def test_target_specific_qbx(actx_factory, op, helmholtz_k, qbx_order):
logging.basicConfig(level=logging.INFO)
actx = actx_factory()
target_order = 4
fmm_tol = 1e-3
from meshmode.mesh.generation import generate_sphere
mesh = generate_sphere(1, target_order)
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import \
InterpolatoryQuadratureSimplexGroupFactory
from pytential.qbx import QBXLayerPotentialSource
pre_density_discr = Discretization(
actx, mesh, InterpolatoryQuadratureSimplexGroupFactory(target_order))
from sumpy.expansion.level_to_order import SimpleExpansionOrderFinder
qbx = QBXLayerPotentialSource(
pre_density_discr,
4 * target_order,
qbx_order=qbx_order,
fmm_level_to_order=SimpleExpansionOrderFinder(fmm_tol),
fmm_backend="fmmlib",
_expansions_in_tree_have_extent=True,
_expansion_stick_out_factor=0.9,
_use_target_specific_qbx=False,
)
kernel_length_scale = 5 / abs(helmholtz_k) if helmholtz_k else None
places = {
"qbx": qbx,
"qbx_target_specific": qbx.copy(_use_target_specific_qbx=True)
}
from pytential.qbx.refinement import refine_geometry_collection
places = GeometryCollection(places, auto_where="qbx")
places = refine_geometry_collection(
places, kernel_length_scale=kernel_length_scale)
density_discr = places.get_discretization("qbx")
nodes = thaw(density_discr.nodes(), actx)
u_dev = actx.np.sin(nodes[0])
if helmholtz_k == 0:
kernel = LaplaceKernel(3)
kernel_kwargs = {}
else:
kernel = HelmholtzKernel(3, allow_evanescent=True)
kernel_kwargs = {"k": sym.var("k")}
u_sym = sym.var("u")
if op == "S":
op = sym.S
elif op == "D":
op = sym.D
elif op == "Sp":
op = sym.Sp
else:
raise ValueError("unknown operator: '%s'" % op)
expr = op(kernel, u_sym, qbx_forced_limit=-1, **kernel_kwargs)
bound_op = bind(places, expr)
pot_ref = actx.to_numpy(
flatten(bound_op(actx, u=u_dev, k=helmholtz_k), actx))
bound_op = bind(places, expr, auto_where="qbx_target_specific")
pot_tsqbx = actx.to_numpy(
flatten(bound_op(actx, u=u_dev, k=helmholtz_k), actx))
assert np.allclose(pot_tsqbx, pot_ref, atol=1e-13, rtol=1e-13)
def run_source_refinement_test(ctx_factory,
mesh,
order,
helmholtz_k=None,
visualize=False):
cl_ctx = ctx_factory()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue)
# {{{ initial geometry
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import (
InterpolatoryQuadratureSimplexGroupFactory)
discr = Discretization(actx, mesh,
InterpolatoryQuadratureSimplexGroupFactory(order))
lpot_source = QBXLayerPotentialSource(
discr,
qbx_order=order, # not used in refinement
fine_order=order)
places = GeometryCollection(lpot_source)
# }}}
# {{{ refined geometry
kernel_length_scale = 5 / helmholtz_k if helmholtz_k else None
expansion_disturbance_tolerance = 0.025
from pytential.qbx.refinement import refine_geometry_collection
places = refine_geometry_collection(
places,
kernel_length_scale=kernel_length_scale,
expansion_disturbance_tolerance=expansion_disturbance_tolerance,
visualize=visualize)
# }}}
dd = places.auto_source
stage1_density_discr = places.get_discretization(dd.geometry)
from meshmode.dof_array import thaw
stage1_density_nodes = dof_array_to_numpy(
actx, thaw(actx, stage1_density_discr.nodes()))
quad_stage2_density_discr = places.get_discretization(
dd.geometry, sym.QBX_SOURCE_QUAD_STAGE2)
quad_stage2_density_nodes = dof_array_to_numpy(
