def main():
cl_ctx = cl.create_some_context()
queue = cl.CommandQueue(cl_ctx)
from meshmode.mesh.generation import ( # noqa
generate_icosphere, generate_icosahedron, generate_torus)
#mesh = generate_icosphere(1, order=order)
mesh = generate_icosahedron(1, order=order)
#mesh = generate_torus(3, 1, order=order)
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import \
PolynomialWarpAndBlendGroupFactory
discr = Discretization(cl_ctx, mesh,
PolynomialWarpAndBlendGroupFactory(order))
from meshmode.discretization.visualization import make_visualizer
vis = make_visualizer(queue, discr, order)
vis.write_vtk_file("geometry.vtu", [
("f", discr.nodes()[0]),
])
from meshmode.discretization.visualization import \
write_nodal_adjacency_vtk_file
write_nodal_adjacency_vtk_file("adjacency.vtu", mesh)
def test_mesh_without_vertices(ctx_factory):
ctx = ctx_factory()
queue = cl.CommandQueue(ctx)
# create a mesh
from meshmode.mesh.generation import generate_icosphere
mesh = generate_icosphere(r=1.0, order=4)
# create one without the vertices
from meshmode.mesh import Mesh
grp, = mesh.groups
groups = [
grp.copy(nodes=grp.nodes, vertex_indices=None) for grp in mesh.groups
]
mesh = Mesh(None, groups, is_conforming=False)
# try refining it
from meshmode.mesh.refinement import refine_uniformly
mesh = refine_uniformly(mesh, 1)
# make sure the world doesn't end
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import \
InterpolatoryQuadratureSimplexGroupFactory as GroupFactory
discr = Discretization(ctx, mesh, GroupFactory(4))
discr.nodes().with_queue(queue)
from meshmode.discretization.visualization import make_visualizer
make_visualizer(queue, discr, 4)
def main():
cl_ctx = cl.create_some_context()
queue = cl.CommandQueue(cl_ctx)
from meshmode.mesh.generation import ( # noqa
generate_icosphere, generate_icosahedron,
generate_torus)
#mesh = generate_icosphere(1, order=order)
mesh = generate_icosahedron(1, order=order)
#mesh = generate_torus(3, 1, order=order)
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import \
PolynomialWarpAndBlendGroupFactory
discr = Discretization(
cl_ctx, mesh, PolynomialWarpAndBlendGroupFactory(order))
from meshmode.discretization.visualization import make_visualizer
vis = make_visualizer(queue, discr, order)
vis.write_vtk_file("geometry.vtu", [
("f", discr.nodes()[0]),
])
from meshmode.discretization.visualization import \
write_mesh_connectivity_vtk_file
write_mesh_connectivity_vtk_file("connectivity.vtu",
mesh)
def test_mesh_without_vertices(actx_factory):
actx = actx_factory()
# create a mesh
mesh = mgen.generate_icosphere(r=1.0, order=4)
# create one without the vertices
grp, = mesh.groups
groups = [
grp.copy(nodes=grp.nodes, vertex_indices=None) for grp in mesh.groups
]
mesh = Mesh(None, groups, is_conforming=False)
# try refining it
from meshmode.mesh.refinement import refine_uniformly
mesh = refine_uniformly(mesh, 1)
# make sure the world doesn't end
from meshmode.discretization import Discretization
discr = Discretization(actx, mesh,
InterpolatoryQuadratureSimplexGroupFactory(4))
thaw(discr.nodes(), actx)
from meshmode.discretization.visualization import make_visualizer
make_visualizer(actx, discr, 4)
def get_torus_with_ref_mean_curvature(actx, h):
order = 4
r_minor = 1.0
r_major = 3.0
from meshmode.mesh.generation import generate_torus
mesh = generate_torus(r_major, r_minor,
n_major=h, n_minor=h, order=order)
discr = Discretization(actx, mesh,
InterpolatoryQuadratureSimplexGroupFactory(order))
from meshmode.dof_array import thaw
nodes = thaw(actx, discr.nodes())
# copied from meshmode.mesh.generation.generate_torus
a = r_major
b = r_minor
u = actx.np.arctan2(nodes[1], nodes[0])
from pytools.obj_array import flat_obj_array
rvec = flat_obj_array(actx.np.cos(u), actx.np.sin(u), 0*u)
rvec = sum(nodes * rvec) - a
cosv = actx.np.cos(actx.np.arctan2(nodes[2], rvec))
return discr, (a + 2.0 * b * cosv) / (2 * b * (a + b * cosv))
def test_flatten_unflatten(actx_factory):
actx = actx_factory()
ambient_dim = 2
from meshmode.mesh.generation import generate_regular_rect_mesh
mesh = generate_regular_rect_mesh(a=(-0.5, ) * ambient_dim,
b=(+0.5, ) * ambient_dim,
n=(3, ) * ambient_dim,
order=1)
discr = Discretization(actx, mesh, PolynomialWarpAndBlendGroupFactory(3))
a = np.random.randn(discr.ndofs)
from meshmode.dof_array import flatten, unflatten
a_round_trip = actx.to_numpy(
flatten(unflatten(actx, discr, actx.from_numpy(a))))
assert np.array_equal(a, a_round_trip)
from meshmode.dof_array import flatten_to_numpy, unflatten_from_numpy
a_round_trip = flatten_to_numpy(actx, unflatten_from_numpy(actx, discr, a))
assert np.array_equal(a, a_round_trip)
x = thaw(discr.nodes(), actx)
avg_mass = DOFArray(
actx,
tuple([(np.pi + actx.zeros((grp.nelements, 1), a.dtype))
for grp in discr.groups]))
c = MyContainer(name="flatten",
mass=avg_mass,
momentum=make_obj_array([x, x, x]),
enthalpy=x)
from meshmode.dof_array import unflatten_like
c_round_trip = unflatten_like(actx, flatten(c), c)
assert flat_norm(c - c_round_trip) < 1.0e-8
def test_unregularized_off_surface_fmm_vs_direct(ctx_factory):
cl_ctx = ctx_factory()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue)
nelements = 300
target_order = 8
fmm_order = 4
# {{{ geometry
mesh = make_curve_mesh(WobblyCircle.random(8, seed=30),
np.linspace(0, 1, nelements+1),
target_order)
from pytential.unregularized import UnregularizedLayerPotentialSource
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import \
InterpolatoryQuadratureSimplexGroupFactory
density_discr = Discretization(
actx, mesh, InterpolatoryQuadratureSimplexGroupFactory(target_order))
direct = UnregularizedLayerPotentialSource(
density_discr,
fmm_order=False,
)
fmm = direct.copy(
fmm_level_to_order=lambda kernel, kernel_args, tree, level: fmm_order)
sigma = density_discr.zeros(actx) + 1
fplot = FieldPlotter(np.zeros(2), extent=5, npoints=100)
from pytential.target import PointsTarget
ptarget = PointsTarget(fplot.points)
from pytential import GeometryCollection
places = GeometryCollection({
"unregularized_direct": direct,
"unregularized_fmm": fmm,
"targets": ptarget})
# }}}
# {{{ check
from sumpy.kernel import LaplaceKernel
op = sym.D(LaplaceKernel(2), sym.var("sigma"), qbx_forced_limit=None)
direct_fld_in_vol = bind(places, op,
auto_where=("unregularized_direct", "targets"))(
actx, sigma=sigma)
fmm_fld_in_vol = bind(places, op,
auto_where=("unregularized_fmm", "targets"))(actx, sigma=sigma)
err = actx.np.fabs(fmm_fld_in_vol - direct_fld_in_vol)
linf_err = actx.to_numpy(err).max()
print("l_inf error:", linf_err)
assert linf_err < 5e-3
def main():
cl_ctx = cl.create_some_context()
queue = cl.CommandQueue(cl_ctx)
target_order = 10
from functools import partial
nelements = 30
qbx_order = 4
from sumpy.kernel import LaplaceKernel
from meshmode.mesh.generation import ( # noqa
ellipse, cloverleaf, starfish, drop, n_gon, qbx_peanut,
make_curve_mesh)
mesh = make_curve_mesh(partial(ellipse, 1),
np.linspace(0, 1, nelements+1),
target_order)
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import \
InterpolatoryQuadratureSimplexGroupFactory
density_discr = Discretization(cl_ctx, mesh,
InterpolatoryQuadratureSimplexGroupFactory(target_order))
from pytential.qbx import QBXLayerPotentialSource
qbx = QBXLayerPotentialSource(density_discr, 4*target_order,
qbx_order, fmm_order=False)
from pytools.obj_array import join_fields
sig_sym = sym.var("sig")
knl = LaplaceKernel(2)
op = join_fields(
sym.tangential_derivative(mesh.ambient_dim,
sym.D(knl, sig_sym, qbx_forced_limit=+1)).as_scalar(),
sym.tangential_derivative(mesh.ambient_dim,
sym.D(knl, sig_sym, qbx_forced_limit=-1)).as_scalar(),
)
nodes = density_discr.nodes().with_queue(queue)
angle = cl.clmath.atan2(nodes[1], nodes[0])
n = 10
sig = cl.clmath.sin(n*angle)
dt_sig = n*cl.clmath.cos(n*angle)
res = bind(qbx, op)(queue, sig=sig)
extval = res[0].get()
intval = res[1].get()
pv = 0.5*(extval + intval)
dt_sig_h = dt_sig.get()
import matplotlib.pyplot as pt
pt.plot(extval, label="+num")
pt.plot(pv + dt_sig_h*0.5, label="+ex")
pt.legend(loc="best")
pt.show()
def __init__(self, array_context, mesh, order=None,
quad_tag_to_group_factory=None, mpi_communicator=None):
"""
:param quad_tag_to_group_factory: A mapping from quadrature tags (typically
strings--but may be any hashable/comparable object) to a
:class:`~meshmode.discretization.poly_element.ElementGroupFactory`
indicating with which quadrature discretization the operations are
to be carried out, or *None* to indicate that operations with this
quadrature tag should be carried out with the standard volume
discretization.
