def test_krylov_solver_lu():
mesh = UnitSquareMesh(MPI.comm_world, 12, 12)
V = FunctionSpace(mesh, ("Lagrange", 1))
u, v = TrialFunction(V), TestFunction(V)
a = inner(u, v) * dx
L = inner(1.0, v) * dx
A = assemble_matrix(a)
A.assemble()
b = assemble_vector(L)
b.ghostUpdate(addv=PETSc.InsertMode.ADD, mode=PETSc.ScatterMode.REVERSE)
norm = 13.0
solver = PETScKrylovSolver(mesh.mpi_comm())
solver.set_options_prefix("test_lu_")
PETScOptions.set("test_lu_ksp_type", "preonly")
PETScOptions.set("test_lu_pc_type", "lu")
solver.set_from_options()
x = A.createVecRight()
solver.set_operator(A)
solver.solve(x, b)
# *Tight* tolerance for LU solves
assert round(x.norm(PETSc.NormType.N2) - norm, 12) == 0
def amg_solve(N, method):
# Elasticity parameters
E = 1.0e9
nu = 0.3
mu = E / (2.0 * (1.0 + nu))
lmbda = E * nu / ((1.0 + nu) * (1.0 - 2.0 * nu))
# Stress computation
def sigma(v):
return 2.0 * mu * sym(grad(v)) + lmbda * tr(sym(
grad(v))) * Identity(2)
# Define problem
mesh = UnitSquareMesh(MPI.comm_world, N, N)
V = VectorFunctionSpace(mesh, 'Lagrange', 1)
bc0 = Function(V)
with bc0.vector().localForm() as bc_local:
bc_local.set(0.0)
def boundary(x, only_boundary):
return [only_boundary] * x.shape(0)
bc = DirichletBC(V.sub(0), bc0, boundary)
u = TrialFunction(V)
v = TestFunction(V)
# Forms
a, L = inner(sigma(u), grad(v)) * dx, dot(ufl.as_vector(
(1.0, 1.0)), v) * dx
# Assemble linear algebra objects
A = assemble_matrix(a, [bc])
A.assemble()
b = assemble_vector(L)
apply_lifting(b, [a], [[bc]])
b.ghostUpdate(addv=PETSc.InsertMode.ADD,
mode=PETSc.ScatterMode.REVERSE)
set_bc(b, [bc])
# Create solution function
u = Function(V)
# Create near null space basis and orthonormalize
null_space = build_nullspace(V, u.vector())
# Attached near-null space to matrix
A.set_near_nullspace(null_space)
# Test that basis is orthonormal
assert null_space.is_orthonormal()
# Create PETSC smoothed aggregation AMG preconditioner, and
# create CG solver
solver = PETScKrylovSolver("cg", method)
# Set matrix operator
solver.set_operator(A)
# Compute solution and return number of iterations
return solver.solve(u.vector(), b)
def amg_solve(N, method):
# Elasticity parameters
E = 1.0e9
nu = 0.3
mu = E / (2.0 * (1.0 + nu))
lmbda = E * nu / ((1.0 + nu) * (1.0 - 2.0 * nu))
# Stress computation
def sigma(v):
return 2.0 * mu * sym(grad(v)) + lmbda * tr(sym(
grad(v))) * Identity(2)
# Define problem
mesh = UnitSquareMesh(MPI.comm_world, N, N)
V = VectorFunctionSpace(mesh, 'Lagrange', 1)
bc0 = Function(V)
bc = DirichletBC(V.sub(0), bc0, lambda x, on_boundary: on_boundary)
u = TrialFunction(V)
v = TestFunction(V)
# Forms
a, L = inner(sigma(u), grad(v)) * dx, dot(ufl.as_vector(
(1.0, 1.0)), v) * dx
# Assemble linear algebra objects
A, b = assemble_system(a, L, bc)
# Create solution function
u = Function(V)
# Create near null space basis and orthonormalize
null_space = build_nullspace(V, u.vector())
