def main(N, family, bci):
bc = bcs[bci]
if bci == 0:
SD = FunctionSpace(N,
family=family,
bc=bc,
domain=domain,
mean=mean[family.lower()])
else:
SD = FunctionSpace(N, family=family, bc=bc, domain=domain)
u = TrialFunction(SD)
v = TestFunction(SD)
# Get f on quad points
fj = Array(SD, buffer=fe)
# Compute right hand side of Poisson equation
f_hat = Function(SD)
f_hat = inner(v, fj, output_array=f_hat)
# Get left hand side of Poisson equation
A = inner(v, div(grad(u)))
u_hat = Function(SD).set_boundary_dofs()
if isinstance(A, list):
bc_mat = extract_bc_matrices([A])
A = A[0]
f_hat -= bc_mat[0].matvec(u_hat, Function(SD))
u_hat = A.solve(f_hat, u_hat)
uj = u_hat.backward()
uh = uj.forward()
# Compare with analytical solution
ua = Array(SD, buffer=ue)
assert np.allclose(uj, ua), np.linalg.norm(uj - ua)
if 'pytest' not in os.environ:
print("Error=%2.16e" % (np.sqrt(dx((uj - ua)**2))))
import matplotlib.pyplot as plt
plt.plot(SD.mesh(), uj, 'b', SD.mesh(), ua, 'r')
u = TrialFunction(T)
v = TestFunction(T)
# Get f on quad points
fj = Array(T, buffer=fe)
# Compute right hand side of biharmonic equation
f_hat = inner(v, fj)
# Get left hand side of biharmonic equation
matrices = inner(v, div(grad(div(grad(u)))))
u_hat = Function(T).set_boundary_dofs() # Solution spectral space
if SD.has_nonhomogeneous_bcs:
bc_mats = extract_bc_matrices([matrices])
w0 = np.zeros_like(u_hat)
for mat in bc_mats:
f_hat -= mat.matvec(u_hat, w0)
# Create linear algebra solver
H = BiharmonicSolver(*matrices)
# Solve and transform to real space
u_hat = H(u_hat, f_hat) # Solve
uq = u_hat.backward()
# Compare with analytical solution
uj = Array(T, buffer=ue)
print(abs(uj - uq).max())
N = 32
SD = FunctionSpace(N, family=family, bc={'left': ('N', 1), 'right': ('N', 1)})
u = TrialFunction(SD)
v = TestFunction(SD)
# Get f on quad points
fj = Array(SD, buffer=fe)
# Compute right hand side of Poisson equation
f_hat = Function(SD, buffer=inner(v, fj))
# Get left hand side of Poisson equation
A = inner(v, div(grad(u)))
B = extract_bc_matrices([A])[0]
A = A[0]
u_hat = Function(SD).set_boundary_dofs()
f_hat -= B.matvec(u_hat, Function(SD))
u_hat = A.solve(f_hat, u_hat)
# Solve and transform to real space
u = np.zeros(N) # Solution real space
u = SD.backward(u_hat, u)
# Compare with analytical solution
uj = Array(SD, buffer=ue)
print(abs(uj - u).max())
assert np.allclose(uj, u)
if 'pytest' not in os.environ: