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, x):
"""Function to build null space for 3D elasticity"""
# Create list of vectors for null space
nullspace_basis = [PETScVector(x) for i in range(6)]
# 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)
V.sub(2).dofmap().set(nullspace_basis[2], 1.0)
# Build rotational null space basis
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()
# Create vector space basis and orthogonalize
basis = VectorSpaceBasis(nullspace_basis)
basis.orthonormalize()
return basis
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)]
# 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)
V.sub(2).dofmap().set(nullspace_basis[2], 1.0)
# Build rotational null space basis
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)
# 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, 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)]
# 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)
for x in nullspace_basis:
x.apply("insert")
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 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