def test_maxwell_electric_field_screen(default_parameters, helpers,
device_interface, precision):
"""Test Maxwell electric field on sphere."""
from bempp.api import get_precision
from bempp.api import function_space
from bempp.api.operators.boundary.maxwell import electric_field
grid = helpers.load_grid("structured_grid")
space1 = function_space(grid, "RWG", 0)
space2 = function_space(grid, "SNC", 0)
discrete_op = electric_field(
space1,
space1,
space2,
2.5,
assembler="dense",
device_interface=device_interface,
precision=precision,
parameters=default_parameters,
).weak_form()
if precision == "single":
rtol = 1e-5
atol = 1e-7
else:
rtol = 1e-10
atol = 1e-14
expected = helpers.load_npy_data(
"maxwell_electric_field_structured_boundary")
_np.testing.assert_allclose(discrete_op.A, expected, rtol=rtol, atol=atol)
def test_sparse_identity_snc_bc(default_parameters, helpers, device_interface,
precision):
"""Test singular assembler for the sparse L^2 identity with snc/bc basis."""
from bempp.api import function_space
from bempp.api.operators.boundary.sparse import identity
grid = helpers.load_grid("sphere")
expected = helpers.load_npy_data("sparse_identity_snc_bc")
bc = function_space(grid, "BC", 0)
snc = function_space(grid, "SNC", 0)
actual = (identity(
bc,
bc,
snc,
parameters=default_parameters,
device_interface=device_interface,
precision=precision,
).weak_form().A.todense())
if precision == "single":
atol = 1e-7
else:
atol = 1e-14
_np.testing.assert_allclose(actual, expected, atol=atol)
def test_maxwell_far_field_segments(default_parameters, helpers,
device_interface, precision):
"""Test Maxwell far field on segments."""
import bempp.api
from bempp.api import function_space
from bempp.api.operators.far_field.maxwell import electric_field
from bempp.api.operators.far_field.maxwell import magnetic_field
from bempp.api.grid.grid import grid_from_segments
grid = bempp.api.shapes.multitrace_cube()
seglists = [[1, 2, 3, 4, 5, 6], [6, 7, 8, 9, 10, 11]]
swapped_normal_lists = [{}, {6}]
rand = _np.random.RandomState(0)
points = rand.randn(3, 10)
points /= _np.linalg.norm(points, axis=0)
for op in [electric_field, magnetic_field]:
for seglist, swapped_normals in zip(seglists, swapped_normal_lists):
new_grid = grid_from_segments(grid, seglist)
coeffs = rand.rand(new_grid.number_of_edges)
space1 = function_space(
grid,
"RWG",
0,
segments=seglist,
swapped_normals=swapped_normals,
include_boundary_dofs=True,
)
space2 = function_space(new_grid,
"RWG",
0,
swapped_normals=swapped_normals)
fun1 = bempp.api.GridFunction(space1, coefficients=coeffs)
fun2 = bempp.api.GridFunction(space2, coefficients=coeffs)
actual = (op(
space1,
points,
2.5,
parameters=default_parameters,
precision=precision,
device_interface=device_interface,
) * fun1)
expected = (op(
space2,
points,
2.5,
parameters=default_parameters,
precision=precision,
device_interface=device_interface,
) * fun2)
_np.testing.assert_allclose(
actual, expected, rtol=helpers.default_tolerance(precision))
def test_helmholtz_far_field_segments_complex_coeffs(default_parameters,
helpers, device_interface,
precision):
"""Test Maxwell potentials on segments with complex coeffs."""
import bempp.api
from bempp.api import function_space
from bempp.api.operators.far_field.helmholtz import single_layer
from bempp.api.operators.far_field.helmholtz import double_layer
from bempp.api.grid.grid import grid_from_segments
grid = bempp.api.shapes.multitrace_cube()
seglists = [[1, 2, 3, 4, 5, 6], [6, 7, 8, 9, 10, 11]]
swapped_normal_lists = [{}, {6}]
rand = _np.random.RandomState(0)
points = rand.randn(3, 10)
points /= _np.linalg.norm(points, axis=0)
for op in [single_layer, double_layer]:
for seglist, swapped_normals in zip(seglists, swapped_normal_lists):
new_grid = grid_from_segments(grid, seglist)
coeffs = rand.rand(new_grid.number_of_vertices) + 1j * rand.rand(
new_grid.number_of_vertices)
space1 = function_space(
grid,
"P",
1,
segments=seglist,
swapped_normals=swapped_normals,
include_boundary_dofs=True,
)
space2 = function_space(new_grid,
"P",
1,
swapped_normals=swapped_normals)
fun1 = bempp.api.GridFunction(space1, coefficients=coeffs)
fun2 = bempp.api.GridFunction(space2, coefficients=coeffs)
actual = (op(
space1,
points,
2.5,
device_interface=device_interface,
precision=precision,
) * fun1)
expected = (op(
space2,
points,
2.5,
device_interface=device_interface,
precision=precision,
) * fun2)
_np.testing.assert_allclose(
actual, expected, rtol=helpers.default_tolerance(precision))
def test_laplace_operators(operator, type0, type1):
"""Test dense assembler for the Laplace operators."""
