V.sub(0).set_x(basis[2], -1.0, 1)
V.sub(1).set_x(basis[2], 1.0, 0)
elif gdim == 3:
V.sub(0).set_x(basis[3], -1.0, 1)
V.sub(1).set_x(basis[3], 1.0, 0)
V.sub(0).set_x(basis[4], 1.0, 2)
V.sub(2).set_x(basis[4], -1.0, 0)
V.sub(2).set_x(basis[5], 1.0, 1)
V.sub(1).set_x(basis[5], -1.0, 2)
return la.VectorSpaceBasis(nullspace_basis)