"""
self._setup_actx = array_context
from meshmode.discretization.poly_element import \
PolynomialWarpAndBlendGroupFactory
if quad_tag_to_group_factory is None:
if order is None:
raise TypeError("one of 'order' and "
"'quad_tag_to_group_factory' must be given")
quad_tag_to_group_factory = {
sym.QTAG_NONE: PolynomialWarpAndBlendGroupFactory(order=order)}
else:
if order is not None:
quad_tag_to_group_factory = quad_tag_to_group_factory.copy()
if sym.QTAG_NONE in quad_tag_to_group_factory:
raise ValueError("if 'order' is given, "
"'quad_tag_to_group_factory' must not have a "
"key of QTAG_NONE")
quad_tag_to_group_factory[sym.QTAG_NONE] = \
PolynomialWarpAndBlendGroupFactory(order=order)
self.quad_tag_to_group_factory = quad_tag_to_group_factory
from meshmode.discretization import Discretization
self._volume_discr = Discretization(array_context, mesh,
self.group_factory_for_quadrature_tag(sym.QTAG_NONE))
# {{{ management of discretization-scoped common subexpressions
from pytools import UniqueNameGenerator
self._discr_scoped_name_gen = UniqueNameGenerator()
self._discr_scoped_subexpr_to_name = {}
self._discr_scoped_subexpr_name_to_value = {}
# }}}
self._dist_boundary_connections = \
self._set_up_distributed_communication(
mpi_communicator, array_context)
self.mpi_communicator = mpi_communicator
def test_modal_coefficients_by_projection(actx_factory, quad_group_factory):
group_cls = SimplexElementGroup
modal_group_factory = ModalSimplexGroupFactory
actx = actx_factory()
order = 10
m_order = 5
# Make a regular rectangle mesh
mesh = mgen.generate_regular_rect_mesh(a=(0, 0),
b=(5, 3),
npoints_per_axis=(10, 6),
order=order,
group_cls=group_cls)
# Make discretizations
nodal_disc = Discretization(actx, mesh, quad_group_factory(order))
modal_disc = Discretization(actx, mesh, modal_group_factory(m_order))
# Make connections one using quadrature projection
nodal_to_modal_conn_quad = NodalToModalDiscretizationConnection(
nodal_disc, modal_disc, allow_approximate_quad=True)
def f(x):
return 2 * actx.np.sin(5 * x)
x_nodal = thaw(nodal_disc.nodes()[0], actx)
nodal_f = f(x_nodal)
# Compute modal coefficients we expect to get
import modepy as mp
grp, = nodal_disc.groups
shape = mp.Simplex(grp.dim)
space = mp.space_for_shape(shape, order=m_order)
basis = mp.orthonormal_basis_for_space(space, shape)
quad = grp.quadrature_rule()
nodal_f_data = actx.to_numpy(nodal_f[0])
vdm = mp.vandermonde(basis.functions, quad.nodes)
w_diag = np.diag(quad.weights)
modal_data = []
for _, nodal_data in enumerate(nodal_f_data):
# Compute modal data in each element: V.T * W * nodal_data
elem_modal_f = np.dot(vdm.T, np.dot(w_diag, nodal_data))
modal_data.append(elem_modal_f)
modal_data = actx.from_numpy(np.asarray(modal_data))
modal_f_expected = DOFArray(actx, data=(modal_data, ))
# Map nodal coefficients using the quadrature-based projection
modal_f_computed = nodal_to_modal_conn_quad(nodal_f)
err = flat_norm(modal_f_expected - modal_f_computed)
assert err <= 1e-13
def __init__(self, actx, mesh, order):
self.order = order
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import \
PolynomialWarpAndBlendGroupFactory
self.group_factory = PolynomialWarpAndBlendGroupFactory(order=order)
self.volume_discr = Discretization(actx, mesh, self.group_factory)
assert self.volume_discr.dim == 2
def test_parallel_vtk_file(actx_factory, dim):
r"""
Simple test just generates a sample parallel PVTU file
and checks it against the expected result. The expected
result is just a file in the tests directory.