grid = bempp.api.shapes.regular_sphere(0)
space0 = function_space(grid, *type0)
space1 = function_space(grid, *type1)
op = operator(space0, space1, space1, assembler="dense")
op.weak_form()
def test_modified_helmholtz_operators(operator, wavenumber, type0, type1):
"""Test dense assembler for the modified Helmholtz operators."""
grid = bempp.api.shapes.regular_sphere(0)
space0 = function_space(grid, *type0)
space1 = function_space(grid, *type1)
op = operator(space0, space1, space1, wavenumber, assembler="dense")
op.weak_form()
def test_maxwell_operators(operator, wavenumber, type0, type1):
"""Test dense assembler for the Maxwell operators."""
grid = bempp.api.shapes.regular_sphere(0)
space0 = function_space(grid, *type0)
space1 = function_space(grid, *type1)
op = operator(space0, space0, space1, wavenumber, assembler="dense")
op.weak_form()
# Check that we cannot swap curl and div conforming spaces for Maxwell
with pytest.raises(ValueError):
op = operator(space1, space1, space0, wavenumber, assembler="dense")
def create_spaces(grid, diri, neum):
trial, test = diri
triad = bem.function_space(grid, trial[0], trial[1])
testd = bem.function_space(grid, test[0], test[1])
spaced = (triad, testd)
trial, test = neum
trian = bem.function_space(grid, trial[0], trial[1])
testn = bem.function_space(grid, test[0], test[1])
spacen = (trian, testn)
return spaced, spacen
def test_maxwell_electric_field_rbc_bc_sphere(default_parameters, helpers,
device_interface, precision,
skip):
"""Test Maxwell electric field on sphere with RBC/BC basis."""
if skip == "circleci":
pytest.skip()
import bempp.api
from bempp.api import function_space
from bempp.api.operators.boundary.maxwell import electric_field
grid = helpers.load_grid("sphere")
space1 = function_space(grid, "BC", 0)
space2 = function_space(grid, "RBC", 0)
rand = _np.random.RandomState(0)
vec = rand.rand(space1.global_dof_count)
bempp.api.GLOBAL_PARAMETERS.fmm.dense_evaluation = True
discrete_op = electric_field(
space1,
space1,
space2,
2.5,
assembler="fmm",
device_interface=device_interface,
precision=precision,
parameters=default_parameters,
).weak_form()
actual = discrete_op @ vec
bempp.api.GLOBAL_PARAMETERS.fmm.dense_evaluation = False
if precision == "single":
rtol = 5e-5
atol = 5e-6
else:
rtol = 1e-10
atol = 1e-14
mat = helpers.load_npy_data("maxwell_electric_field_boundary_rbc_bc")
expected = mat @ vec
_np.testing.assert_allclose(actual, expected, rtol=rtol, atol=atol)
bempp.api.clear_fmm_cache()
def test_helmholtz_single_layer(has_exafmm, wavenumber):
"""Test dense assembler for the Laplace operators."""
if not has_exafmm and not check_for_fmm():
pytest.skip("ExaFMM must be installed to run this test.")
grid = bempp.api.shapes.regular_sphere(2)
space = function_space(grid, "DP", 0)
op1 = helmholtz.single_layer(space,
space,
space,
wavenumber,
assembler="dense")
op2 = helmholtz.single_layer(space,
space,
space,
wavenumber,
assembler="fmm")
fun = bempp.api.GridFunction(space,
coefficients=np.random.rand(
space.global_dof_count))
assert np.allclose((op1 * fun).coefficients, (op2 * fun).coefficients)
bempp.api.clear_fmm_cache()
def test_helmholtz_single_layer_potential_p1_complex_coeffs(
default_parameters, helpers, device_interface, precision):
"""Test Helmholtz slp potential with p1 basis and complex coeffs."""
