def demo_3d_divergence(mesh, u_exact, divu_exact):
# Compute the divergence with Gauss theorem
cr_divu = gauss_divergence(u_exact, mesh=mesh)
# Represent the exact divergence on DG
rank = divu_exact.value_rank()
if rank == 0:
DG = FunctionSpace(mesh, 'DG', 0)
elif rank in [1, 2]:
DG = VectorFunctionSpace(mesh, 'DG', 0)
divu = interpolate(divu_exact, DG)
# Compute the l^oo and l^1 norms
divu.vector().axpy(-1, cr_divu.vector())
error_Loo = divu.vector().norm('linf') / DG.dim()
error_L2 = divu.vector().norm('l2') / DG.dim()
h = mesh.hmin()
# Create global measure of h and errors
comm = mpi_comm_world()
h = MPI.min(comm, mesh.hmin())
error_Loo = MPI.max(comm, error_Loo)
error_L2 = MPI.max(comm, error_L2)
return h, error_Loo, error_L2
def demo_3d_divergence(mesh, u_exact, divu_exact):
# Compute the divergence with Gauss theorem
cr_divu = gauss_divergence(u_exact, mesh=mesh)
# Represent the exact divergence on DG
rank = divu_exact.value_rank()
if rank == 0:
DG = FunctionSpace(mesh, 'DG', 0)
elif rank in [1, 2]:
DG = VectorFunctionSpace(mesh, 'DG', 0)
divu = interpolate(divu_exact, DG)
# Compute the l^oo and l^1 norms
divu.vector().axpy(-1, cr_divu.vector())
error_Loo = divu.vector().norm('linf')/DG.dim()
error_L2 = divu.vector().norm('l2')/DG.dim()
h = mesh.hmin()
# Create global measure of h and errors
comm = mpi_comm_world()
h = MPI.min(comm, mesh.hmin())
error_Loo = MPI.max(comm, error_Loo)
error_L2 = MPI.max(comm, error_L2)
return h, error_Loo, error_L2
def test_GaussDivergence(mesh):
dim = mesh.topology().dim()
expr = ["%s*x[%s]" % (dim, i) for i in range(dim)]
V = VectorFunctionSpace(mesh, 'CG', 1)
u = interpolate(Expression(tuple(expr)), V)
divu = gauss_divergence(u)
DIVU = divu.vector().array()
point_0 = all(abs(DIVU - dim * dim) < 1E-13)
if MPI.rank(mpi_comm_world()) == 0:
assert point_0
def test_GaussDivergence(mesh):
dim = mesh.topology().dim()
expr = ["%s*x[%s]" % (dim, i) for i in range(dim)]
V = VectorFunctionSpace(mesh, "CG", 1)
u = interpolate(Expression(tuple(expr)), V)
divu = gauss_divergence(u)
DIVU = divu.vector().array()
point_0 = all(abs(DIVU - dim * dim) < 1e-13)
if MPI.rank(mpi_comm_world()) == 0:
assert point_0
def test_GaussDivergence(mesh):
dim = mesh.topology().dim()
expr = ["%s*x[%s]" % (dim,i) for i in range(dim)]
V = VectorFunctionSpace(mesh, 'CG', 1)
u = interpolate(Expression(tuple(expr), degree=1), V)
divu = gauss_divergence(u)
DIVU = divu.vector().get_local()
point_0 = all(abs(DIVU - dim*dim) < 1E-13)
if MPI.rank(MPI.comm_world) == 0:
assert point_0