def _test_eigen_solver_sparse(callback_type):
from rbnics.backends.dolfin import EigenSolver
# Define mesh
mesh = UnitSquareMesh(10, 10)
# Define function space
V_element = VectorElement("Lagrange", mesh.ufl_cell(), 2)
Q_element = FiniteElement("Lagrange", mesh.ufl_cell(), 1)
W_element = MixedElement(V_element, Q_element)
W = FunctionSpace(mesh, W_element)
# Create boundaries
class Wall(SubDomain):
def inside(self, x, on_boundary):
return on_boundary and (x[1] < 0 + DOLFIN_EPS
or x[1] > 1 - DOLFIN_EPS)
boundaries = MeshFunction("size_t", mesh, mesh.topology().dim() - 1)
boundaries.set_all(0)
wall = Wall()
wall.mark(boundaries, 1)
# Define variational problem
vq = TestFunction(W)
(v, q) = split(vq)
up = TrialFunction(W)
(u, p) = split(up)
lhs = inner(grad(u), grad(v)) * dx - div(v) * p * dx - div(u) * q * dx
rhs = -inner(p, q) * dx
# Define boundary condition
bc = [DirichletBC(W.sub(0), Constant((0., 0.)), boundaries, 1)]
# Define eigensolver depending on callback type
assert callback_type in ("form callbacks", "tensor callbacks")
if callback_type == "form callbacks":
solver = EigenSolver(W, lhs, rhs, bc)
elif callback_type == "tensor callbacks":
LHS = assemble(lhs)
RHS = assemble(rhs)
solver = EigenSolver(W, LHS, RHS, bc)
# Solve the eigenproblem
solver.set_parameters({
"linear_solver": "mumps",
"problem_type": "gen_non_hermitian",
"spectrum": "target real",
"spectral_transform": "shift-and-invert",
"spectral_shift": 1.e-5
})
solver.solve(1)
r, c = solver.get_eigenvalue(0)
assert abs(c) < 1.e-10
assert r > 0., "r = " + str(r) + " is not positive"
print("Sparse inf-sup constant: ", sqrt(r))
return (sqrt(r), solver.condensed_A, solver.condensed_B)
def _test_eigen_solver_dense(sparse_LHS, sparse_RHS):
from rbnics.backends.online.numpy import EigenSolver, Matrix
# Extract constrained matrices from sparse eigensolver
LHS = Matrix(*sparse_LHS.array().shape)
RHS = Matrix(*sparse_RHS.array().shape)
LHS[:, :] = sparse_LHS.array()
RHS[:, :] = sparse_RHS.array()
# Solve the eigenproblem
solver = EigenSolver(None, LHS, RHS)
solver.set_parameters({
"problem_type": "gen_non_hermitian",
"spectrum": "smallest real",
})
solver.solve(1)
r, c = solver.get_eigenvalue(0)
assert abs(c) < 1.e-10
assert r > 0., "r = " + str(r) + " is not positive"
print("Dense inf-sup constant: ", sqrt(r))
return (sqrt(r), LHS, RHS)