from bempp.api import function_space
from bempp.api import GridFunction
from bempp.api.operators.potential.helmholtz import single_layer
grid = helpers.load_grid("sphere")
space = function_space(grid, "P", 1)
data = helpers.load_npz_data("helmholtz_single_layer_potential_p1")
points = data["points"]
coefficients = _np.random.rand(
space.global_dof_count) + 1j * _np.random.rand(space.global_dof_count)
fun = GridFunction(space, coefficients=coefficients)
fun_real = GridFunction(space, coefficients=_np.real(coefficients))
fun_complex = GridFunction(space, coefficients=_np.imag(coefficients))
op = single_layer(
space,
points,
WAVENUMBER,
parameters=default_parameters,
precision=precision,
device_interface=device_interface,
)
expected = op.evaluate(fun_real) + 1j * op.evaluate(fun_complex)
actual = op.evaluate(fun)
_np.testing.assert_allclose(actual,
expected,
rtol=helpers.default_tolerance(precision))
def __init__(self,
kcomplex,
n,
geofile='sphere-simple.script.geo',
meshname='tmp.msh'):
self.ks = [kcomplex]
self.kExt = kcomplex
self.n = n
self.kInt = kcomplex * np.sqrt(n)
self.geofile = geofile
self.meshname = meshname
with open('in.geo', 'w') as fp:
fp.write("k = {};".format(np.abs(self.kInt)))
with open('out.geo', 'w') as fp:
fp.write('\nSave "{}";\n'.format(meshname))
call(['gmsh', geofile, '-'])
self.grid = grid = bem.import_grid(meshname)
self.space = space = bem.function_space(grid, "P", 1)
self.shape = self.space.global_dof_count
self.collect()
self.weak_form()
def test_modified_helmholtz_single_layer(default_parameters, helpers,
precision, device_interface):
"""Test dense assembler for modified Helmholtz."""
from bempp.api import function_space
from bempp.api.operators.boundary.modified_helmholtz import single_layer
grid = helpers.load_grid("sphere")
space = function_space(grid, "P", 1)
discrete_op = single_layer(
space,
space,
space,
OMEGA,
assembler="dense",
precision=precision,
device_interface=device_interface,
parameters=default_parameters,
).weak_form()
# Bempp 3 assembles modified Helmholtz as complex type, so cast to real.
expected = _np.real(
helpers.load_npy_data("modified_helmholtz_single_layer_boundary"))
_np.testing.assert_allclose(discrete_op.to_dense(),
expected,
rtol=helpers.default_tolerance(precision))
def test_maxwell_magnetic_field_potential_rwg(default_parameters, helpers,
device_interface, precision):
"""Test Maxwell magnetic potential."""
from bempp.api import function_space
from bempp.api import GridFunction
from bempp.api.operators.potential.maxwell import magnetic_field
grid = helpers.load_grid("sphere")
space = function_space(grid, "RWG", 0)
data = helpers.load_npz_data("maxwell_magnetic_field_potential")
coefficients = data["vec"]
points = data["points"]
expected = data["result"]
fun = GridFunction(space, coefficients=coefficients)
actual = magnetic_field(
space,
points,
WAVENUMBER,
parameters=default_parameters,
precision=precision,
device_interface=device_interface,
).evaluate(fun)
_np.testing.assert_allclose(actual,
expected,
rtol=helpers.default_tolerance(precision))
def test_laplace_single_layer_potential_p0(default_parameters, helpers,
device_interface, precision):
"""Test Laplace slp potential with p0 basis."""
from bempp.api import function_space
from bempp.api import GridFunction
from bempp.api.operators.potential.laplace import single_layer
grid = helpers.load_grid("sphere")
space = function_space(grid, "DP", 0)
data = helpers.load_npz_data("laplace_single_layer_potential_p0")
coefficients = data["vec"]
points = data["points"]
expected = data["result"]
fun = GridFunction(space, coefficients=coefficients)
actual = single_layer(
space,
points,
parameters=default_parameters,
precision=precision,
device_interface=device_interface,
).evaluate(fun)
_np.testing.assert_allclose(actual,
expected,
rtol=helpers.default_tolerance(precision))
def test_helmholtz_adjoint_double_layer_p1_cont(default_parameters, helpers,
precision, device_interface):
"""Test dense assembler for the Helmholtz adjoint dlp with p1 basis."""
from bempp.api import function_space
from bempp.api.operators.boundary.helmholtz import adjoint_double_layer
grid = helpers.load_grid("sphere")
space = function_space(grid, "P", 1)
discrete_op = adjoint_double_layer(
space,
space,
space,
WAVENUMBER,
assembler="dense",
precision=precision,
device_interface=device_interface,
parameters=default_parameters,
).weak_form()
expected = helpers.load_npy_data("helmholtz_adj_double_layer_boundary")
_np.testing.assert_allclose(discrete_op.to_dense(),
expected,
rtol=helpers.default_tolerance(precision))
def test_laplace_hypersingular(default_parameters, helpers, precision,
device_interface):
"""Test dense assembler for the Laplace hypersingular operator."""
