def build_broken_elastic_nullspace(V):
"""Function to build incorrect null space for 2D elasticity"""
# Create list of vectors for null space
nullspace_basis = [
la.PETScVector(V.dofmap().index_map()) 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()
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 = [
la.PETScVector(V.dofmap().index_map()) 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()
return la.VectorSpaceBasis(nullspace_basis)