def build_pressure_null_space(self):
# Prepare function used to correct pressure values
null_fcn = Function(self.subspace("p"))
null_fcn.vector()[:] = 1.0
# Create vector that spans the null space and normalize
null_vec = Vector(null_fcn.vector())
null_vec *= 1.0 / null_vec.norm("l2")
# FIXME: Check what are relevant norms for different Krylov methods
# Create null space basis object
null_space = VectorSpaceBasis([null_vec])
return (null_space, null_fcn)
def build_pressure_null_space(self):
# Prepare function used to correct pressure values
W_ns = self.function_spaces()[1]
# NOTE: The following works only for nodal elements
# null_fcn = Function(W_ns)
# W_ns.sub(1).dofmap().set(null_fcn.vector(), 1.0)
null_fcn = self._get_constant_pressure(W_ns)
# Create vector that spans the null space and normalize
null_vec = Vector(null_fcn.vector())
null_vec *= 1.0 / null_vec.norm("l2")
# FIXME: Check what are relevant norms for different Krylov methods
# Create null space basis object
null_space = VectorSpaceBasis([null_vec])
return (null_space, null_fcn)
def residualCheck(A, B, U, d):
"""
Test the l2 norm of the residual:
r[:,i] = d[i] B U[:,i] - A U[:,i]
"""
u = Vector()
Au = Vector()
Bu = Vector()
Binv_r = Vector()
A.init_vector(u, 1)
A.init_vector(Au, 0)
B.init_vector(Bu, 0)
B.init_vector(Binv_r, 0)
nvec = d.shape[0]
print("lambda", "||Au - lambdaBu||")
for i in range(0, nvec):
u.set_local(U[:, i])
A.mult(u, Au)
B.mult(u, Bu)
Au.axpy(-d[i], Bu)
print(d[i], Au.norm("l2"))