from bempp.api import function_space
from bempp.api.operators.boundary.laplace import hypersingular
grid = helpers.load_grid("sphere")
space = function_space(grid, "P", 1)
discrete_op = hypersingular(
space,
space,
space,
assembler="dense",
precision=precision,
device_interface=device_interface,
parameters=default_parameters,
).weak_form()
expected = helpers.load_npy_data("laplace_hypersingular_boundary")
_np.testing.assert_allclose(discrete_op.A,
expected,
rtol=helpers.default_tolerance(precision))
def test_modified_helmholtz_adjoint_double_layer(
default_parameters, helpers, precision, device_interface
):
"""Test dense assembler for the Helmholtz adjoint dlp."""
from bempp.api import function_space
from bempp.api.operators.boundary.modified_helmholtz import adjoint_double_layer
grid = helpers.load_grid("sphere")
space = function_space(grid, "P", 1)
discrete_op = adjoint_double_layer(
space,
space,
space,
OMEGA,
assembler="dense",
precision=precision,
device_interface=device_interface,
parameters=default_parameters,
).weak_form()
expected = _np.real(
helpers.load_npy_data("modified_helmholtz_adj_double_layer_boundary")
)
_np.testing.assert_allclose(
discrete_op.A, expected, rtol=helpers.default_tolerance(precision)
)
def test_helmholtz_double_layer_potential_p1(default_parameters, helpers,
device_interface, precision):
"""Test Helmholtz dlp potential with p1 basis."""
from bempp.api import function_space
from bempp.api import GridFunction
from bempp.api.operators.potential.helmholtz import double_layer
grid = helpers.load_grid("sphere")
space = function_space(grid, "P", 1)
data = helpers.load_npz_data("helmholtz_double_layer_potential_p1")
coefficients = data["vec"]
points = data["points"]
expected = data["result"]
fun = GridFunction(space, coefficients=coefficients)
actual = double_layer(
space,
points,
WAVENUMBER,
parameters=default_parameters,
precision=precision,
device_interface=device_interface,
).evaluate(fun)
_np.testing.assert_allclose(actual,
expected,
rtol=helpers.default_tolerance(precision))
def __init__(self, kcomplex, eps, nlambda,
geofile='sphere-simple.script.geo', meshname='sphere.msh'):
self.ks = [kcomplex]
self.kExt = kcomplex
self.eps = eps
self.nlambda = nlambda
self.kInt = kcomplex * np.sqrt(eps)
self.geofile = geofile
self.meshname = meshname
with open('in.geo', 'w') as fp:
fp.write("k = {};".format(np.abs(self.kExt)))
fp.write("eps = {};".format(np.abs(self.eps)))
fp.write("nlambda = {};".format(np.abs(self.nlambda)))
with open('out.geo', 'w') as fp:
fp.write('\nSave "{}";\n'.format(meshname))
call(['gmsh', geofile, '-'])
self.grid = grid = bem.import_grid(meshname)
self.space = space = bem.function_space(grid, "P", 1)
self.shape = self.space.global_dof_count
self.collect()
self.weak_form()
def test_hypersingular_fails_for_wrong_space(type0, type1):
"""Expected failure for wrong spaces."""
grid = bempp.api.shapes.regular_sphere(0)
space0 = function_space(grid, *type0)
space1 = function_space(grid, *type1)
with pytest.raises(ValueError):
laplace.hypersingular(space0, space1, space1, assembler="dense").weak_form()
with pytest.raises(ValueError):
helmholtz.hypersingular(
space0, space1, space1, 1.5, assembler="dense"
).weak_form()
with pytest.raises(ValueError):
modified_helmholtz.hypersingular(
space0, space1, space1, 1.5, assembler="dense"
).weak_form()
def helmholtz_potential_dense_large_p0_benchmark(benchmark,
default_parameters):
"""Benchmark for Helmholtz potential evaluation on large sphere"""
from bempp.api.operators.potential.helmholtz import single_layer
from bempp.api import function_space
import numpy as np
grid = bempp.api.shapes.regular_sphere(6)
space = function_space(grid, "DP", 0)
npoints = 10000
theta = np.linspace(0, 2 * np.pi, npoints)
points = np.vstack(
[np.cos(theta),
np.sin(theta), 3 * np.ones(npoints, dtype="float64")])
coefficients = np.random.randn(
space.global_dof_count) + 1j * np.random.randn(space.global_dof_count)
grid_fun = bempp.api.GridFunction(space, coefficients=coefficients)
fun = lambda: single_layer(
space, points, 2.5, parameters=default_parameters).evaluate(grid_fun)
benchmark(fun)
def test_helmholtz_single_layer_p0(
default_parameters, helpers, precision, device_interface
):
"""Test dense assembler for the Helmholtz slp with p0 basis."""
from bempp.api import function_space
from bempp.api.operators.boundary.helmholtz import single_layer
grid = helpers.load_grid("sphere")
space = function_space(grid, "DP", 0)
discrete_op = single_layer(
space,
space,
space,
WAVENUMBER,
assembler="dense",
parameters=default_parameters,
device_interface=device_interface,
precision=precision,
).weak_form()
expected = helpers.load_npy_data("helmholtz_single_layer_boundary_p0_p0")
_np.testing.assert_allclose(
discrete_op.A, expected, rtol=helpers.default_tolerance(precision)
)
def test_maxwell_magnetic_field_complex_sphere_evaluator(
default_parameters, helpers, device_interface, precision):
"""Test Maxwell magnetic field evaluator on sphere with complex wavenumber."""
from bempp.api import get_precision
from bempp.api import function_space
from bempp.api.operators.boundary.maxwell import magnetic_field
grid = helpers.load_grid("sphere")
space1 = function_space(grid, "RWG", 0)
space2 = function_space(grid, "SNC", 0)
discrete_op = magnetic_field(
space1,
space1,
space2,
2.5 + 1j,
assembler="dense_evaluator",
device_interface=device_interface,
precision=precision,
parameters=default_parameters,
).weak_form()
mat = magnetic_field(
space1,
space1,
space2,
2.5 + 1j,
assembler="dense",
device_interface=device_interface,
precision=precision,
parameters=default_parameters,
).weak_form()
x = _np.random.RandomState(0).randn(space1.global_dof_count)
actual = discrete_op @ x
expected = mat @ x
if precision == "single":
tol = 1e-4
else:
tol = 1e-12
_np.testing.assert_allclose(actual, expected, rtol=tol)
def test_maxwell_operators(points, operator, wavenumber, space_type):
"""Test dense assembler for the Helmholtz operators."""
grid = bempp.api.shapes.regular_sphere(0)
space = function_space(grid, *space_type)
fun = bempp.api.GridFunction(space,
coefficients=np.random.rand(
space.global_dof_count))
operator(space, points, wavenumber).evaluate(fun)
def p1_trace(fenics_space):
"""
Return the P1 trace operator.
This function returns a pair (space, trace_matrix),
where space is a BEM++ space object and trace_matrix is the corresponding
matrix that maps the coefficients of a FEniCS function to its boundary
trace coefficients in the corresponding BEM++ space.
"""
import dolfin #pylint: disable=import-error
from bempp.api.fenics_interface.coupling import fenics_space_info
from bempp.api import function_space, grid_from_element_data
import numpy as np
family, degree = fenics_space_info(fenics_space)
if not (family == 'Lagrange' and degree == 1):
raise ValueError("fenics_space must be a p1 Lagrange space")
mesh = fenics_space.mesh()
boundary_mesh = dolfin.BoundaryMesh(mesh, "exterior", False)
bm_nodes = boundary_mesh.entity_map(0).array().astype(np.int64)
bm_coords = boundary_mesh.coordinates()
bm_cells = boundary_mesh.cells()
bempp_boundary_grid = grid_from_element_data(bm_coords.transpose(),
bm_cells.transpose())
# First get trace space
space = function_space(bempp_boundary_grid, "P", 1)
# Now compute the mapping from FEniCS dofs to BEM++ dofs.
# First the BEM++ dofs from the boundary vertices
from scipy.sparse import coo_matrix
bempp_dofs_from_b_vertices = p1_dof_to_vertex_matrix(space).transpose()
# Now FEniCS vertices to boundary dofs
b_vertices_from_vertices = coo_matrix(
(np.ones(len(bm_nodes)), (np.arange(len(bm_nodes)), bm_nodes)),
shape=(len(bm_nodes), mesh.num_vertices()),
dtype='float64').tocsc()
# Finally FEniCS dofs to vertices.
vertices_from_fenics_dofs = coo_matrix(
(np.ones(mesh.num_vertices()), (dolfin.dof_to_vertex_map(fenics_space),
np.arange(mesh.num_vertices()))),
shape=(mesh.num_vertices(), mesh.num_vertices()),
dtype='float64').tocsc()
# Get trace matrix by multiplication
trace_matrix = bempp_dofs_from_b_vertices * \
b_vertices_from_vertices * vertices_from_fenics_dofs
# Now return everything
return space, trace_matrix
def test_helmholtz_potentials_segments(default_parameters, helpers,
device_interface, precision):
"""Test Helmholtz potentials on segments."""
import bempp.api
from bempp.api import function_space
from bempp.api.operators.potential.helmholtz import single_layer
from bempp.api.operators.potential.helmholtz import double_layer
from bempp.api.grid.grid import grid_from_segments
grid = bempp.api.shapes.multitrace_cube()
seglists = [[1, 2, 3, 4, 5, 6], [6, 7, 8, 9, 10, 11]]
swapped_normal_lists = [{}, {6}]
rand = _np.random.RandomState(0)
for op in [single_layer, double_layer]:
for seglist, swapped_normals in zip(seglists, swapped_normal_lists):
new_grid = grid_from_segments(grid, seglist)
coeffs = rand.rand(new_grid.number_of_vertices)
space1 = function_space(
grid,
"P",
1,
segments=seglist,
swapped_normals=swapped_normals,
include_boundary_dofs=True,
)
space2 = function_space(new_grid,
"P",
1,
swapped_normals=swapped_normals)
points = _np.array([2.3, 1.3, 1.5]).reshape(3, 1) + rand.rand(3, 5)
fun1 = bempp.api.GridFunction(space1, coefficients=coeffs)
fun2 = bempp.api.GridFunction(space2, coefficients=coeffs)
actual = op(space1, points, 2.5) * fun1
expected = op(space2, points, 2.5) * fun2
_np.testing.assert_allclose(
actual, expected, rtol=helpers.default_tolerance(precision))
def test_laplace_single_layer_evaluator_complex(default_parameters, helpers,
precision, device_interface):
"""Test dense evaluator with complex vector."""
from bempp.api import function_space
from bempp.api.operators.boundary.laplace import single_layer
grid = helpers.load_grid("sphere")
space1 = function_space(grid, "DP", 0)
space2 = function_space(grid, "DP", 0)
discrete_op = single_layer(
space1,
space1,
space2,
assembler="dense_evaluator",
parameters=default_parameters,
device_interface=device_interface,
precision=precision,
).weak_form()
mat = single_layer(
space1,
space1,
space2,
assembler="dense",
parameters=default_parameters,
device_interface=device_interface,
precision=precision,
).weak_form()
x = _np.random.RandomState(0).rand(
space1.global_dof_count) + 1j * _np.random.RandomState(0).rand(
space1.global_dof_count)
actual = discrete_op @ x
expected = mat @ x
if precision == "single":
tol = 2e-4
else:
tol = 1e-12
_np.testing.assert_allclose(actual, expected, rtol=tol)
def perturbate(grid, t, kappa_pert=None):
P1 = bem.function_space(grid, 'P', 1)
grid_funz = bem.GridFunction(P1, fun=Phiz)
elements = grid.leaf_view.elements
vertices = grid.leaf_view.vertices
normals = P1.global_dof_normals
x, y, z = vertices
vertices[2, :] = z + t * grid_funz.coefficients
return bem.grid_from_element_data(vertices, elements)
def discretize(grid, *methods_list):
"""
Returns a named tuple containing the discretised boundaries of the
given grid according to the method specified.
"""
space = {}
methods = list(set(methods_list))
assert len(methods) > 0, "You must provide disretisation methods."
for method_key in methods:
method = method_key.split(".")[0]
space[method_key] = function_space(grid, method, 0)
return space
def test_maxwell_electric_field_bc_sphere(default_parameters, helpers,
device_interface, precision):
"""Test Maxwell electric field on sphere with BC basis."""
from bempp.api import get_precision
from bempp.api import function_space
from bempp.api.operators.boundary.maxwell import electric_field
grid = helpers.load_grid("sphere")
space1 = function_space(grid, "BC", 0)
space2 = function_space(grid, "SNC", 0)
rand = _np.random.RandomState(0)
vec = rand.rand(space1.global_dof_count)
discrete_op = electric_field(
space1,
space1,
space2,
2.5,
assembler="dense_evaluator",
device_interface=device_interface,
precision=precision,
parameters=default_parameters,
).weak_form()
actual = discrete_op @ vec
if precision == "single":
rtol = 1e-5
atol = 1e-6
else:
rtol = 1e-10
atol = 1e-14
mat = helpers.load_npy_data("maxwell_electric_field_boundary_bc")
expected = mat @ vec
_np.testing.assert_allclose(actual, expected, rtol=rtol, atol=atol)
def generic_pn_trace(fenics_space):
import dolfin
from .coupling import fenics_space_info
from bempp.api import function_space, grid_from_element_data, GridFunction
from bempp.api.common import global_parameters
import numpy as np
family,degree = fenics_space_info(fenics_space)
if not (family=='Lagrange'):
raise ValueError("fenics_space different from Lagrange space not yet tested!")