actx, thaw(actx, quad_stage2_density_discr.nodes()))
int_centers = dof_array_to_numpy(
actx,
bind(places, sym.expansion_centers(lpot_source.ambient_dim, -1))(actx))
ext_centers = dof_array_to_numpy(
actx,
bind(places, sym.expansion_centers(lpot_source.ambient_dim, +1))(actx))
expansion_radii = dof_array_to_numpy(
actx,
bind(places, sym.expansion_radii(lpot_source.ambient_dim))(actx))
dd = dd.copy(granularity=sym.GRANULARITY_ELEMENT)
source_danger_zone_radii = dof_array_to_numpy(
actx,
bind(
places,
sym._source_danger_zone_radii(lpot_source.ambient_dim,
dofdesc=dd.to_stage2()))(actx))
quad_res = dof_array_to_numpy(
actx,
bind(places, sym._quad_resolution(lpot_source.ambient_dim,
dofdesc=dd))(actx))
# {{{ check if satisfying criteria
def check_disk_undisturbed_by_sources(centers_panel, sources_panel):
if centers_panel.element_nr == sources_panel.element_nr:
# Same panel
return
my_int_centers = int_centers[:, centers_panel.discr_slice]
my_ext_centers = ext_centers[:, centers_panel.discr_slice]
all_centers = np.append(my_int_centers, my_ext_centers, axis=-1)
nodes = stage1_density_nodes[:, sources_panel.discr_slice]
# =distance(centers of panel 1, panel 2)
dist = (la.norm(
(all_centers[..., np.newaxis] - nodes[:, np.newaxis, ...]).T,
axis=-1).min())
# Criterion:
# A center cannot be closer to another panel than to its originating
# panel.
rad = expansion_radii[centers_panel.discr_slice]
assert (dist >= rad * (1-expansion_disturbance_tolerance)).all(), \
(dist, rad, centers_panel.element_nr, sources_panel.element_nr)
def check_sufficient_quadrature_resolution(centers_panel, sources_panel):
dz_radius = source_danger_zone_radii[sources_panel.element_nr]
my_int_centers = int_centers[:, centers_panel.discr_slice]
my_ext_centers = ext_centers[:, centers_panel.discr_slice]
all_centers = np.append(my_int_centers, my_ext_centers, axis=-1)
nodes = quad_stage2_density_nodes[:, sources_panel.discr_slice]
# =distance(centers of panel 1, panel 2)
dist = (la.norm(
(all_centers[..., np.newaxis] - nodes[:, np.newaxis, ...]).T,
axis=-1).min())
# Criterion:
# The quadrature contribution from each panel is as accurate
# as from the center's own source panel.
assert dist >= dz_radius, \
(dist, dz_radius, centers_panel.element_nr, sources_panel.element_nr)
def check_quad_res_to_helmholtz_k_ratio(panel):
# Check wavenumber to panel size ratio.
assert quad_res[panel.element_nr] * helmholtz_k <= 5
for i, panel_1 in enumerate(iter_elements(stage1_density_discr)):
for panel_2 in iter_elements(stage1_density_discr):
check_disk_undisturbed_by_sources(panel_1, panel_2)
for panel_2 in iter_elements(quad_stage2_density_discr):
check_sufficient_quadrature_resolution(panel_1, panel_2)
if helmholtz_k is not None:
check_quad_res_to_helmholtz_k_ratio(panel_1)
def test_compare_cl_and_py_cost_model(ctx_factory):
nelements = 3600
target_order = 16
fmm_order = 5
qbx_order = fmm_order
ctx = ctx_factory()
queue = cl.CommandQueue(ctx)
actx = PyOpenCLArrayContext(queue)
# {{{ Construct geometry
from meshmode.mesh.generation import make_curve_mesh, starfish
mesh = make_curve_mesh(starfish, np.linspace(0, 1, nelements), target_order)
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import \
InterpolatoryQuadratureSimplexGroupFactory
pre_density_discr = Discretization(
actx, mesh,
InterpolatoryQuadratureSimplexGroupFactory(target_order)