# Attached near-null space to matrix
A.set_near_nullspace(null_space)
# Test that basis is orthonormal
assert null_space.is_orthonormal()
# Create PETSC smoothed aggregation AMG preconditioner, and
# create CG solver
solver = PETScKrylovSolver("cg", method)
# Set matrix operator
solver.set_operator(A)
# Compute solution and return number of iterations
return solver.solve(u.vector(), b)
def test_krylov_solver_lu():
mesh = UnitSquareMesh(MPI.comm_world, 12, 12)
V = FunctionSpace(mesh, ("Lagrange", 1))
u, v = TrialFunction(V), TestFunction(V)
a = Constant(1.0) * inner(u, v) * dx
L = inner(Constant(1.0), v) * dx
A = assemble(a)
b = assemble(L)
norm = 13.0
solver = PETScKrylovSolver(mesh.mpi_comm())
solver.set_options_prefix("test_lu_")
PETScOptions.set("test_lu_ksp_type", "preonly")
PETScOptions.set("test_lu_pc_type", "lu")
solver.set_from_options()
x = PETScVector()
solver.set_operator(A)
solver.solve(x, b)
# *Tight* tolerance for LU solves
assert round(x.norm(cpp.la.Norm.l2) - norm, 12) == 0
def xtest_mg_solver_stokes():
mesh0 = UnitCubeMesh(2, 2, 2)
mesh1 = UnitCubeMesh(4, 4, 4)
mesh2 = UnitCubeMesh(8, 8, 8)
Ve = VectorElement("CG", mesh0.ufl_cell(), 2)
Qe = FiniteElement("CG", mesh0.ufl_cell(), 1)
Ze = MixedElement([Ve, Qe])
Z0 = FunctionSpace(mesh0, Ze)
Z1 = FunctionSpace(mesh1, Ze)
Z2 = FunctionSpace(mesh2, Ze)
W = Z2
# Boundaries
def right(x, on_boundary):
return x[0] > (1.0 - DOLFIN_EPS)
def left(x, on_boundary):
return x[0] < DOLFIN_EPS
def top_bottom(x, on_boundary):
return x[1] > 1.0 - DOLFIN_EPS or x[1] < DOLFIN_EPS
# No-slip boundary condition for velocity
noslip = Constant((0.0, 0.0, 0.0))
bc0 = DirichletBC(W.sub(0), noslip, top_bottom)
# Inflow boundary condition for velocity
inflow = Expression(("-sin(x[1]*pi)", "0.0", "0.0"), degree=2)
bc1 = DirichletBC(W.sub(0), inflow, right)
# Collect boundary conditions
bcs = [bc0, bc1]
# Define variational problem
(u, p) = TrialFunctions(W)
(v, q) = TestFunctions(W)
f = Constant((0.0, 0.0, 0.0))
a = inner(grad(u), grad(v)) * dx + div(v) * p * dx + q * div(u) * dx
L = inner(f, v) * dx
# Form for use in constructing preconditioner matrix
b = inner(grad(u), grad(v)) * dx + p * q * dx
# Assemble system
A, bb = assemble_system(a, L, bcs)
# Assemble preconditioner system
P, btmp = assemble_system(b, L, bcs)
spaces = [Z0, Z1, Z2]
dm_collection = PETScDMCollection(spaces)
solver = PETScKrylovSolver()
solver.set_operators(A, P)
PETScOptions.set("ksp_type", "gcr")
PETScOptions.set("pc_type", "mg")
PETScOptions.set("pc_mg_levels", 3)
PETScOptions.set("pc_mg_galerkin")
PETScOptions.set("ksp_monitor_true_residual")
PETScOptions.set("ksp_atol", 1.0e-10)
PETScOptions.set("ksp_rtol", 1.0e-10)
solver.set_from_options()
from petsc4py import PETSc
ksp = solver.ksp()
ksp.setDM(dm_collection.dm())
ksp.setDMActive(False)
x = PETScVector()
