def build_nullspace(V):
"""Function to build null space for 3D elasticity"""
# Create list of vectors for null space
index_map = V.dofmap.index_map
nullspace_basis = [cpp.la.create_vector(index_map) for i in range(6)]
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)
V.sub(2).dofmap.set(basis[2], 1.0)
# Build rotational null space basis
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)
# Create vector space basis and orthogonalize
basis = VectorSpaceBasis(nullspace_basis)
basis.orthonormalize()
_x = [basis[i] for i in range(6)]
nsp = PETSc.NullSpace()
nsp.create(_x)
return nsp
def build_nullspace(V):
"""Function to build null space for 3D elasticity"""
# Create list of vectors for null space
index_map = V.dofmap.index_map
nullspace_basis = [cpp.la.create_vector(index_map) for i in range(6)]
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(3):
basis[i][V.sub(i).dofmap.list.array()] = 1.0
# Build rotational null space basis
x = V.tabulate_dof_coordinates()
dofs = [V.sub(i).dofmap.list.array() for i in range(3)]
basis[3][dofs[0]] = -x[dofs[0], 1]
basis[3][dofs[1]] = x[dofs[1], 0]
basis[4][dofs[0]] = x[dofs[0], 2]
basis[4][dofs[2]] = -x[dofs[2], 0]
basis[5][dofs[2]] = x[dofs[2], 1]
basis[5][dofs[1]] = -x[dofs[1], 2]
# Create vector space basis and orthogonalize
basis = VectorSpaceBasis(nullspace_basis)
basis.orthonormalize()
_x = [basis[i] for i in range(6)]
nsp = PETSc.NullSpace().create(vectors=_x)
return nsp
def build_nullspace(V, x):
"""Function to build null space for 2D elasticity"""
# Create list of vectors for null space
nullspace_basis = [x.copy() for i in range(3)]
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)
null_space = VectorSpaceBasis(nullspace_basis)
null_space.orthonormalize()
return null_space
def build_nullspace(V, x):
"""Function to build null space for 2D elasticity"""
# Create list of vectors for null space
nullspace_basis = [x.copy() for i in range(3)]
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 null space basis
dofs = [V.sub(i).dofmap.list.array() for i in range(2)]
for i in range(2):
basis[i][dofs[i]] = 1.0
x = V.tabulate_dof_coordinates()
basis[2][dofs[0]] = -x[dofs[0], 1]
basis[2][dofs[1]] = x[dofs[1], 0]
null_space = VectorSpaceBasis(nullspace_basis)
null_space.orthonormalize()
return null_space