mesh = fenics_space.mesh()
bm = dolfin.BoundaryMesh(mesh, "exterior", False)
bm_nodes = bm.entity_map(0).array().astype(np.int64)
bm_coords = bm.coordinates()
bm_cells = bm.cells()
bempp_boundary_grid = grid_from_element_data(bm_coords.transpose(), bm_cells.transpose())
# Create compatible trace function space
space = function_space(bempp_boundary_grid, "P", degree)
# Now compute the mapping from BEM++ dofs to FEniCS dofs
from scipy.sparse import coo_matrix
parameters = global_parameters()
parameters.quadrature.far.single_order = 5 # TODO: use interplolation order accoriding to target space order
def FenicsData(x, n, domain_index, result):
value = np.empty(1)
u_FEM.eval(value, x)
result[0] = value
u_FEM = dolfin.Function(fenics_space)
N = u_FEM.vector().size()
u_FEM.vector()[:] = np.arange(N)
u_BEM = GridFunction(space, dual_space=space, fun=FenicsData, parameters=parameters)
FEM2BEM = np.rint(u_BEM.coefficients).astype(np.int64)
if max(abs(FEM2BEM-u_BEM.coefficients)) > 0.1:
raise ValueError("interpolation from FEM to BEM space too inaccurate.")
NB = len(FEM2BEM)
trace_matrix = coo_matrix((
np.ones(NB),(np.arange(NB),FEM2BEM)),
shape=(NB,N),dtype='float64').tocsc()
# Now return everything
return space, trace_matrix
def p1_trace(fenics_space):
import dolfin
from .coupling import fenics_space_info
from bempp.api import function_space, grid_from_element_data
import numpy as np
family, degree = fenics_space_info(fenics_space)
if not (family == 'Lagrange' and degree == 1):
raise ValueError("fenics_space must be a p1 Lagrange space")
mesh = fenics_space.mesh()
bm = dolfin.BoundaryMesh(mesh, "exterior", False)
bm_nodes = bm.entity_map(0).array().astype(np.int64)
bm_coords = bm.coordinates()
bm_cells = bm.cells()
bempp_boundary_grid = grid_from_element_data(bm_coords.transpose(), bm_cells.transpose())
# First get trace space
space = function_space(bempp_boundary_grid, "P", 1)
# Now compute the mapping from BEM++ dofs to FEniCS dofs
# First the BEM++ dofs to the boundary vertices
from scipy.sparse import coo_matrix
vertex_indices = np.arange(space.global_dof_count)
data = np.ones(space.global_dof_count)
bempp_dofs_from_b_vertices = p1_dof_to_vertex_matrix(space).transpose()
# Now the boundary vertices to all the vertices
b_vertices_from_vertices = coo_matrix((
np.ones(len(bm_nodes)), (np.arange(len(bm_nodes)), bm_nodes)),
shape=(len(bm_nodes), mesh.num_vertices()), dtype='float64').tocsc()
# Finally the vertices to FEniCS dofs
vertices_from_fenics_dofs = coo_matrix((
np.ones(mesh.num_vertices()), (dolfin.dof_to_vertex_map(fenics_space), np.arange(mesh.num_vertices()))),
shape=(mesh.num_vertices(), mesh.num_vertices()), dtype='float64').tocsc()
# Get trace matrix by multiplication
trace_matrix = bempp_dofs_from_b_vertices * b_vertices_from_vertices * vertices_from_fenics_dofs
# Now return everything
return space, trace_matrix
def __init__(self, kcomplex, n, geofile="sphere-simple.script.geo", meshname="tmp.msh"):
self.ks = [kcomplex]
self.kExt = kcomplex
self.n = n
self.kInt = kcomplex * np.sqrt(n)
self.geofile = geofile
self.meshname = meshname
with open("in.geo", "w") as fp:
fp.write("k = {};".format(np.abs(self.kInt)))
with open("out.geo", "w") as fp:
fp.write('\nSave "{}";\n'.format(meshname))
call(["gmsh", geofile, "-"])
self.grid = grid = bem.import_grid(meshname)
self.space = space = bem.function_space(grid, "P", 1)
self.shape = self.space.global_dof_count
self.collect()
self.weak_form()
import numpy as np import scipy.linalg as la import scipy.sparse as sp import scipy.sparse.linalg as spla import matplotlib.pyplot as plt import bempp.api as bem k = 0.2 lmbda = 2 * np.pi / k nlmbda = 15 grid = bem.shapes.sphere(h=lmbda/nlmbda) P1 = bem.function_space(grid, "P", 1) #P0 = bem.function_space(grid, "DP", 0) P0 = bem.function_space(grid, "P", 1) N0, N1 = P0.global_dof_count, P1.global_dof_count opV = bem.operators.boundary.helmholtz.single_layer(P0, P0, P0, k) opI0 = bem.operators.boundary.sparse.identity(P0, P0, P0) opK = bem.operators.boundary.helmholtz.double_layer(P1, P0, P0, k) opI10 = bem.operators.boundary.sparse.identity(P1, P0, P0) opQ = bem.operators.boundary.helmholtz.adjoint_double_layer(P0, P1, P1, k) opI01 = bem.operators.boundary.sparse.identity(P0, P1, P1) opW = bem.operators.boundary.helmholtz.hypersingular(P1, P1, P1, k)
def fs(grid, **kwargs):
return bem.function_space(grid, "P", 1, **kwargs)
def evalZeros(point, normal, dom_ind, result):
result[0] = 0. + 1j * 0.