solver.solve(x, bb)
# Check multigrid solution against LU solver
solver = LUSolver(A) # noqa
x_lu = PETScVector()
solver.solve(x_lu, bb)
assert round((x - x_lu).norm("l2"), 10) == 0
# Clear all PETSc options
opts = PETSc.Options()
for key in opts.getAll():
opts.delValue(key)
def test_mg_solver_laplace():
# Create meshes and function spaces
meshes = [UnitSquareMesh(N, N) for N in [16, 32, 64]]
V = [FunctionSpace(mesh, "Lagrange", 1) for mesh in meshes]
# Create variational problem on fine grid
u, v = TrialFunction(V[-1]), TestFunction(V[-1])
a = dot(grad(u), grad(v)) * dx
L = v * dx
bc = DirichletBC(V[-1], Constant(0.0), "on_boundary")
A, b = assemble_system(a, L, bc)
# Create collection of PETSc DM objects
dm_collection = PETScDMCollection(V)
# Create PETSc Krylov solver and set operator
solver = PETScKrylovSolver()
solver.set_operator(A)
# Set PETSc solver type
PETScOptions.set("ksp_type", "richardson")
PETScOptions.set("pc_type", "mg")
# Set PETSc MG type and levels
PETScOptions.set("pc_mg_levels", len(V))
PETScOptions.set("pc_mg_galerkin")
# Set smoother
PETScOptions.set("mg_levels_ksp_type", "chebyshev")
PETScOptions.set("mg_levels_pc_type", "jacobi")
# Set tolerance and monitor residual
PETScOptions.set("ksp_monitor_true_residual")
PETScOptions.set("ksp_atol", 1.0e-12)
PETScOptions.set("ksp_rtol", 1.0e-12)
solver.set_from_options()
# Get fine grid DM and attach fine grid DM to solver
solver.set_dm(dm_collection.get_dm(-1))
solver.set_dm_active(False)
# Solve
x = PETScVector()
solver.solve(x, b)
# Check multigrid solution against LU solver solution
solver = LUSolver(A) # noqa
x_lu = PETScVector()
solver.solve(x_lu, b)
assert round((x - x_lu).norm("l2"), 10) == 0
# Clear all PETSc options
from petsc4py import PETSc
opts = PETSc.Options()
for key in opts.getAll():
opts.delValue(key)
PETScOptions.set("ksp_rtol", 1.0e-12)
PETScOptions.set("pc_type", "gamg")
# Use Chebyshev smoothing for multigrid
PETScOptions.set("mg_levels_ksp_type", "chebyshev")
PETScOptions.set("mg_levels_pc_type", "jacobi")
# Improve estimate of eigenvalues for Chebyshev smoothing
PETScOptions.set("mg_levels_esteig_ksp_type", "cg")
PETScOptions.set("mg_levels_ksp_chebyshev_esteig_steps", 20)
# Monitor solver
PETScOptions.set("ksp_monitor")
# Create CG Krylov solver and turn convergence monitoring on
solver = PETScKrylovSolver(MPI.comm_world)
# solver = PETScKrylovSolver()
solver.set_from_options()
# Set matrix operator
solver.set_operator(A)
# Compute solution
solver.solve(u.vector(), b)
# Save solution to XDMF format
file = XDMFFile(MPI.comm_world, "elasticity.xdmf")
file.write(u)
unorm = u.vector().norm(dolfin.cpp.la.Norm.l2)
if MPI.rank(mesh.mpi_comm()) == 0:
def solve():
# Whether to use custom Numba kernels instead of FFC
useCustomKernels = True
# Generate a unit cube with (n+1)^3 vertices
n = 22
mesh = UnitCubeMesh(MPI.comm_world, n, n, n)
