def test_numba_assembly():
mesh = UnitSquareMesh(MPI.COMM_WORLD, 13, 13)
V = FunctionSpace(mesh, ("Lagrange", 1))
integrals = {
IntegralType.cell: ([(-1, tabulate_tensor_A.address),
(12, tabulate_tensor_A.address),
(2, tabulate_tensor_A.address)], None)
}
a = cpp.fem.Form([V._cpp_object, V._cpp_object], integrals, [], [], False)
integrals = {IntegralType.cell: ([(-1, tabulate_tensor_b.address)], None)}
L = cpp.fem.Form([V._cpp_object], integrals, [], [], False)
A = dolfinx.fem.assemble_matrix(a)
A.assemble()
b = dolfinx.fem.assemble_vector(L)
b.ghostUpdate(addv=PETSc.InsertMode.ADD, mode=PETSc.ScatterMode.REVERSE)
Anorm = A.norm(PETSc.NormType.FROBENIUS)
bnorm = b.norm(PETSc.NormType.N2)
assert (np.isclose(Anorm, 56.124860801609124))
assert (np.isclose(bnorm, 0.0739710713711999))
list_timings(MPI.COMM_WORLD, [TimingType.wall])
def test_numba_assembly():
mesh = UnitSquareMesh(MPI.comm_world, 13, 13)
V = FunctionSpace(mesh, ("Lagrange", 1))
a = cpp.fem.Form([V._cpp_object, V._cpp_object])
a.set_tabulate_tensor(FormIntegrals.Type.cell, -1,
tabulate_tensor_A.address)
a.set_tabulate_tensor(FormIntegrals.Type.cell, 12,
tabulate_tensor_A.address)
a.set_tabulate_tensor(FormIntegrals.Type.cell, 2,
tabulate_tensor_A.address)
L = cpp.fem.Form([V._cpp_object])
L.set_tabulate_tensor(FormIntegrals.Type.cell, -1,
tabulate_tensor_b.address)
A = dolfinx.fem.assemble_matrix(a)
A.assemble()
b = dolfinx.fem.assemble_vector(L)
b.ghostUpdate(addv=PETSc.InsertMode.ADD, mode=PETSc.ScatterMode.REVERSE)
Anorm = A.norm(PETSc.NormType.FROBENIUS)
bnorm = b.norm(PETSc.NormType.N2)
assert (np.isclose(Anorm, 56.124860801609124))
assert (np.isclose(bnorm, 0.0739710713711999))
list_timings(MPI.comm_world, [TimingType.wall])
def test_cffi_assembly():
mesh = UnitSquareMesh(MPI.COMM_WORLD, 13, 13)
V = FunctionSpace(mesh, ("Lagrange", 1))
if mesh.mpi_comm().rank == 0:
from cffi import FFI
ffibuilder = FFI()
ffibuilder.set_source(
"_cffi_kernelA", r"""
#include <math.h>
#include <stdalign.h>
void tabulate_tensor_poissonA(double* restrict A, const double* w,
const double* c,
const double* restrict coordinate_dofs,
const int* entity_local_index,
const int* cell_orientation)
{
// Precomputed values of basis functions and precomputations
// FE* dimensions: [entities][points][dofs]
// PI* dimensions: [entities][dofs][dofs] or [entities][dofs]
// PM* dimensions: [entities][dofs][dofs]
alignas(32) static const double FE3_C0_D01_Q1[1][1][2] = { { { -1.0, 1.0 } } };
// Unstructured piecewise computations
const double J_c0 = coordinate_dofs[0] * FE3_C0_D01_Q1[0][0][0] + coordinate_dofs[2] * FE3_C0_D01_Q1[0][0][1];
const double J_c3 = coordinate_dofs[1] * FE3_C0_D01_Q1[0][0][0] + coordinate_dofs[5] * FE3_C0_D01_Q1[0][0][1];
const double J_c1 = coordinate_dofs[0] * FE3_C0_D01_Q1[0][0][0] + coordinate_dofs[4] * FE3_C0_D01_Q1[0][0][1];
const double J_c2 = coordinate_dofs[1] * FE3_C0_D01_Q1[0][0][0] + coordinate_dofs[3] * FE3_C0_D01_Q1[0][0][1];
alignas(32) double sp[20];
sp[0] = J_c0 * J_c3;
sp[1] = J_c1 * J_c2;
sp[2] = sp[0] + -1 * sp[1];
sp[3] = J_c0 / sp[2];
sp[4] = -1 * J_c1 / sp[2];
sp[5] = sp[3] * sp[3];
sp[6] = sp[3] * sp[4];