inf = '0'
rhss = [] * len(domains)
rhs = [] * len(domains)
neighbors = domains.getNeighborOf(inf)
for ii in range(len(domains)):
name = domains.getName(ii)
dom = domains.getEntry(name)
jj = domains.getIndexDom(dom['name'])
print('==Domain: {0} #{1}'.format(dom['name'], ii))
space_d = bem.function_space(grid, kind_d[0], kind_d[1], domains=dom['interfaces'])
space_n = bem.function_space(grid, kind_n[0], kind_n[1], domains=dom['interfaces'])
if dom['name'] == inf:
IncDirichletTrace = bem.GridFunction(space_d, fun=evalIncDirichletTrace)
IncNeumannTrace = bem.GridFunction(space_n, fun=evalIncNeumannTrace)
idir, ineu = IncDirichletTrace, - IncNeumannTrace
elif dom in neighbors:
IncDirichletTrace = bem.GridFunction(space_d, fun=evalIncDirichletTrace)
IncNeumannTrace = bem.GridFunction(space_n, fun=evalIncNeumannTrace)
idir, ineu = - IncDirichletTrace, - IncNeumannTrace
else:
IncDirichletTrace = bem.GridFunction(space_d, fun=evalZeros)
IncNeumannTrace = bem.GridFunction(space_n, fun=evalZeros)
resn = [-1]
return resn, ts, x
#
H = [1., 0.75, 0.5, 0.25, 0.1, 0.075] #, 0.05, 0.025]
Dof = np.zeros((len(H), 7))
Its = np.zeros((len(H), 7))
Tps = np.zeros((len(H), 7))
STps = np.zeros((len(H), 7))
for i, h in enumerate(H):
print(h)
grid = bem.shapes.sphere(h=h)
P0 = bem.function_space(grid, "DP", 0)
P1 = bem.function_space(grid, "P", 1)
P0d = bem.function_space(grid, "DUAL", 0)
P1b = bem.function_space(grid, "B-P", 1)
opV00 = bem.operators.boundary.laplace.single_layer(P0, P1, P0)
# opW00 = bem.operators.boundary.helmholtz.hypersingular(P0, P1, P0,
# wave_number=0.1)
opJ00 = bem.operators.boundary.sparse.identity(P0, P1, P0)
opV = bem.operators.boundary.laplace.single_layer(P0d, P1b, P0d)
opW = bem.operators.boundary.laplace.hypersingular(P1b, P0d, P1b)
opJ = bem.operators.boundary.sparse.identity(opV.domain,
opW.dual_to_range,
t = 2*np.pi * np.linspace(0, 1, N)
Psi = psi(t)
kRef = Psi[0]
kRef = 1.
kExt, kInt = kRef, np.sqrt(n) * kRef
with open('in.geo', 'w') as fp:
fp.write("k = {};".format(np.abs(kInt)))
from subprocess import call
call(['gmsh', 'sphere-simple.script.geo', '-'])
meshname = 'sphere-simple.msh'
grid = bem.import_grid(meshname)
space = bem.function_space(grid, "P", 1)
shape = space.global_dof_count
K0 = bem.operators.boundary.helmholtz.double_layer(space, space, space, kExt)
V0 = bem.operators.boundary.helmholtz.single_layer(space, space, space, kExt)
W0 = bem.operators.boundary.helmholtz.hypersingular(space, space, space, kExt)
Q0 = bem.operators.boundary.helmholtz.adjoint_double_layer(space, space, space, kExt)
sK0, sQ0 = -K0, -Q0
K1 = bem.operators.boundary.helmholtz.double_layer(space, space, space, kInt)
V1 = bem.operators.boundary.helmholtz.single_layer(space, space, space, kInt)
W1 = bem.operators.boundary.helmholtz.hypersingular(space, space, space, kInt)
Q1 = bem.operators.boundary.helmholtz.adjoint_double_layer(space, space, space, kInt)
Id = bem.operators.boundary.sparse.identity(space, space, space)