"""
logging.basicConfig(level=logging.INFO)
actx = actx_factory()
nelements = 64
target_order = 4
if dim == 1:
mesh = mgen.make_curve_mesh(mgen.NArmedStarfish(5, 0.25),
np.linspace(0.0, 1.0, nelements + 1),
target_order)
elif dim == 2:
mesh = mgen.generate_torus(5.0, 1.0, order=target_order)
elif dim == 3:
mesh = mgen.generate_warped_rect_mesh(dim,
target_order,
nelements_side=4)
else:
raise ValueError("unknown dimensionality")
from meshmode.discretization import Discretization
discr = Discretization(
actx, mesh, InterpolatoryQuadratureSimplexGroupFactory(target_order))
from meshmode.discretization.visualization import make_visualizer
vis = make_visualizer(actx, discr, target_order)
class FakeComm:
def Get_rank(self): # noqa: N802
return 0
def Get_size(self): # noqa: N802
return 2
file_name_pattern = f"visualizer_vtk_linear_{dim}_{{rank}}.vtu"
pvtu_filename = file_name_pattern.format(rank=0).replace("vtu", "pvtu")
vis.write_parallel_vtk_file(
FakeComm(),
file_name_pattern,
[("scalar", discr.zeros(actx)),
("vector", make_obj_array([discr.zeros(actx) for i in range(dim)]))],
overwrite=True)
import os
assert os.path.exists(pvtu_filename)
import filecmp
assert filecmp.cmp(f"ref-{pvtu_filename}", pvtu_filename)
def test_copy_visualizer(actx_factory, ambient_dim, visualize=True):
actx = actx_factory()
target_order = 4
if ambient_dim == 2:
nelements = 128
mesh = mgen.make_curve_mesh(partial(mgen.ellipse, 1.0),
np.linspace(0.0, 1.0, nelements + 1),
target_order)
elif ambient_dim == 3:
mesh = mgen.generate_icosphere(1.0,
target_order,
uniform_refinement_rounds=2)
else:
raise ValueError(f"unsupported dimension: {ambient_dim}")
from meshmode.mesh.processing import affine_map
translated_mesh = affine_map(mesh,
b=np.array([2.5, 0.0, 0.0][:ambient_dim]))
from meshmode.discretization import Discretization
discr = Discretization(actx, mesh,
PolynomialWarpAndBlendGroupFactory(target_order))
translated_discr = Discretization(
actx, translated_mesh,
PolynomialWarpAndBlendGroupFactory(target_order))
from meshmode.discretization.visualization import make_visualizer
vis = make_visualizer(actx, discr, target_order, force_equidistant=True)
assert vis._vtk_connectivity
assert vis._vtk_lagrange_connectivity
translated_vis = vis.copy_with_same_connectivity(actx, translated_discr)
assert translated_vis._cached_vtk_connectivity is not None
assert translated_vis._cached_vtk_lagrange_connectivity is not None
assert translated_vis._vtk_connectivity \
is vis._vtk_connectivity
assert translated_vis._vtk_lagrange_connectivity \
is vis._vtk_lagrange_connectivity
if not visualize:
return
vis.write_vtk_file(f"visualizer_copy_{ambient_dim}d_orig.vtu", [],
overwrite=True)
translated_vis.write_vtk_file(
f"visualizer_copy_{ambient_dim}d_translated.vtu", [], overwrite=True)
def discr_from_dd(self, dd):
dd = as_dofdesc(dd)
discr_tag = dd.discretization_tag
if discr_tag is DISCR_TAG_MODAL:
return self._modal_discr(dd.domain_tag)
if dd.is_volume():
if discr_tag is not DISCR_TAG_BASE:
return self._discr_tag_volume_discr(discr_tag)
return self._volume_discr
if discr_tag is not DISCR_TAG_BASE:
no_quad_discr = self.discr_from_dd(DOFDesc(dd.domain_tag))
from meshmode.discretization import Discretization
return Discretization(
self._setup_actx, no_quad_discr.mesh,
self.group_factory_for_discretization_tag(discr_tag))
assert discr_tag is DISCR_TAG_BASE
if dd.domain_tag is FACE_RESTR_ALL:
return self._all_faces_volume_connection().to_discr
elif dd.domain_tag is FACE_RESTR_INTERIOR:
return self._interior_faces_connection().to_discr
elif dd.is_boundary_or_partition_interface():
return self._boundary_connection(dd.domain_tag.tag).to_discr
else:
raise ValueError("DOF desc tag not understood: " + str(dd))
def test_geometry(ctx_factory):
cl_ctx = ctx_factory()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue)
nelements = 30
order = 5
mesh = make_curve_mesh(partial(ellipse, 1),
np.linspace(0, 1, nelements+1),
order)
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import \
InterpolatoryQuadratureSimplexGroupFactory
discr = Discretization(actx, mesh,
InterpolatoryQuadratureSimplexGroupFactory(order))
import pytential.symbolic.primitives as prim
area_sym = prim.integral(2, 1, 1)
area = bind(discr, area_sym)(actx)
err = abs(area-2*np.pi)
print(err)
assert err < 1e-3
def test_nonequal_rect_mesh_generation(actx_factory,
dim,
mesh_type,
visualize=False):
"""Test that ``generate_regular_rect_mesh`` works with non-equal arguments
across axes.
"""
actx = actx_factory()
mesh = mgen.generate_regular_rect_mesh(a=(0, ) * dim,
b=(5, 3, 4)[:dim],
npoints_per_axis=(10, 6, 7)[:dim],
order=3,
mesh_type=mesh_type)
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import \
PolynomialWarpAndBlendGroupFactory as GroupFactory
discr = Discretization(actx, mesh, GroupFactory(3))
if visualize:
from meshmode.discretization.visualization import make_visualizer
vis = make_visualizer(actx, discr, 3)
vis.write_vtk_file("nonuniform.vtu", [], overwrite=True)
def starfish_lpot_source(queue, n_arms):
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import (
InterpolatoryQuadratureSimplexGroupFactory)
from meshmode.mesh.generation import make_curve_mesh, NArmedStarfish
mesh = make_curve_mesh(NArmedStarfish(n_arms, 0.8),
np.linspace(0, 1, 1 + PANELS_PER_ARM * n_arms),
TARGET_ORDER)
pre_density_discr = Discretization(
queue.context, mesh,
InterpolatoryQuadratureSimplexGroupFactory(TARGET_ORDER))
lpot_kwargs = DEFAULT_LPOT_KWARGS.copy()
lpot_kwargs.update(target_association_tolerance=0.025,
_expansion_stick_out_factor=TCF,
fmm_order=FMM_ORDER,
qbx_order=QBX_ORDER,
fmm_backend="fmmlib")
from pytential.qbx import QBXLayerPotentialSource
lpot_source = QBXLayerPotentialSource(pre_density_discr,
OVSMP_FACTOR * TARGET_ORDER,
**lpot_kwargs)
lpot_source, _ = lpot_source.with_refinement()
return lpot_source
def _modal_discr(self, domain_tag):
from meshmode.discretization import Discretization
discr_base = self.discr_from_dd(DOFDesc(domain_tag, DISCR_TAG_BASE))
return Discretization(
self._setup_actx, discr_base.mesh,
self.group_factory_for_discretization_tag(DISCR_TAG_MODAL))
def _build_qbx_discr(queue,
ndim=2,
nelements=30,
target_order=7,
qbx_order=4,
curve_f=None):
if curve_f is None:
curve_f = NArmedStarfish(5, 0.25)
if ndim == 2:
mesh = make_curve_mesh(curve_f,
np.linspace(0, 1, nelements + 1),
target_order)
elif ndim == 3:
mesh = generate_torus(10.0, 2.0, order=target_order)
else:
raise ValueError("unsupported ambient dimension")
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import \
InterpolatoryQuadratureSimplexGroupFactory
from pytential.qbx import QBXLayerPotentialSource
density_discr = Discretization(
queue.context, mesh,
InterpolatoryQuadratureSimplexGroupFactory(target_order))
qbx, _ = QBXLayerPotentialSource(density_discr,
fine_order=4 * target_order,
qbx_order=qbx_order,
fmm_order=False).with_refinement()
return qbx
def test_interpolation(actx_factory, name, source_discr_stage, target_granularity):
actx = actx_factory()
nelements = 32
target_order = 7
qbx_order = 4
where = sym.as_dofdesc("test_interpolation")
from_dd = sym.DOFDescriptor(
geometry=where.geometry,
discr_stage=source_discr_stage,
granularity=sym.GRANULARITY_NODE)
to_dd = sym.DOFDescriptor(
geometry=where.geometry,
discr_stage=sym.QBX_SOURCE_QUAD_STAGE2,
granularity=target_granularity)
mesh = mgen.make_curve_mesh(mgen.starfish,
np.linspace(0.0, 1.0, nelements + 1),
target_order)
discr = Discretization(actx, mesh,
InterpolatoryQuadratureSimplexGroupFactory(target_order))
from pytential.qbx import QBXLayerPotentialSource
qbx = QBXLayerPotentialSource(discr,
fine_order=4 * target_order,
qbx_order=qbx_order,
fmm_order=False)
from pytential import GeometryCollection
places = GeometryCollection(qbx, auto_where=where)
sigma_sym = sym.var("sigma")
op_sym = sym.sin(sym.interp(from_dd, to_dd, sigma_sym))
bound_op = bind(places, op_sym, auto_where=where)
def discr_and_nodes(stage):
density_discr = places.get_discretization(where.geometry, stage)
return density_discr, actx.to_numpy(
flatten(density_discr.nodes(), actx)
).reshape(density_discr.ambient_dim, -1)
_, target_nodes = discr_and_nodes(sym.QBX_SOURCE_QUAD_STAGE2)
source_discr, source_nodes = discr_and_nodes(source_discr_stage)
