# Take scalar product
g_hat = Function(T)
g_hat = inner(v, gj, output_array=g_hat)
# Assemble matrices.
if by_parts:
mats = inner(grad(v), grad(u))
mats += [inner(v, alpha * u)]
else:
mats = inner(v, -div(grad(u)) + alpha * u)
# Solve
u_hat = Function(T)
Sol1 = SolverGeneric1ND(mats)
u_hat = Sol1(g_hat, u_hat)
# Transform back to real space.
uj = u_hat.backward()
uq = Array(T, buffer=ue)
print('Error =', np.linalg.norm(uj - uq))
if 'pytest' not in os.environ:
# Postprocess
# Refine for a nicer plot. Refine simply pads Functions with zeros, which
# gives more quadrature points. u_hat has NxM quadrature points, refine
# using any higher number.
u_hat2 = u_hat.refine([N * 3, M * 3])
ur = u_hat2.backward(kind='uniform')
from mayavi import mlab
mats = inner(grad(v), grad(u))
mats += [inner(v, alpha*u)]
# case m=0
if comm.Get_rank() == 0:
mats0 = inner(grad(v0), grad(u0))
mats0 += [inner(v0, alpha*u0)]
else:
mats = inner(v, -div(grad(u))+alpha*u)
# case m=0
if comm.Get_rank() == 0:
mats0 = inner(v0, -div(grad(u0))+alpha*u0)
# Solve
# case m > 0
u_hat = Function(T)
Sol1 = SolverGeneric1ND(mats)
u_hat = Sol1(f_hat, u_hat)
# case m = 0
u0_hat = Function(T0)
if comm.Get_rank() == 0:
Sol0 = SolverGeneric1ND(mats0)
u0_hat = Sol0(f0_hat, u0_hat)
comm.Bcast(u0_hat, root=0)
# Transform back to real space. Broadcast 1D solution
sl = T.local_slice(False)
uj = u_hat.backward() + u0_hat.backward()[:, sl[1]]
uq = Array(T, buffer=ue)
print('Error =', np.linalg.norm(uj-uq))
assert np.linalg.norm(uj-uq) < 1e-8