)
qbx = QBXLayerPotentialSource(
pre_density_discr, 4 * target_order,
qbx_order,
fmm_order=fmm_order
)
places = GeometryCollection(qbx)
from pytential.qbx.refinement import refine_geometry_collection
places = refine_geometry_collection(places)
target_discrs_and_qbx_sides = tuple([(qbx.density_discr, 0)])
geo_data_dev = qbx.qbx_fmm_geometry_data(
places, places.auto_source.geometry, target_discrs_and_qbx_sides
)
from pytential.qbx.utils import ToHostTransferredGeoDataWrapper
geo_data = ToHostTransferredGeoDataWrapper(queue, geo_data_dev)
# }}}
# {{{ Construct cost models
cl_cost_model = QBXCostModel()
python_cost_model = _PythonQBXCostModel()
tree = geo_data.tree()
xlat_cost = make_pde_aware_translation_cost_model(
tree.targets.shape[0], tree.nlevels
)
constant_one_params = QBXCostModel.get_unit_calibration_params()
constant_one_params["p_qbx"] = 5
for ilevel in range(tree.nlevels):
constant_one_params["p_fmm_lev%d" % ilevel] = 10
cl_cost_factors = cl_cost_model.qbx_cost_factors_for_kernels_from_model(
queue, tree.nlevels, xlat_cost, constant_one_params
)
python_cost_factors = python_cost_model.qbx_cost_factors_for_kernels_from_model(
None, tree.nlevels, xlat_cost, constant_one_params
)
# }}}
# {{{ Test process_form_qbxl
cl_ndirect_sources_per_target_box = (
cl_cost_model.get_ndirect_sources_per_target_box(
queue, geo_data_dev.traversal()
)
)
queue.finish()
start_time = time.time()
cl_p2qbxl = cl_cost_model.process_form_qbxl(
queue, geo_data_dev, cl_cost_factors["p2qbxl_cost"],
cl_ndirect_sources_per_target_box
)
queue.finish()
logger.info("OpenCL time for process_form_qbxl: {}".format(
str(time.time() - start_time)
))
python_ndirect_sources_per_target_box = (
python_cost_model.get_ndirect_sources_per_target_box(
queue, geo_data.traversal()
)
)
start_time = time.time()
python_p2qbxl = python_cost_model.process_form_qbxl(
queue, geo_data, python_cost_factors["p2qbxl_cost"],
python_ndirect_sources_per_target_box
)
logger.info("Python time for process_form_qbxl: {}".format(
str(time.time() - start_time)
))
assert np.array_equal(cl_p2qbxl.get(), python_p2qbxl)
# }}}
# {{{ Test process_m2qbxl
queue.finish()
start_time = time.time()
cl_m2qbxl = cl_cost_model.process_m2qbxl(
queue, geo_data_dev, cl_cost_factors["m2qbxl_cost"]
)
queue.finish()
logger.info("OpenCL time for process_m2qbxl: {}".format(
str(time.time() - start_time)
))
start_time = time.time()
python_m2qbxl = python_cost_model.process_m2qbxl(
queue, geo_data, python_cost_factors["m2qbxl_cost"]
)
logger.info("Python time for process_m2qbxl: {}".format(
str(time.time() - start_time)
))
assert np.array_equal(cl_m2qbxl.get(), python_m2qbxl)
# }}}
# {{{ Test process_l2qbxl
queue.finish()
start_time = time.time()
cl_l2qbxl = cl_cost_model.process_l2qbxl(
queue, geo_data_dev, cl_cost_factors["l2qbxl_cost"]
)
queue.finish()
logger.info("OpenCL time for process_l2qbxl: {}".format(
str(time.time() - start_time)
))
start_time = time.time()
python_l2qbxl = python_cost_model.process_l2qbxl(
queue, geo_data, python_cost_factors["l2qbxl_cost"]
)
logger.info("Python time for process_l2qbxl: {}".format(
str(time.time() - start_time)
))
assert np.array_equal(cl_l2qbxl.get(), python_l2qbxl)
# }}}
# {{{ Test process_eval_qbxl
queue.finish()
start_time = time.time()
cl_eval_qbxl = cl_cost_model.process_eval_qbxl(