sigma_target = np.sin(la.norm(target_nodes, axis=0))
sigma_dev = unflatten(
thaw(source_discr.nodes()[0], actx),
actx.from_numpy(la.norm(source_nodes, axis=0)), actx)
sigma_target_interp = actx.to_numpy(
flatten(bound_op(actx, sigma=sigma_dev), actx)
)
if name in ("default", "default_explicit", "stage2", "quad"):
error = la.norm(sigma_target_interp - sigma_target) / la.norm(sigma_target)
assert error < 1.0e-10
elif name in ("stage2_center",):
assert len(sigma_target_interp) == 2 * len(sigma_target)
else:
raise ValueError(f"unknown test case name: {name}")
def lpot_source_from_mesh(queue, mesh, lpot_kwargs=None):
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import (
InterpolatoryQuadratureSimplexGroupFactory)
target_order = TARGET_ORDER
pre_density_discr = Discretization(
queue.context, mesh,
InterpolatoryQuadratureSimplexGroupFactory(target_order))
refiner_extra_kwargs = {
"_force_stage2_uniform_refinement_rounds":
(FORCE_STAGE2_UNIFORM_REFINEMENT_ROUNDS),
"_scaled_max_curvature_threshold": (SCALED_MAX_CURVATURE_THRESHOLD),
}
if lpot_kwargs is None:
lpot_kwargs = DEFAULT_LPOT_KWARGS
from pytential.qbx import QBXLayerPotentialSource
lpot_source = QBXLayerPotentialSource(
pre_density_discr,
OVSMP_FACTOR * target_order,
**lpot_kwargs,
)
lpot_source, _ = lpot_source.with_refinement(**refiner_extra_kwargs)
return lpot_source
def get_ellipse_with_ref_mean_curvature(cl_ctx, nelements, aspect=1):
order = 4
mesh = make_curve_mesh(partial(ellipse, aspect),
np.linspace(0, 1, nelements + 1), order)
discr = Discretization(cl_ctx, mesh,
InterpolatoryQuadratureSimplexGroupFactory(order))
with cl.CommandQueue(cl_ctx) as queue:
nodes = discr.nodes().get(queue=queue)
a = 1
b = 1 / aspect
t = np.arctan2(nodes[1] * aspect, nodes[0])
return discr, a * b / ((a * np.sin(t))**2 + (b * np.cos(t))**2)**(3 / 2)
def get_lpot_source(actx: PyOpenCLArrayContext, dim):
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import (
InterpolatoryQuadratureSimplexGroupFactory)
target_order = TARGET_ORDER
if dim == 2:
from meshmode.mesh.generation import starfish, make_curve_mesh
mesh = make_curve_mesh(starfish, np.linspace(0, 1, 50), order=target_order)
elif dim == 3:
from meshmode.mesh.generation import generate_torus
mesh = generate_torus(2, 1, order=target_order)
else:
raise ValueError("unsupported dimension: %d" % dim)
pre_density_discr = Discretization(
actx, mesh,
InterpolatoryQuadratureSimplexGroupFactory(target_order))
lpot_kwargs = DEFAULT_LPOT_KWARGS.copy()
lpot_kwargs.update(
_expansion_stick_out_factor=TCF,
fmm_order=FMM_ORDER,
qbx_order=QBX_ORDER,
fmm_backend="fmmlib",
)
from pytential.qbx import QBXLayerPotentialSource
lpot_source = QBXLayerPotentialSource(
pre_density_discr, OVSMP_FACTOR*target_order,
**lpot_kwargs)
return lpot_source
def discr_from_dd(self, dd):
dd = sym.as_dofdesc(dd)
qtag = dd.quadrature_tag
if dd.is_volume():
if qtag is not sym.QTAG_NONE:
return self._quad_volume_discr(qtag)
return self._volume_discr
if qtag is not sym.QTAG_NONE:
no_quad_discr = self.discr_from_dd(sym.DOFDesc(dd.domain_tag))
from meshmode.discretization import Discretization
return Discretization(self._volume_discr.cl_context,
no_quad_discr.mesh,
self.group_factory_for_quadrature_tag(qtag))
assert qtag is sym.QTAG_NONE
if dd.domain_tag is sym.FACE_RESTR_ALL:
return self._all_faces_volume_connection().to_discr
elif dd.domain_tag is sym.FACE_RESTR_INTERIOR:
return self._interior_faces_connection().to_discr
elif dd.is_boundary():
return self._boundary_connection(dd.domain_tag).to_discr
else:
raise ValueError("DOF desc tag not understood: " + str(dd))
def complete_setup(self):
"""
Returns the tuple ``remote_to_local_bdry_conn``
where `remote_to_local_bdry_conn` is a
:class:`DirectDiscretizationConnection` that gives the connection that
performs data exchange across faces from partition `i_remote_part` to the
local mesh.
"""
remote_bdry_mesh, remote_group_infos = self.mpi_comm.recv(
source=self.i_remote_part, tag=TAG_SEND_BOUNDARY)
logger.debug("rank %d: Received rank %d data", self.i_local_part,
self.i_remote_part)
from meshmode.discretization import Discretization
# Connect local_mesh to remote_mesh
from meshmode.discretization.connection import make_partition_connection
remote_to_local_bdry_conn = make_partition_connection(
self.array_context,
local_bdry_conn=self.local_bdry_conn,
i_local_part=self.i_local_part,
remote_bdry_discr=Discretization(self.array_context,
remote_bdry_mesh,
self.bdry_grp_factory),
remote_group_infos=remote_group_infos)
self.send_req.wait()
return remote_to_local_bdry_conn
def create_discretization(queue, ndim,
nelements=42,
mesh_order=5,
discr_order=5):
ctx = queue.context
# construct mesh
if ndim == 2:
from functools import partial
from meshmode.mesh.generation import make_curve_mesh, ellipse
mesh = make_curve_mesh(partial(ellipse, 2),
np.linspace(0.0, 1.0, nelements + 1),
order=mesh_order)
elif ndim == 3:
from meshmode.mesh.generation import generate_torus
mesh = generate_torus(10.0, 5.0, order=mesh_order)
else:
raise ValueError("Unsupported dimension: {}".format(ndim))
# create discretization
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import \
InterpolatoryQuadratureSimplexGroupFactory
discr = Discretization(ctx, mesh,
InterpolatoryQuadratureSimplexGroupFactory(discr_order))
return discr
def test_tangential_onb(ctx_factory):
cl_ctx = ctx_factory()
queue = cl.CommandQueue(cl_ctx)
from meshmode.mesh.generation import generate_torus
mesh = generate_torus(5, 2, order=3)
discr = Discretization(cl_ctx, mesh,
InterpolatoryQuadratureSimplexGroupFactory(3))
tob = sym.tangential_onb(mesh.ambient_dim)
nvecs = tob.shape[1]
# make sure tangential_onb is mutually orthogonal and normalized
orth_check = bind(
discr,
sym.make_obj_array([
np.dot(tob[:, i], tob[:, j]) - (1 if i == j else 0)
for i in range(nvecs) for j in range(nvecs)
]))(queue)
for i, orth_i in enumerate(orth_check):
assert (cl.clmath.fabs(orth_i) < 1e-13).get().all()
# make sure tangential_onb is orthogonal to normal
orth_check = bind(
discr,
sym.make_obj_array([
np.dot(tob[:, i],
sym.normal(mesh.ambient_dim).as_vector())
for i in range(nvecs)
]))(queue)
for i, orth_i in enumerate(orth_check):
assert (cl.clmath.fabs(orth_i) < 1e-13).get().all()
def test_tangential_onb(actx_factory):
actx = actx_factory()
from meshmode.mesh.generation import generate_torus
mesh = generate_torus(5, 2, order=3)
discr = Discretization(
actx, mesh, InterpolatoryQuadratureSimplexGroupFactory(3))
tob = sym.tangential_onb(mesh.ambient_dim)
nvecs = tob.shape[1]
# make sure tangential_onb is mutually orthogonal and normalized
orth_check = bind(discr, sym.make_obj_array([
np.dot(tob[:, i], tob[:, j]) - (1 if i == j else 0)
for i in range(nvecs) for j in range(nvecs)])
)(actx)
for orth_i in orth_check:
assert actx.to_numpy(
actx.np.all(actx.np.abs(orth_i) < 1e-13)
)
# make sure tangential_onb is orthogonal to normal
orth_check = bind(discr, sym.make_obj_array([
np.dot(tob[:, i], sym.normal(mesh.ambient_dim).as_vector())
for i in range(nvecs)])
)(actx)
for orth_i in orth_check:
assert actx.to_numpy(
actx.np.all(actx.np.abs(orth_i) < 1e-13)
)
def test_merge_and_map(ctx_getter, visualize=False):
from meshmode.mesh.io import generate_gmsh, FileSource
mesh_order = 3
mesh = generate_gmsh(
FileSource("blob-2d.step"),
2,
order=mesh_order,
force_ambient_dim=2,
other_options=["-string", "Mesh.CharacteristicLengthMax = 0.02;"])
from meshmode.mesh.processing import merge_disjoint_meshes, affine_map
mesh2 = affine_map(mesh, A=np.eye(2), b=np.array([5, 0]))
mesh3 = merge_disjoint_meshes((mesh2, mesh))
if visualize:
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import \
PolynomialWarpAndBlendGroupFactory
cl_ctx = ctx_getter()
queue = cl.CommandQueue(cl_ctx)
discr = Discretization(cl_ctx, mesh3,
PolynomialWarpAndBlendGroupFactory(3))
from meshmode.discretization.visualization import make_visualizer
vis = make_visualizer(queue, discr, 1)
vis.write_vtk_file("merged.vtu", [])
def __init__(self, density_discr, fine_order, qbx_order, fmm_order,
# FIXME set debug=False once everything works
expansion_getter=None, real_dtype=np.float64, debug=True):
"""
:arg fine_order: The total degree to which the (upsampled)
underlying quadrature is exact.