Q = FunctionSpace(mesh, "Lagrange", 1)
u = TrialFunction(Q)
v = TestFunction(Q)
# Define the boundary: vertices where any component is in machine precision accuracy 0 or 1
def boundary(x):
return np.sum(np.logical_or(x < DOLFIN_EPS, x > 1.0 - DOLFIN_EPS),
axis=1) > 0
u0 = Constant(0.0)
bc = DirichletBC(Q, u0, boundary)
# Initialize bilinear form and rhs
a = dolfin.cpp.fem.Form([Q._cpp_object, Q._cpp_object])
L = dolfin.cpp.fem.Form([Q._cpp_object])
# Signature of tabulate_tensor functions
sig = nb.types.void(nb.types.CPointer(nb.types.double),
nb.types.CPointer(nb.types.CPointer(nb.types.double)),
nb.types.CPointer(nb.types.double), nb.types.intc)
# Compile the python functions using Numba
fnA = nb.cfunc(sig, cache=True, nopython=True)(tabulate_tensor_A)
fnL = nb.cfunc(sig, cache=True, nopython=True)(tabulate_tensor_L)
module_name = "_laplace_kernel"
# Build the kernel
ffi = cffi.FFI()
ffi.set_source(module_name, TABULATE_C)
ffi.cdef(TABULATE_H)
ffi.compile()
# Import the compiled kernel
kernel_mod = importlib.import_module(module_name)
ffi, lib = kernel_mod.ffi, kernel_mod.lib
# Get pointer to the compiled function
fnA_ptr = ffi.cast("uintptr_t", ffi.addressof(lib, "tabulate_tensor_A"))
# Get pointers to Numba functions
#fnA_ptr = fnA.address
fnL_ptr = fnL.address
if useCustomKernels:
# Configure Forms to use own tabulate functions
a.set_cell_tabulate(0, fnA_ptr)
L.set_cell_tabulate(0, fnL_ptr)
else:
# Use FFC
# Bilinear form
jit_result = ffc_jit(dot(grad(u), grad(v)) * dx)
ufc_form = dolfin.cpp.fem.make_ufc_form(jit_result[0])
a = dolfin.cpp.fem.Form(ufc_form, [Q._cpp_object, Q._cpp_object])
# Rhs
f = Expression("2.0", element=Q.ufl_element())
jit_result = ffc_jit(f * v * dx)
ufc_form = dolfin.cpp.fem.make_ufc_form(jit_result[0])
L = dolfin.cpp.fem.Form(ufc_form, [Q._cpp_object])
# Attach rhs expression as coefficient
L.set_coefficient(0, f._cpp_object)
assembler = dolfin.cpp.fem.Assembler([[a]], [L], [bc])
A = PETScMatrix()
b = PETScVector()
# Perform assembly
start = time.time()
assembler.assemble(A, dolfin.cpp.fem.Assembler.BlockType.monolithic)
end = time.time()
# We don't care about the RHS
assembler.assemble(b, dolfin.cpp.fem.Assembler.BlockType.monolithic)
print(f"Time for assembly: {(end-start)*1000.0}ms")
Anorm = A.norm(dolfin.cpp.la.Norm.frobenius)
bnorm = b.norm(dolfin.cpp.la.Norm.l2)
print(Anorm, bnorm)
# Norms obtained with FFC and n=13
assert (np.isclose(Anorm, 60.86192203436385))
assert (np.isclose(bnorm, 0.018075523965828778))
comm = L.mesh().mpi_comm()
solver = PETScKrylovSolver(comm)
u = Function(Q)
solver.set_operator(A)
solver.solve(u.vector(), b)
# Export result
file = XDMFFile(MPI.comm_world, "poisson_3d.xdmf")
file.write(u, XDMFFile.Encoding.HDF5)
def test_krylov_reuse_pc_lu():
"""Test that LU re-factorisation is only performed after
set_operator(A) is called"""