queue, geo_data_dev, cl_cost_factors["qbxl2p_cost"]
)
queue.finish()
logger.info("OpenCL time for process_eval_qbxl: {}".format(
str(time.time() - start_time)
))
start_time = time.time()
python_eval_qbxl = python_cost_model.process_eval_qbxl(
queue, geo_data, python_cost_factors["qbxl2p_cost"]
)
logger.info("Python time for process_eval_qbxl: {}".format(
str(time.time() - start_time)
))
assert np.array_equal(cl_eval_qbxl.get(), python_eval_qbxl)
# }}}
# {{{ Test eval_target_specific_qbxl
queue.finish()
start_time = time.time()
cl_eval_target_specific_qbxl = cl_cost_model.process_eval_target_specific_qbxl(
queue, geo_data_dev, cl_cost_factors["p2p_tsqbx_cost"],
cl_ndirect_sources_per_target_box
)
queue.finish()
logger.info("OpenCL time for eval_target_specific_qbxl: {}".format(
str(time.time() - start_time)
))
start_time = time.time()
python_eval_target_specific_qbxl = \
python_cost_model.process_eval_target_specific_qbxl(
queue, geo_data, python_cost_factors["p2p_tsqbx_cost"],
python_ndirect_sources_per_target_box
)
logger.info("Python time for eval_target_specific_qbxl: {}".format(
str(time.time() - start_time)
))
assert np.array_equal(
cl_eval_target_specific_qbxl.get(), python_eval_target_specific_qbxl
)
extend_factor=vis_extend_factor)
from pytential.target import PointsTarget
plot_targets = PointsTarget(fplot.points)
places.update({
"qbx_target_tol":
qbx.copy(target_association_tolerance=0.15),
"plot_targets":
plot_targets
})
places = GeometryCollection(places, auto_where=case.name)
if case.use_refinement:
from pytential.qbx.refinement import refine_geometry_collection
places = refine_geometry_collection(places, **refiner_extra_kwargs)
dd = sym.as_dofdesc(case.name).to_stage1()
density_discr = places.get_discretization(dd.geometry)
logger.info("nelements: %d", density_discr.mesh.nelements)
logger.info("ndofs: %d", density_discr.ndofs)
if case.use_refinement:
logger.info("%d elements before refinement",
qbx.density_discr.mesh.nelements)
discr = places.get_discretization(dd.geometry, sym.QBX_SOURCE_STAGE1)
logger.info("%d stage-1 elements after refinement",
discr.mesh.nelements)
qbx = QBXLayerPotentialSource(
pre_density_discr, 4*target_order,
case.qbx_order,
fmm_order=case.fmm_order,
fmm_backend=case.fmm_backend,
target_association_tolerance=1.0e-1,
_expansions_in_tree_have_extent=True,
_expansion_stick_out_factor=getattr(
case, "_expansion_stick_out_factor", 0),
)
places = GeometryCollection(qbx)
from pytential.qbx.refinement import refine_geometry_collection
kernel_length_scale = 5 / case.k if case.k else None
places = refine_geometry_collection(places,
kernel_length_scale=kernel_length_scale)
# {{{ compute values of a solution to the PDE
density_discr = places.get_discretization(places.auto_source.geometry)
from meshmode.dof_array import thaw, flatten, unflatten
nodes_host = [actx.to_numpy(axis)
for axis in flatten(thaw(actx, density_discr.nodes()))]
normal = bind(places, sym.normal(d))(actx).as_vector(object)
normal_host = [actx.to_numpy(axis)for axis in flatten(normal)]
if k != 0:
if d == 2:
angle = 0.3
wave_vec = np.array([np.cos(angle), np.sin(angle)])
def test_build_matrix(ctx_factory, k, curve_fn, op_type, visualize=False):
"""Checks that the matrix built with `symbolic.execution.build_matrix`
gives the same (to tolerance) answer as a direct evaluation.