:arg fmm_order: `False` for direct calculation. ``None`` will set
a reasonable(-ish?) default.
"""
self.fine_density_discr = Discretization(
density_discr.cl_context, density_discr.mesh,
QuadratureSimplexGroupFactory(fine_order), real_dtype)
from meshmode.discretization.connection import make_same_mesh_connection
with cl.CommandQueue(density_discr.cl_context) as queue:
self.resampler = make_same_mesh_connection(
queue,
self.fine_density_discr, density_discr)
if fmm_order is None:
fmm_order = qbx_order + 1
self.qbx_order = qbx_order
self.density_discr = density_discr
self.fmm_order = fmm_order
self.debug = debug
# only used in non-FMM case
if expansion_getter is None:
from sumpy.expansion.local import LineTaylorLocalExpansion
expansion_getter = LineTaylorLocalExpansion
self.expansion_getter = expansion_getter
def complete_setup(self):
"""
Returns the tuple ``remote_to_local_bdry_conn``
where `remote_to_local_bdry_conn` is a
:class:`DirectDiscretizationConnection` that gives the connection that
performs data exchange across faces from partition `i_remote_part` to the
local mesh.
"""
remote_data = self.mpi_comm.recv(source=self.i_remote_part,
tag=TAG_SEND_BOUNDARY)
logger.debug('rank %d: Received rank %d data', self.i_local_part,
self.i_remote_part)
from meshmode.discretization import Discretization
remote_bdry_mesh = remote_data['bdry_mesh']
remote_bdry = Discretization(self.queue.context, remote_bdry_mesh,
self.bdry_grp_factory)
remote_adj_groups = remote_data['adj']
remote_to_elem_faces = remote_data['to_elem_faces']
remote_to_elem_indices = remote_data['to_elem_indices']
# Connect local_mesh to remote_mesh
from meshmode.discretization.connection import make_partition_connection
remote_to_local_bdry_conn = make_partition_connection(
self.local_bdry_conn, self.i_local_part, remote_bdry,
remote_adj_groups, remote_to_elem_faces, remote_to_elem_indices)
self.send_req.wait()
return remote_to_local_bdry_conn
def test_off_surface_eval(actx_factory, use_fmm, visualize=False):
logging.basicConfig(level=logging.INFO)
actx = actx_factory()
# prevent cache 'splosion
from sympy.core.cache import clear_cache
clear_cache()
nelements = 30
target_order = 8
qbx_order = 3
if use_fmm:
fmm_order = qbx_order
else:
fmm_order = False
mesh = mgen.make_curve_mesh(partial(mgen.ellipse, 3),
np.linspace(0, 1, nelements + 1), target_order)
from pytential.qbx import QBXLayerPotentialSource
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,
)
from pytential.target import PointsTarget
fplot = FieldPlotter(np.zeros(2), extent=0.54, npoints=30)
targets = PointsTarget(actx.freeze(actx.from_numpy(fplot.points)))
places = GeometryCollection((qbx, targets))
density_discr = places.get_discretization(places.auto_source.geometry)
from sumpy.kernel import LaplaceKernel
op = sym.D(LaplaceKernel(2), sym.var("sigma"), qbx_forced_limit=-2)
sigma = density_discr.zeros(actx) + 1
fld_in_vol = bind(places, op)(actx, sigma=sigma)
fld_in_vol_exact = -1
linf_err = actx.to_numpy(
actx.np.linalg.norm(fld_in_vol - fld_in_vol_exact, ord=np.inf))
logger.info("l_inf error: %.12e", linf_err)
if visualize:
fplot.show_scalar_in_matplotlib(actx.to_numpy(fld_in_vol))
import matplotlib.pyplot as pt
pt.colorbar()
pt.show()
assert linf_err < 1e-3
def test_boundary_interpolation(ctx_getter):
cl_ctx = ctx_getter()
queue = cl.CommandQueue(cl_ctx)
from meshmode.mesh.io import generate_gmsh, FileSource
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import \
InterpolatoryQuadratureSimplexGroupFactory
from meshmode.discretization.connection import make_boundary_restriction
from pytools.convergence import EOCRecorder
eoc_rec = EOCRecorder()
order = 4
for h in [1e-1, 3e-2, 1e-2]:
print("BEGIN GEN")
mesh = generate_gmsh(
FileSource("blob-2d.step"), 2, order=order,
force_ambient_dim=2,
other_options=[
"-string", "Mesh.CharacteristicLengthMax = %s;" % h]
)
print("END GEN")
vol_discr = Discretization(cl_ctx, mesh,
InterpolatoryQuadratureSimplexGroupFactory(order))
print("h=%s -> %d elements" % (
h, sum(mgrp.nelements for mgrp in mesh.groups)))
x = vol_discr.nodes()[0].with_queue(queue)
f = 0.1*cl.clmath.sin(30*x)
bdry_mesh, bdry_discr, bdry_connection = make_boundary_restriction(
queue, vol_discr, InterpolatoryQuadratureSimplexGroupFactory(order))
bdry_x = bdry_discr.nodes()[0].with_queue(queue)
bdry_f = 0.1*cl.clmath.sin(30*bdry_x)
bdry_f_2 = bdry_connection(queue, f)
err = la.norm((bdry_f-bdry_f_2).get(), np.inf)
eoc_rec.add_data_point(h, err)
print(eoc_rec)
assert eoc_rec.order_estimate() >= order-0.5
def test_unregularized_off_surface_fmm_vs_direct(ctx_getter):
cl_ctx = ctx_getter()
queue = cl.CommandQueue(cl_ctx)
nelements = 300
target_order = 8
fmm_order = 4
mesh = make_curve_mesh(WobblyCircle.random(8, seed=30),
np.linspace(0, 1, nelements+1),
target_order)
from pytential.unregularized import UnregularizedLayerPotentialSource
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import \
InterpolatoryQuadratureSimplexGroupFactory
density_discr = Discretization(
cl_ctx, mesh, InterpolatoryQuadratureSimplexGroupFactory(target_order))
direct = UnregularizedLayerPotentialSource(
density_discr,
fmm_order=False,
)
fmm = direct.copy(
fmm_level_to_order=lambda kernel, kernel_args, tree, level: fmm_order)
sigma = density_discr.zeros(queue) + 1
fplot = FieldPlotter(np.zeros(2), extent=5, npoints=100)
from pytential.target import PointsTarget
ptarget = PointsTarget(fplot.points)
from sumpy.kernel import LaplaceKernel
op = sym.D(LaplaceKernel(2), sym.var("sigma"), qbx_forced_limit=None)
direct_fld_in_vol = bind((direct, ptarget), op)(queue, sigma=sigma)
fmm_fld_in_vol = bind((fmm, ptarget), op)(queue, sigma=sigma)
err = cl.clmath.fabs(fmm_fld_in_vol - direct_fld_in_vol)
linf_err = cl.array.max(err).get()
print("l_inf error:", linf_err)
assert linf_err < 5e-3
def test_sanity_qhull_nd(ctx_getter, dim, order):
pytest.importorskip("scipy")
logging.basicConfig(level=logging.INFO)
ctx = ctx_getter()
queue = cl.CommandQueue(ctx)
from scipy.spatial import Delaunay
verts = np.random.rand(1000, dim)
dtri = Delaunay(verts)
from meshmode.mesh.io import from_vertices_and_simplices
mesh = from_vertices_and_simplices(dtri.points.T, dtri.simplices,
fix_orientation=True)
from meshmode.discretization import Discretization
low_discr = Discretization(ctx, mesh,
PolynomialEquidistantGroupFactory(order))
high_discr = Discretization(ctx, mesh,
PolynomialEquidistantGroupFactory(order+1))
from meshmode.discretization.connection import make_same_mesh_connection
cnx = make_same_mesh_connection(high_discr, low_discr)