# Test requires PETSc version 3.5 or later. Use petsc4py to check
# version number.
try:
from petsc4py import PETSc
except ImportError:
pytest.skip("petsc4py required to check PETSc version")
else:
if not PETSc.Sys.getVersion() >= (3, 5, 0):
pytest.skip("PETSc version must be 3.5 of higher")
mesh = UnitSquareMesh(MPI.comm_world, 12, 12)
V = FunctionSpace(mesh, ("Lagrange", 1))
u, v = TrialFunction(V), TestFunction(V)
a = Constant(1.0) * u * v * dx
L = Constant(1.0) * v * dx
assembler = fem.Assembler(a, L)
A = assembler.assemble_matrix()
b = assembler.assemble_vector()
norm = 13.0
solver = PETScKrylovSolver(mesh.mpi_comm())
solver.set_options_prefix("test_lu_")
PETScOptions.set("test_lu_ksp_type", "preonly")
PETScOptions.set("test_lu_pc_type", "lu")
solver.set_from_options()
solver.set_operator(A)
x = PETScVector(mesh.mpi_comm())
solver.solve(x, b)
assert round(x.norm(cpp.la.Norm.l2) - norm, 10) == 0
assembler = fem.assemble.Assembler(Constant(0.5) * u * v * dx, L)
assembler.assemble(A)
x = PETScVector(mesh.mpi_comm())
solver.solve(x, b)
assert round(x.norm(cpp.la.Norm.l2) - 2.0 * norm, 10) == 0
solver.set_operator(A)
solver.solve(x, b)
assert round(x.norm(cpp.la.Norm.l2) - 2.0 * norm, 10) == 0
def test_krylov_reuse_pc():
"Test preconditioner re-use with PETScKrylovSolver"
# Define problem
mesh = UnitSquareMesh(MPI.comm_world, 8, 8)
V = FunctionSpace(mesh, ('Lagrange', 1))
bc = DirichletBC(V, Constant(0.0), lambda x, on_boundary: on_boundary)
u = TrialFunction(V)
v = TestFunction(V)
# Forms
a, L = inner(grad(u), grad(v)) * dx, dot(Constant(1.0), v) * dx
A, P = PETScMatrix(), PETScMatrix()
b = PETScVector()
# Assemble linear algebra objects
assemble(a, tensor=A) # noqa
assemble(a, tensor=P) # noqa
assemble(L, tensor=b) # noqa
# Apply boundary conditions
bc.apply(A)
bc.apply(P)
bc.apply(b)
# Create Krysolv solver and set operators
solver = PETScKrylovSolver("gmres", "bjacobi")
solver.set_operators(A, P)
# Solve
x = PETScVector()
num_iter_ref = solver.solve(x, b)
# Change preconditioner matrix (bad matrix) and solve (PC will be
# updated)
a_p = u * v * dx
assemble(a_p, tensor=P) # noqa
bc.apply(P)
x = PETScVector()
num_iter_mod = solver.solve(x, b)
assert num_iter_mod > num_iter_ref
# Change preconditioner matrix (good matrix) and solve (PC will be
# updated)
a_p = a
assemble(a_p, tensor=P) # noqa
bc.apply(P)
x = PETScVector()
num_iter = solver.solve(x, b)
assert num_iter == num_iter_ref
# Change preconditioner matrix (bad matrix) and solve (PC will not
# be updated)
solver.set_reuse_preconditioner(True)
a_p = u * v * dx
assemble(a_p, tensor=P) # noqa
bc.apply(P)
x = PETScVector()
num_iter = solver.solve(x, b)
assert num_iter == num_iter_ref
# Update preconditioner (bad PC, will increase iteration count)
solver.set_reuse_preconditioner(False)
x = PETScVector()
num_iter = solver.solve(x, b)
assert num_iter == num_iter_mod
def solve(n_runs: int, mesh_size: int, element: FiniteElement,
reference_tensor: ReferenceTensor, kernel_generator):
# Whether to use custom kernels instead of FFC
useCustomKernels = True
# Generate a unit cube with (n+1)^3 vertices
mesh = generate_mesh(mesh_size)
print("Mesh generated.")
A0 = reference_tensor
Q = FunctionSpace(mesh, element)
u = TrialFunction(Q)
v = TestFunction(Q)
# Define the boundary: vertices where any component is in machine precision accuracy 0 or 1
def boundary(x):
return np.sum(np.logical_or(x < DOLFIN_EPS, x > 1.0 - DOLFIN_EPS),
axis=1) > 0
u0 = Constant(0.0)
bc = DirichletBC(Q, u0, boundary)
if useCustomKernels:
# Initialize bilinear form and rhs
a = dolfin.cpp.fem.Form([Q._cpp_object, Q._cpp_object])
L = dolfin.cpp.fem.Form([Q._cpp_object])
# Signature of tabulate_tensor functions
sig = nb.types.void(
nb.types.CPointer(nb.types.double),
nb.types.CPointer(nb.types.CPointer(nb.types.double)),
nb.types.CPointer(nb.types.double), nb.types.intc)
# Compile the python functions using Numba
fnA = nb.cfunc(sig, cache=True,
nopython=True)(numba_kernels.tabulate_tensor_A)
fnL = nb.cfunc(sig, cache=True,
nopython=True)(numba_kernels.tabulate_tensor_L)
module_name = "_laplace_kernel"
compile_poisson_kernel(module_name,
kernel_generator,
A0,
verbose=False)
print("Finished compiling kernel.")