"""
cl_ctx = ctx_factory()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue)
# prevent cache 'splosion
from sympy.core.cache import clear_cache
clear_cache()
case = extra.CurveTestCase(name="curve",
knl_class_or_helmholtz_k=k,
curve_fn=curve_fn,
op_type=op_type,
target_order=7,
qbx_order=4,
resolutions=[30])
logger.info("\n%s", case)
# {{{ geometry
qbx = case.get_layer_potential(actx, case.resolutions[-1],
case.target_order)
from pytential.qbx.refinement import refine_geometry_collection
places = GeometryCollection(qbx, auto_where=case.name)
places = refine_geometry_collection(places,
kernel_length_scale=(5 /
k if k else None))
dd = places.auto_source.to_stage1()
density_discr = places.get_discretization(dd.geometry)
logger.info("nelements: %d", density_discr.mesh.nelements)
logger.info("ndofs: %d", density_discr.ndofs)
# }}}
# {{{ symbolic
sym_u, sym_op = case.get_operator(places.ambient_dim)
bound_op = bind(places, sym_op)
# }}}
# {{{ dense matrix
from pytential.symbolic.execution import build_matrix
mat = actx.to_numpy(
build_matrix(actx,
places,
sym_op,
sym_u,
context=case.knl_concrete_kwargs))
if visualize:
try:
import matplotlib.pyplot as pt
except ImportError:
visualize = False
if visualize:
from sumpy.tools import build_matrix as build_matrix_via_matvec
mat2 = bound_op.scipy_op(actx,
"u",
dtype=mat.dtype,
**case.knl_concrete_kwargs)
mat2 = build_matrix_via_matvec(mat2)
logger.info(
"real %.5e imag %.5e",
la.norm((mat - mat2).real, "fro") / la.norm(mat2.real, "fro"),
la.norm((mat - mat2).imag, "fro") / la.norm(mat2.imag, "fro"))
pt.subplot(121)
pt.imshow(np.log10(np.abs(1.0e-20 + (mat - mat2).real)))
pt.colorbar()
pt.subplot(122)
pt.imshow(np.log10(np.abs(1.0e-20 + (mat - mat2).imag)))
pt.colorbar()
pt.show()
pt.clf()
if visualize:
pt.subplot(121)
pt.imshow(mat.real)
pt.colorbar()
pt.subplot(122)
pt.imshow(mat.imag)
pt.colorbar()
pt.show()
pt.clf()
# }}}
# {{{ check
from pytential.utils import unflatten_from_numpy, flatten_to_numpy
np.random.seed(12)
for i in range(5):
if isinstance(sym_u, np.ndarray):
u = make_obj_array([
np.random.randn(density_discr.ndofs) for _ in range(len(sym_u))
])
else:
u = np.random.randn(density_discr.ndofs)
u_dev = unflatten_from_numpy(actx, density_discr, u)
res_matvec = np.hstack(
flatten_to_numpy(
actx, bound_op(actx, u=u_dev, **case.knl_concrete_kwargs)))
res_mat = mat.dot(np.hstack(u))
abs_err = la.norm(res_mat - res_matvec, np.inf)
rel_err = abs_err / la.norm(res_matvec, np.inf)
logger.info("AbsErr {:.5e} RelErr {:.5e}".format(abs_err, rel_err))
assert rel_err < 1.0e-13, 'iteration: {}'.format(i)
def test_build_matrix_conditioning(actx_factory,
side,
op_type,
visualize=False):
"""Checks that :math:`I + K`, where :math:`K` is compact gives a
well-conditioned operator when it should. For example, the exterior Laplace
problem has a nullspace, so we check that and remove it.