def f(x):
return 0.1*cl.clmath.sin(x)
x_low = low_discr.nodes()[0].with_queue(queue)
f_low = f(x_low)
x_high = high_discr.nodes()[0].with_queue(queue)
f_high_ref = f(x_high)
f_high_num = cnx(queue, f_low)
err = (f_high_ref-f_high_num).get()
err = la.norm(err, np.inf)/la.norm(f_high_ref.get(), np.inf)
print(err)
assert err < 1e-2
def get_ellipse_with_ref_mean_curvature(cl_ctx, aspect=1):
nelements = 20
order = 16
mesh = make_curve_mesh(
partial(ellipse, aspect),
np.linspace(0, 1, nelements+1),
order)
a = 1
b = 1/aspect
discr = Discretization(cl_ctx, mesh,
InterpolatoryQuadratureSimplexGroupFactory(order))
with cl.CommandQueue(cl_ctx) as queue:
nodes = discr.nodes().get(queue=queue)
t = np.arctan2(nodes[1] * aspect, nodes[0])
return discr, a*b / ((a*np.sin(t))**2 + (b*np.cos(t))**2)**(3/2)
def timing_run(nx, ny):
import logging
logging.basicConfig(level=logging.WARNING) # INFO for more progress info
cl_ctx = cl.create_some_context()
queue = cl.CommandQueue(cl_ctx)
mesh = make_mesh(nx=nx, ny=ny)
density_discr = Discretization(
cl_ctx, mesh,
InterpolatoryQuadratureSimplexGroupFactory(bdry_quad_order))
from pytential.qbx import (
QBXLayerPotentialSource, QBXTargetAssociationFailedException)
qbx = QBXLayerPotentialSource(
density_discr, fine_order=bdry_ovsmp_quad_order, qbx_order=qbx_order,
fmm_order=fmm_order
)
# {{{ describe bvp
from sumpy.kernel import HelmholtzKernel
kernel = HelmholtzKernel(2)
cse = sym.cse
sigma_sym = sym.var("sigma")
sqrt_w = sym.sqrt_jac_q_weight(2)
inv_sqrt_w_sigma = cse(sigma_sym/sqrt_w)
# Brakhage-Werner parameter
alpha = 1j
# -1 for interior Dirichlet
# +1 for exterior Dirichlet
loc_sign = +1
bdry_op_sym = (-loc_sign*0.5*sigma_sym
+ sqrt_w*(
alpha*sym.S(kernel, inv_sqrt_w_sigma, k=sym.var("k"))
- sym.D(kernel, inv_sqrt_w_sigma, k=sym.var("k"))
))
# }}}
bound_op = bind(qbx, bdry_op_sym)
# {{{ fix rhs and solve
mode_nr = 3
nodes = density_discr.nodes().with_queue(queue)
angle = cl.clmath.atan2(nodes[1], nodes[0])
sigma = cl.clmath.cos(mode_nr*angle)
# }}}
# {{{ postprocess/visualize
repr_kwargs = dict(k=sym.var("k"), qbx_forced_limit=+1)
sym_op = sym.S(kernel, sym.var("sigma"), **repr_kwargs)
bound_op = bind(qbx, sym_op)
print("FMM WARM-UP RUN 1: %d elements" % mesh.nelements)
bound_op(queue, sigma=sigma, k=k)
print("FMM WARM-UP RUN 2: %d elements" % mesh.nelements)
bound_op(queue, sigma=sigma, k=k)
queue.finish()
print("FMM TIMING RUN: %d elements" % mesh.nelements)
from time import time
t_start = time()
bound_op(queue, sigma=sigma, k=k)
queue.finish()
elapsed = time()-t_start
print("FMM TIMING RUN DONE: %d elements -> %g s"
% (mesh.nelements, elapsed))
return (mesh.nelements, elapsed)
if 0:
from sumpy.visualization import FieldPlotter
fplot = FieldPlotter(np.zeros(2), extent=5, npoints=1500)
targets = cl.array.to_device(queue, fplot.points)
qbx_tgt_tol = qbx.copy(target_association_tolerance=0.05)
indicator_qbx = qbx_tgt_tol.copy(
fmm_level_to_order=lambda lev: 7, qbx_order=2)
ones_density = density_discr.zeros(queue)
ones_density.fill(1)
indicator = bind(
(indicator_qbx, PointsTarget(targets)),
sym_op)(
queue, sigma=ones_density).get()
qbx_stick_out = qbx.copy(target_stick_out_factor=0.1)
try:
fld_in_vol = bind(
(qbx_stick_out, PointsTarget(targets)),
sym_op)(queue, sigma=sigma, k=k).get()
except QBXTargetAssociationFailedException as e:
fplot.write_vtk_file(
"failed-targets.vts",
[
("failed", e.failed_target_flags.get(queue))
]
)
raise
#fplot.show_scalar_in_mayavi(fld_in_vol.real, max_val=5)
fplot.write_vtk_file(
"potential-scaling.vts",
[
("potential", fld_in_vol),
("indicator", indicator)
]
)
#kernel = OneKernel()
from meshmode.mesh.generation import ( # noqa
make_curve_mesh, starfish, ellipse, drop)
mesh = make_curve_mesh(
#lambda t: ellipse(1, t),
starfish,
np.linspace(0, 1, nelements+1),
target_order)
from pytential.qbx import QBXLayerPotentialSource
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import \
InterpolatoryQuadratureSimplexGroupFactory
density_discr = Discretization(
cl_ctx, mesh, InterpolatoryQuadratureSimplexGroupFactory(target_order))
qbx = QBXLayerPotentialSource(density_discr, 4*target_order, qbx_order,
fmm_order=qbx_order)
nodes = density_discr.nodes().with_queue(queue)
angle = cl.clmath.atan2(nodes[1], nodes[0])
from pytential import bind, sym
d = sym.Derivative()
#op = d.nabla[0] * d(sym.S(kernel, sym.var("sigma")))
op = sym.D(kernel, sym.var("sigma"))
#op = sym.S(kernel, sym.var("sigma"))
sigma = cl.clmath.cos(mode_nr*angle)
def refine_and_generate_chart_function(mesh, filename, function):
from time import clock
cl_ctx = cl.create_some_context()
queue = cl.CommandQueue(cl_ctx)
print("NELEMENTS: ", mesh.nelements)
#print mesh
for i in range(len(mesh.groups[0].vertex_indices[0])):
for k in range(len(mesh.vertices)):
print(mesh.vertices[k, i])
#check_nodal_adj_against_geometry(mesh);
r = Refiner(mesh)
#random.seed(0)
#times = 3
num_elements = []
time_t = []
#nelements = mesh.nelements
while True:
print("NELS:", mesh.nelements)
#flags = get_corner_flags(mesh)
flags = get_function_flags(mesh, function)
nels = 0
for i in flags:
if i:
nels += 1
if nels == 0:
break
print("LKJASLFKJALKASF:", nels)
num_elements.append(nels)
#flags = get_corner_flags(mesh)
beg = clock()
mesh = r.refine(flags)
end = clock()
time_taken = end - beg
time_t.append(time_taken)
#if nelements == mesh.nelements:
#break
#nelements = mesh.nelements
#from meshmode.mesh.visualization import draw_2d_mesh
#draw_2d_mesh(mesh, True, True, True, fill=None)
#import matplotlib.pyplot as pt
#pt.show()
#poss_flags = np.zeros(len(mesh.groups[0].vertex_indices))
#for i in range(0, len(flags)):
# poss_flags[i] = flags[i]
#for i in range(len(flags), len(poss_flags)):
# poss_flags[i] = 1
import matplotlib.pyplot as pt
pt.xlabel('Number of elements being refined')
pt.ylabel('Time taken')
pt.plot(num_elements, time_t, "o")
pt.savefig(filename, format='pdf')
pt.clf()
print('DONE REFINING')
'''
flags = np.zeros(len(mesh.groups[0].vertex_indices))
flags[0] = 1
flags[1] = 1
mesh = r.refine(flags)
flags = np.zeros(len(mesh.groups[0].vertex_indices))
flags[0] = 1
flags[1] = 1
flags[2] = 1
mesh = r.refine(flags)
'''
#check_nodal_adj_against_geometry(mesh)
#r.print_rays(70)
#r.print_rays(117)
#r.print_hanging_elements(10)
#r.print_hanging_elements(117)
#r.print_hanging_elements(757)
#from meshmode.mesh.visualization import draw_2d_mesh
#draw_2d_mesh(mesh, False, False, False, fill=None)
#import matplotlib.pyplot as pt
#pt.show()
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import \