# Import the compiled kernel
kernel_mod = importlib.import_module(f"simd.tmp.{module_name}")
ffi, lib = kernel_mod.ffi, kernel_mod.lib
# Get pointer to the compiled function
fnA_ptr = ffi.cast("uintptr_t", ffi.addressof(lib,
"tabulate_tensor_A"))
# Get pointers to Numba functions
# fnA_ptr = fnA.address
fnL_ptr = fnL.address
# Configure Forms to use own tabulate functions
a.set_cell_tabulate(0, fnA_ptr)
L.set_cell_tabulate(0, fnL_ptr)
else:
# Use FFC
# Bilinear form
jit_result = ffc_jit(dot(grad(u), grad(v)) * dx)
ufc_form = dolfin.cpp.fem.make_ufc_form(jit_result[0])
a = dolfin.cpp.fem.Form(ufc_form, [Q._cpp_object, Q._cpp_object])
# Rhs
f = Expression("2.0", element=Q.ufl_element())
jit_result = ffc_jit(f * v * dx)
ufc_form = dolfin.cpp.fem.make_ufc_form(jit_result[0])
L = dolfin.cpp.fem.Form(ufc_form, [Q._cpp_object])
# Attach rhs expression as coefficient
L.set_coefficient(0, f._cpp_object)
print("Built form.")
assembler = dolfin.cpp.fem.Assembler([[a]], [L], [bc])
A = PETScMatrix()
b = PETScVector()
# Callable that performs assembly of matrix
assembly_callable = lambda: assembler.assemble(
A, dolfin.cpp.fem.Assembler.BlockType.monolithic)
# Get timings for assembly of matrix over several runs
time_avg, time_min, time_max = utils.timing(n_runs,
assembly_callable,
verbose=True)
print(
f"Timings for element matrix assembly (n={n_runs}) avg: {round(time_avg*1000, 2)}ms, min: {round(time_min*1000, 2)}ms, max: {round(time_max*1000, 2)}ms"
)
# Assemble again to get correct results
A = PETScMatrix()
assembler.assemble(A, dolfin.cpp.fem.Assembler.BlockType.monolithic)
assembler.assemble(b, dolfin.cpp.fem.Assembler.BlockType.monolithic)
Anorm = A.norm(dolfin.cpp.la.Norm.frobenius)
bnorm = b.norm(dolfin.cpp.la.Norm.l2)
print(Anorm, bnorm)
# Check norms of assembled system
if useCustomKernels:
# Norms obtained with FFC and n=22
assert (np.isclose(Anorm, 118.19435458024503))
#assert (np.isclose(bnorm, 0.009396467472097566))
return
# Solve the system
comm = L.mesh().mpi_comm()
solver = PETScKrylovSolver(comm)
u = Function(Q)
solver.set_operator(A)
solver.solve(u.vector(), b)
# Export result
file = XDMFFile(MPI.comm_world, "poisson_3d.xdmf")
file.write(u, XDMFFile.Encoding.HDF5)
b = PETScVector()
print("Running assembly...")
assembler.assemble(A, dolfin.cpp.fem.Assembler.BlockType.monolithic)
assembler.assemble(b, dolfin.cpp.fem.Assembler.BlockType.monolithic)
Anorm = A.norm(dolfin.cpp.la.Norm.frobenius)
bnorm = b.norm(dolfin.cpp.la.Norm.l2)
print("A.norm(frobenius)={:.12e}\nb.norm(l2)={:.12e}".format(Anorm, bnorm))
# Norms obtained with n=22 and bcs
assert (np.isclose(Anorm, 60.86192203436385))
assert (np.isclose(bnorm, 0.018075523965828778))
# Norms obtained with n=22 and no bcs
#assert (np.isclose(Anorm, 29.416127208482518))
#assert (np.isclose(bnorm, 0.018726593629987284))
print("Running solver...")