sp[7] = sp[4] * sp[4];
sp[8] = J_c3 / sp[2];
sp[9] = -1 * J_c2 / sp[2];
sp[10] = sp[9] * sp[9];
sp[11] = sp[8] * sp[9];
sp[12] = sp[8] * sp[8];
sp[13] = sp[5] + sp[10];
sp[14] = sp[6] + sp[11];
sp[15] = sp[12] + sp[7];
sp[16] = fabs(sp[2]);
sp[17] = sp[13] * sp[16];
sp[18] = sp[14] * sp[16];
sp[19] = sp[15] * sp[16];
// UFLACS block mode: preintegrated
A[0] = 0.5 * sp[19] + 0.5 * sp[18] + 0.5 * sp[18] + 0.5 * sp[17];
A[1] = -0.5 * sp[19] + -0.5 * sp[18];
A[2] = -0.5 * sp[18] + -0.5 * sp[17];
A[3] = -0.5 * sp[19] + -0.5 * sp[18];
A[4] = 0.5 * sp[19];
A[5] = 0.5 * sp[18];
A[6] = -0.5 * sp[18] + -0.5 * sp[17];
A[7] = 0.5 * sp[18];
A[8] = 0.5 * sp[17];
}
void tabulate_tensor_poissonL(double* restrict A, const double* w,
const double* c,
const double* restrict coordinate_dofs,
const int* entity_local_index,
const int* cell_orientation)
{
// Precomputed values of basis functions and precomputations
// FE* dimensions: [entities][points][dofs]
// PI* dimensions: [entities][dofs][dofs] or [entities][dofs]
// PM* dimensions: [entities][dofs][dofs]
alignas(32) static const double FE4_C0_D01_Q1[1][1][2] = { { { -1.0, 1.0 } } };
// Unstructured piecewise computations
const double J_c0 = coordinate_dofs[0] * FE4_C0_D01_Q1[0][0][0] + coordinate_dofs[2] * FE4_C0_D01_Q1[0][0][1];
const double J_c3 = coordinate_dofs[1] * FE4_C0_D01_Q1[0][0][0] + coordinate_dofs[5] * FE4_C0_D01_Q1[0][0][1];
const double J_c1 = coordinate_dofs[0] * FE4_C0_D01_Q1[0][0][0] + coordinate_dofs[4] * FE4_C0_D01_Q1[0][0][1];
const double J_c2 = coordinate_dofs[1] * FE4_C0_D01_Q1[0][0][0] + coordinate_dofs[3] * FE4_C0_D01_Q1[0][0][1];
alignas(32) double sp[4];
sp[0] = J_c0 * J_c3;
sp[1] = J_c1 * J_c2;
sp[2] = sp[0] + -1 * sp[1];
sp[3] = fabs(sp[2]);
// UFLACS block mode: preintegrated
A[0] = 0.1666666666666667 * sp[3];
A[1] = 0.1666666666666667 * sp[3];
A[2] = 0.1666666666666667 * sp[3];
}
""")
ffibuilder.cdef("""
void tabulate_tensor_poissonA(double* restrict A, const double* w,
const double* c,
const double* restrict coordinate_dofs,
const int* entity_local_index,
const int* cell_orientation);
void tabulate_tensor_poissonL(double* restrict A, const double* w,
const double* c,
const double* restrict coordinate_dofs,
const int* entity_local_index,
const int* cell_orientation);
""")
ffibuilder.compile(verbose=True)
mesh.mpi_comm().Barrier()
from _cffi_kernelA import ffi, lib
ptrA = ffi.cast("intptr_t", ffi.addressof(lib, "tabulate_tensor_poissonA"))
integrals = {IntegralType.cell: ([(-1, ptrA)], None)}
a = cpp.fem.Form([V._cpp_object, V._cpp_object], integrals, [], [], False)
ptrL = ffi.cast("intptr_t", ffi.addressof(lib, "tabulate_tensor_poissonL"))
integrals = {IntegralType.cell: ([(-1, ptrL)], None)}
L = cpp.fem.Form([V._cpp_object], integrals, [], [], False)
A = dolfinx.fem.assemble_matrix(a)
A.assemble()
b = dolfinx.fem.assemble_vector(L)
b.ghostUpdate(addv=PETSc.InsertMode.ADD, mode=PETSc.ScatterMode.REVERSE)
Anorm = A.norm(PETSc.NormType.FROBENIUS)
bnorm = b.norm(PETSc.NormType.N2)
assert (np.isclose(Anorm, 56.124860801609124))
assert (np.isclose(bnorm, 0.0739710713711999))
list_timings(MPI.COMM_WORLD, [TimingType.wall])