PolynomialWarpAndBlendGroupFactory
discr = Discretization(
cl_ctx, mesh, PolynomialWarpAndBlendGroupFactory(order))
from meshmode.discretization.visualization import make_visualizer
vis = make_visualizer(queue, discr, order)
remove_if_exists("connectivity2.vtu")
remove_if_exists("geometry2.vtu")
vis.write_vtk_file("geometry2.vtu", [
("f", discr.nodes()[0]),
])
from meshmode.discretization.visualization import \
write_nodal_adjacency_vtk_file
write_nodal_adjacency_vtk_file("connectivity2.vtu",
mesh)
def run_int_eq_test(
cl_ctx, queue, curve_f, nelements, qbx_order, bc_type, loc_sign, k,
target_order, source_order):
mesh = make_curve_mesh(curve_f,
np.linspace(0, 1, nelements+1),
target_order)
if 0:
from pytential.visualization import show_mesh
show_mesh(mesh)
pt.gca().set_aspect("equal")
pt.show()
from pytential.qbx import QBXLayerPotentialSource
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import \
InterpolatoryQuadratureSimplexGroupFactory
density_discr = Discretization(
cl_ctx, mesh, InterpolatoryQuadratureSimplexGroupFactory(target_order))
if source_order is None:
source_order = 4*target_order
qbx = QBXLayerPotentialSource(
density_discr, fine_order=source_order, qbx_order=qbx_order,
# Don't use FMM for now
fmm_order=False)
# {{{ set up operator
from pytential.symbolic.pde.scalar import (
DirichletOperator,
NeumannOperator)
from sumpy.kernel import LaplaceKernel, HelmholtzKernel, AxisTargetDerivative
if k:
knl = HelmholtzKernel(2)
knl_kwargs = {"k": k}
else:
knl = LaplaceKernel(2)
knl_kwargs = {}
if knl.is_complex_valued:
dtype = np.complex128
else:
dtype = np.float64
if bc_type == "dirichlet":
op = DirichletOperator((knl, knl_kwargs), loc_sign, use_l2_weighting=True)
elif bc_type == "neumann":
op = NeumannOperator((knl, knl_kwargs), loc_sign, use_l2_weighting=True,
use_improved_operator=False)
else:
assert False
op_u = op.operator(sym.var("u"))
# }}}
# {{{ set up test data
inner_radius = 0.1
outer_radius = 2
if loc_sign < 0:
test_src_geo_radius = outer_radius
test_tgt_geo_radius = inner_radius
else:
test_src_geo_radius = inner_radius
test_tgt_geo_radius = outer_radius
point_sources = make_circular_point_group(10, test_src_geo_radius,
func=lambda x: x**1.5)
test_targets = make_circular_point_group(20, test_tgt_geo_radius)
np.random.seed(22)
source_charges = np.random.randn(point_sources.shape[1])
source_charges[-1] = -np.sum(source_charges[:-1])
source_charges = source_charges.astype(dtype)
assert np.sum(source_charges) < 1e-15
# }}}
if 0:
# show geometry, centers, normals
nodes_h = density_discr.nodes().get(queue=queue)
pt.plot(nodes_h[0], nodes_h[1], "x-")
normal = bind(density_discr, sym.normal())(queue).as_vector(np.object)
pt.quiver(nodes_h[0], nodes_h[1], normal[0].get(queue), normal[1].get(queue))
pt.gca().set_aspect("equal")
pt.show()
# {{{ establish BCs
from sumpy.p2p import P2P
pot_p2p = P2P(cl_ctx,
[knl], exclude_self=False, value_dtypes=dtype)
evt, (test_direct,) = pot_p2p(
queue, test_targets, point_sources, [source_charges],
out_host=False, **knl_kwargs)
nodes = density_discr.nodes()
evt, (src_pot,) = pot_p2p(
queue, nodes, point_sources, [source_charges],
**knl_kwargs)
grad_p2p = P2P(cl_ctx,
[AxisTargetDerivative(0, knl), AxisTargetDerivative(1, knl)],
exclude_self=False, value_dtypes=dtype)
evt, (src_grad0, src_grad1) = grad_p2p(
queue, nodes, point_sources, [source_charges],
**knl_kwargs)
if bc_type == "dirichlet":
bc = src_pot
elif bc_type == "neumann":
normal = bind(density_discr, sym.normal())(queue).as_vector(np.object)
bc = (src_grad0*normal[0] + src_grad1*normal[1])
# }}}
# {{{ solve
bound_op = bind(qbx, op_u)
rhs = bind(density_discr, op.prepare_rhs(sym.var("bc")))(queue, bc=bc)
from pytential.solve import gmres
gmres_result = gmres(
bound_op.scipy_op(queue, "u", k=k),
rhs, tol=1e-14, progress=True,
hard_failure=False)
u = gmres_result.solution
print("gmres state:", gmres_result.state)
if 0:
# {{{ build matrix for spectrum check
from sumpy.tools import build_matrix
mat = build_matrix(bound_op.scipy_op("u"))
w, v = la.eig(mat)
if 0:
pt.imshow(np.log10(1e-20+np.abs(mat)))
pt.colorbar()
pt.show()
#assert abs(s[-1]) < 1e-13, "h
#assert abs(s[-2]) > 1e-7
#from pudb import set_trace; set_trace()
# }}}
# }}}
# {{{ error check
from pytential.target import PointsTarget
bound_tgt_op = bind((qbx, PointsTarget(test_targets)),
op.representation(sym.var("u")))
test_via_bdry = bound_tgt_op(queue, u=u, k=k)
err = test_direct-test_via_bdry
err = err.get()
test_direct = test_direct.get()
test_via_bdry = test_via_bdry.get()
# {{{ remove effect of net source charge
if k == 0 and bc_type == "neumann" and loc_sign == -1:
# remove constant offset in interior Laplace Neumann error
tgt_ones = np.ones_like(test_direct)
tgt_ones = tgt_ones/la.norm(tgt_ones)
err = err - np.vdot(tgt_ones, err)*tgt_ones
# }}}
rel_err_2 = la.norm(err)/la.norm(test_direct)
rel_err_inf = la.norm(err, np.inf)/la.norm(test_direct, np.inf)
# }}}
print("rel_err_2: %g rel_err_inf: %g" % (rel_err_2, rel_err_inf))
# {{{ test tangential derivative
bound_t_deriv_op = bind(qbx,
op.representation(
sym.var("u"), map_potentials=sym.tangential_derivative,
qbx_forced_limit=loc_sign))
#print(bound_t_deriv_op.code)
tang_deriv_from_src = bound_t_deriv_op(queue, u=u).as_scalar().get()
tangent = bind(
density_discr,
sym.pseudoscalar()/sym.area_element())(queue).as_vector(np.object)
tang_deriv_ref = (src_grad0 * tangent[0] + src_grad1 * tangent[1]).get()
if 0:
pt.plot(tang_deriv_ref.real)
pt.plot(tang_deriv_from_src.real)
pt.show()
td_err = tang_deriv_from_src - tang_deriv_ref
rel_td_err_inf = la.norm(td_err, np.inf)/la.norm(tang_deriv_ref, np.inf)
print("rel_td_err_inf: %g" % rel_td_err_inf)
# }}}
# {{{ plotting
if 0:
fplot = FieldPlotter(np.zeros(2),
extent=1.25*2*max(test_src_geo_radius, test_tgt_geo_radius),
npoints=200)
#pt.plot(u)
#pt.show()
evt, (fld_from_src,) = pot_p2p(
queue, fplot.points, point_sources, [source_charges],
**knl_kwargs)
fld_from_bdry = bind(
(qbx, PointsTarget(fplot.points)),
op.representation(sym.var("u"))
)(queue, u=u, k=k)
fld_from_src = fld_from_src.get()
fld_from_bdry = fld_from_bdry.get()
nodes = density_discr.nodes().get(queue=queue)
def prep():
pt.plot(point_sources[0], point_sources[1], "o",
label="Monopole 'Point Charges'")
pt.plot(test_targets[0], test_targets[1], "v",
label="Observation Points")
pt.plot(nodes[0], nodes[1], "k-",
label=r"$\Gamma$")
from matplotlib.cm import get_cmap
cmap = get_cmap()
cmap._init()
if 0:
cmap._lut[(cmap.N*99)//100:, -1] = 0 # make last percent transparent?