comm = L.mesh().mpi_comm()
solver = PETScKrylovSolver(comm)
u = Function(Q)
solver.set_operator(A)
solver.solve(u.vector(), b)
unorm = u.vector().norm(dolfin.cpp.la.Norm.l2)
print("u.norm(l2)={:.12e}".format(unorm))
assert (np.isclose(unorm, 5.1387821818667))
def assembly():
# Whether to use custom kernels instead of FFC
useCustomKernels = True
# Generate a unit cube with (n+1)^3 vertices
n = 20
mesh = UnitCubeMesh(MPI.comm_world, n, n, n)
Q = FunctionSpace(mesh, "Lagrange", 1)
u = TrialFunction(Q)
v = TestFunction(Q)
def boundary0(x):
wrong = np.logical_or(x[:, 1] < DOLFIN_EPS, x[:, 1] > 1.0 - DOLFIN_EPS)
one = np.logical_or(x[:, 0] < DOLFIN_EPS, x[:, 0] > 1.0 - DOLFIN_EPS)
two = np.logical_or(x[:, 2] < DOLFIN_EPS, x[:, 2] > 1.0 - DOLFIN_EPS)
return np.logical_and(np.logical_or(one, two), np.logical_not(wrong))
def boundary1(x):
return np.logical_or(x[:, 1] < DOLFIN_EPS, x[:, 1] > 1.0 - DOLFIN_EPS)
u0 = Constant(0.0)
bc0 = DirichletBC(Q, u0, boundary0)
u1 = Constant(1.0)
bc1 = DirichletBC(Q, u1, boundary1)
# Initialize bilinear form and rhs
a = dolfin.cpp.fem.Form([Q._cpp_object, Q._cpp_object])
L = dolfin.cpp.fem.Form([Q._cpp_object])
# Signature of tabulate_tensor functions
sig = nb.types.void(nb.types.CPointer(nb.types.double),
nb.types.CPointer(nb.types.CPointer(nb.types.double)),
nb.types.CPointer(nb.types.double), nb.types.intc)
# Compile the numba functions
fnA = nb.cfunc(sig, cache=True, nopython=True)(tabulate_tensor_A)
fnb = nb.cfunc(sig, cache=True, nopython=True)(tabulate_tensor_b)
if useCustomKernels:
# Configure Forms to use own tabulate functions
a.set_cell_tabulate(0, fnA.address)
L.set_cell_tabulate(0, fnb.address)
else:
# Use FFC
jit_result = ffc_jit(dot(grad(u), grad(v)) * dx)
ufc_form = dolfin.cpp.fem.make_ufc_form(jit_result[0])
a = dolfin.cpp.fem.Form(ufc_form, [Q._cpp_object, Q._cpp_object])
f = Expression("20.0", element=Q.ufl_element())
jit_result = ffc_jit(f * v * dx)
ufc_form = dolfin.cpp.fem.make_ufc_form(jit_result[0])
L = dolfin.cpp.fem.Form(ufc_form, [Q._cpp_object])
L.set_coefficient(0, f._cpp_object)
start = time.time()
assembler = dolfin.cpp.fem.Assembler([[a]], [L], [bc0, bc1])
A = PETScMatrix()
b = PETScVector()
assembler.assemble(A, dolfin.cpp.fem.Assembler.BlockType.monolithic)
assembler.assemble(b, dolfin.cpp.fem.Assembler.BlockType.monolithic)
end = time.time()
print(f"Time for assembly: {(end-start)*1000.0}ms")
Anorm = A.norm(dolfin.cpp.la.Norm.frobenius)
bnorm = b.norm(dolfin.cpp.la.Norm.l2)
print(Anorm, bnorm)
# Norms obtained with FFC and n=20
#assert (np.isclose(Anorm, 55.82812911070811))
#assert (np.isclose(bnorm, 29.73261456296761))
comm = L.mesh().mpi_comm()
solver = PETScKrylovSolver(comm)
u = Function(Q)
solver.set_operator(A)
solver.solve(u.vector(), b)
file = XDMFFile(MPI.comm_world, "poisson_3d.xdmf")
file.write(u, XDMFFile.Encoding.HDF5)