"""
actx = actx_factory()
# prevent cache explosion
from sympy.core.cache import clear_cache
clear_cache()
case = extra.CurveTestCase(
name="ellipse",
curve_fn=lambda t: ellipse(3.0, t),
target_order=16,
source_ovsmp=1,
qbx_order=4,
resolutions=[64],
op_type=op_type,
side=side,
)
logger.info("\n%s", case)
# {{{ geometry
qbx = case.get_layer_potential(actx, case.resolutions[-1],
case.target_order)
from pytential.qbx.refinement import refine_geometry_collection
places = GeometryCollection(qbx, auto_where=case.name)
places = refine_geometry_collection(
places, refine_discr_stage=sym.QBX_SOURCE_QUAD_STAGE2)
dd = places.auto_source.to_stage1()
density_discr = places.get_discretization(dd.geometry)
logger.info("nelements: %d", density_discr.mesh.nelements)
logger.info("ndofs: %d", density_discr.ndofs)
# }}}
# {{{ check matrix
from pytential.symbolic.execution import build_matrix
sym_u, sym_op = case.get_operator(places.ambient_dim,
qbx_forced_limit="avg")
mat = actx.to_numpy(
build_matrix(actx,
places,
sym_op,
sym_u,
context=case.knl_concrete_kwargs))
kappa = la.cond(mat)
_, sigma, _ = la.svd(mat)
logger.info("cond: %.5e sigma_max %.5e", kappa, sigma[0])
# NOTE: exterior Laplace has a nullspace
if side == +1 and op_type == "double":
assert kappa > 1.0e+9
assert sigma[-1] < 1.0e-9
else:
assert kappa < 1.0e+1
assert sigma[-1] > 1.0e-2
# remove the nullspace and check that it worked
if side == +1 and op_type == "double":
# NOTE: this adds the "mean" to remove the nullspace for the operator
# See `pytential.symbolic.pde.scalar` for the equivalent formulation
w = actx.to_numpy(
flatten(
bind(places,
sym.sqrt_jac_q_weight(places.ambient_dim)**2)(actx),
actx))
w = np.tile(w.reshape(-1, 1), w.size).T
kappa = la.cond(mat + w)
assert kappa < 1.0e+2
# }}}
# {{{ plot
if not visualize:
return
side = "int" if side == -1 else "ext"
import matplotlib.pyplot as plt
plt.imshow(mat)
plt.colorbar()
plt.title(fr"$\kappa(A) = {kappa:.5e}$")
plt.savefig(f"test_cond_{op_type}_{side}_mat")
plt.clf()
plt.plot(sigma)
plt.ylabel(r"$\sigma$")
plt.grid()
plt.savefig(f"test_cond_{op_type}_{side}_svd")
plt.clf()
def run_source_refinement_test(actx_factory,
mesh,
order,
helmholtz_k=None,
surface_name="surface",
visualize=False):
actx = actx_factory()
# {{{ initial geometry
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import \
InterpolatoryQuadratureGroupFactory
discr = Discretization(actx, mesh,
InterpolatoryQuadratureGroupFactory(order))
lpot_source = QBXLayerPotentialSource(
discr,
qbx_order=order, # not used in refinement
fine_order=order)
places = GeometryCollection(lpot_source)
logger.info("nelements: %d", discr.mesh.nelements)
logger.info("ndofs: %d", discr.ndofs)
# }}}
# {{{ refined geometry
def _visualize_quad_resolution(_places, dd, suffix):
if dd.discr_stage is None:
vis_discr = lpot_source.density_discr
else:
vis_discr = _places.get_discretization(dd.geometry, dd.discr_stage)
stretch = bind(_places,
sym._simplex_mapping_max_stretch_factor(
_places.ambient_dim, with_elementwise_max=False),
auto_where=dd)(actx)
from meshmode.discretization.visualization import make_visualizer
vis = make_visualizer(actx, vis_discr, order, force_equidistant=True)
vis.write_vtk_file(
f"global-qbx-source-refinement-{surface_name}-{order}-{suffix}.vtu",
[("stretch", stretch)],
overwrite=True,
use_high_order=True)
kernel_length_scale = 5 / helmholtz_k if helmholtz_k else None
expansion_disturbance_tolerance = 0.025
from pytential.qbx.refinement import refine_geometry_collection
places = refine_geometry_collection(
places,
kernel_length_scale=kernel_length_scale,
expansion_disturbance_tolerance=expansion_disturbance_tolerance,
visualize=False)
if visualize:
dd = places.auto_source
_visualize_quad_resolution(places, dd.copy(discr_stage=None),
"original")
_visualize_quad_resolution(places, dd.to_stage1(), "stage1")
_visualize_quad_resolution(places, dd.to_stage2(), "stage2")
# }}}
dd = places.auto_source
ambient_dim = places.ambient_dim
stage1_density_discr = places.get_discretization(dd.geometry)
stage1_density_nodes = actx.to_numpy(
flatten(stage1_density_discr.nodes(), actx)).reshape(ambient_dim, -1)
quad_stage2_density_discr = places.get_discretization(
dd.geometry, sym.QBX_SOURCE_QUAD_STAGE2)
quad_stage2_density_nodes = actx.to_numpy(
flatten(quad_stage2_density_discr.nodes(),
actx)).reshape(ambient_dim, -1)
int_centers = actx.to_numpy(
flatten(
bind(places, sym.expansion_centers(ambient_dim, -1))(actx),
actx)).reshape(ambient_dim, -1)
ext_centers = actx.to_numpy(
flatten(
bind(places, sym.expansion_centers(ambient_dim, +1))(actx),
actx)).reshape(ambient_dim, -1)
expansion_radii = actx.to_numpy(
flatten(bind(places, sym.expansion_radii(ambient_dim))(actx), actx))
dd = dd.copy(granularity=sym.GRANULARITY_ELEMENT)
source_danger_zone_radii = actx.to_numpy(
flatten(
bind(
places,
sym._source_danger_zone_radii(ambient_dim,
dofdesc=dd.to_stage2()))(actx),
actx))
quad_res = actx.to_numpy(
flatten(
bind(places, sym._quad_resolution(ambient_dim, dofdesc=dd))(actx),
actx))
# {{{ check if satisfying criteria
def check_disk_undisturbed_by_sources(centers_element, sources_element):
if centers_element.index == sources_element.index:
# Same element
return
my_int_centers = int_centers[:, centers_element.discr_slice]
my_ext_centers = ext_centers[:, centers_element.discr_slice]
all_centers = np.append(my_int_centers, my_ext_centers, axis=-1)
nodes = stage1_density_nodes[:, sources_element.discr_slice]
# =distance(centers of element 1, element 2)
dist = (la.norm(
(all_centers[..., np.newaxis] - nodes[:, np.newaxis, ...]).T,
axis=-1).min())
# Criterion:
# A center cannot be closer to another element than to its originating
# element.
rad = expansion_radii[centers_element.discr_slice]
assert np.all(
dist >= rad *
(1 - expansion_disturbance_tolerance)), (dist, rad,
centers_element.index,
sources_element.index)
def check_sufficient_quadrature_resolution(centers_element,
sources_element):
dz_radius = source_danger_zone_radii[sources_element.index]
my_int_centers = int_centers[:, centers_element.discr_slice]
my_ext_centers = ext_centers[:, centers_element.discr_slice]
all_centers = np.append(my_int_centers, my_ext_centers, axis=-1)
nodes = quad_stage2_density_nodes[:, sources_element.discr_slice]
# =distance(centers of element 1, element 2)
dist = (la.norm(
(all_centers[..., np.newaxis] - nodes[:, np.newaxis, ...]).T,
axis=-1).min())
# Criterion:
# The quadrature contribution from each element is as accurate
# as from the center's own source element.
assert dist >= dz_radius, \
(dist, dz_radius, centers_element.index, sources_element.index)
def check_quad_res_to_helmholtz_k_ratio(element):
# Check wavenumber to element size ratio.
assert quad_res[element.index] * helmholtz_k <= 5
for element_1 in iter_elements(stage1_density_discr):
for element_2 in iter_elements(stage1_density_discr):
check_disk_undisturbed_by_sources(element_1, element_2)
for element_2 in iter_elements(quad_stage2_density_discr):
check_sufficient_quadrature_resolution(element_1, element_2)
if helmholtz_k is not None:
check_quad_res_to_helmholtz_k_ratio(element_1)