prep()
if 1:
pt.subplot(131)
pt.title("Field error (loc_sign=%s)" % loc_sign)
log_err = np.log10(1e-20+np.abs(fld_from_src-fld_from_bdry))
log_err = np.minimum(-3, log_err)
fplot.show_scalar_in_matplotlib(log_err, cmap=cmap)
#from matplotlib.colors import Normalize
#im.set_norm(Normalize(vmin=-6, vmax=1))
cb = pt.colorbar(shrink=0.9)
cb.set_label(r"$\log_{10}(\mathdefault{Error})$")
if 1:
pt.subplot(132)
prep()
pt.title("Source Field")
fplot.show_scalar_in_matplotlib(
fld_from_src.real, max_val=3)
pt.colorbar(shrink=0.9)
if 1:
pt.subplot(133)
prep()
pt.title("Solved Field")
fplot.show_scalar_in_matplotlib(
fld_from_bdry.real, max_val=3)
pt.colorbar(shrink=0.9)
# total field
#fplot.show_scalar_in_matplotlib(
#fld_from_src.real+fld_from_bdry.real, max_val=0.1)
#pt.colorbar()
pt.legend(loc="best", prop=dict(size=15))
from matplotlib.ticker import NullFormatter
pt.gca().xaxis.set_major_formatter(NullFormatter())
pt.gca().yaxis.set_major_formatter(NullFormatter())
pt.gca().set_aspect("equal")
if 0:
border_factor_top = 0.9
border_factor = 0.3
xl, xh = pt.xlim()
xhsize = 0.5*(xh-xl)
pt.xlim(xl-border_factor*xhsize, xh+border_factor*xhsize)
yl, yh = pt.ylim()
yhsize = 0.5*(yh-yl)
pt.ylim(yl-border_factor_top*yhsize, yh+border_factor*yhsize)
#pt.savefig("helmholtz.pdf", dpi=600)
pt.show()
# }}}
class Result(Record):
pass
return Result(
rel_err_2=rel_err_2,
rel_err_inf=rel_err_inf,
rel_td_err_inf=rel_td_err_inf,
gmres_result=gmres_result)
def test_ellipse_eigenvalues(ctx_getter, ellipse_aspect, mode_nr, qbx_order):
logging.basicConfig(level=logging.INFO)
print("ellipse_aspect: %s, mode_nr: %d, qbx_order: %d" % (
ellipse_aspect, mode_nr, qbx_order))
cl_ctx = ctx_getter()
queue = cl.CommandQueue(cl_ctx)
target_order = 7
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import \
InterpolatoryQuadratureSimplexGroupFactory
from pytential.qbx import QBXLayerPotentialSource
from pytools.convergence import EOCRecorder
s_eoc_rec = EOCRecorder()
d_eoc_rec = EOCRecorder()
sp_eoc_rec = EOCRecorder()
if ellipse_aspect != 1:
nelements_values = [60, 100, 150, 200]
else:
nelements_values = [30, 70]
# See
#
# [1] G. J. Rodin and O. Steinbach, "Boundary Element Preconditioners
# for Problems Defined on Slender Domains", SIAM Journal on Scientific
# Computing, Vol. 24, No. 4, pg. 1450, 2003.
# http://dx.doi.org/10.1137/S1064827500372067
for nelements in nelements_values:
mesh = make_curve_mesh(partial(ellipse, ellipse_aspect),
np.linspace(0, 1, nelements+1),
target_order)
fmm_order = qbx_order
if fmm_order > 3:
# FIXME: for now
fmm_order = False
density_discr = Discretization(
cl_ctx, mesh,
InterpolatoryQuadratureSimplexGroupFactory(target_order))
qbx = QBXLayerPotentialSource(density_discr, 4*target_order,
qbx_order, fmm_order=fmm_order)
nodes = density_discr.nodes().with_queue(queue)
if 0:
# plot geometry, centers, normals
centers = qbx.centers(density_discr, 1)
nodes_h = nodes.get()
centers_h = [centers[0].get(), centers[1].get()]
pt.plot(nodes_h[0], nodes_h[1], "x-")
pt.plot(centers_h[0], centers_h[1], "o")
normal = bind(qbx, sym.normal())(queue).as_vector(np.object)
pt.quiver(nodes_h[0], nodes_h[1],
normal[0].get(), normal[1].get())
pt.gca().set_aspect("equal")
pt.show()
angle = cl.clmath.atan2(nodes[1]*ellipse_aspect, nodes[0])
ellipse_fraction = ((1-ellipse_aspect)/(1+ellipse_aspect))**mode_nr
# (2.6) in [1]
J = cl.clmath.sqrt( # noqa
cl.clmath.sin(angle)**2
+ (1/ellipse_aspect)**2 * cl.clmath.cos(angle)**2)
# {{{ single layer
sigma = cl.clmath.cos(mode_nr*angle)/J
s_sigma_op = bind(qbx, sym.S(0, sym.var("sigma")))
s_sigma = s_sigma_op(queue=queue, sigma=sigma)
# SIGN BINGO! :)
s_eigval = 1/(2*mode_nr) * (1 + (-1)**mode_nr * ellipse_fraction)
# (2.12) in [1]
s_sigma_ref = s_eigval*J*sigma
if 0:
#pt.plot(s_sigma.get(), label="result")
#pt.plot(s_sigma_ref.get(), label="ref")
pt.plot((s_sigma_ref-s_sigma).get(), label="err")
pt.legend()
pt.show()
s_err = (
norm(density_discr, queue, s_sigma - s_sigma_ref)
/
norm(density_discr, queue, s_sigma_ref))
s_eoc_rec.add_data_point(1/nelements, s_err)
# }}}
# {{{ double layer
sigma = cl.clmath.cos(mode_nr*angle)
d_sigma_op = bind(qbx, sym.D(0, sym.var("sigma")))
d_sigma = d_sigma_op(queue=queue, sigma=sigma)
# SIGN BINGO! :)
d_eigval = -(-1)**mode_nr * 1/2*ellipse_fraction
d_sigma_ref = d_eigval*sigma
if 0:
pt.plot(d_sigma.get(), label="result")
pt.plot(d_sigma_ref.get(), label="ref")
pt.legend()
pt.show()
if ellipse_aspect == 1:
d_ref_norm = norm(density_discr, queue, sigma)
else:
d_ref_norm = norm(density_discr, queue, d_sigma_ref)
d_err = (
norm(density_discr, queue, d_sigma - d_sigma_ref)
/
d_ref_norm)
d_eoc_rec.add_data_point(1/nelements, d_err)
# }}}
if ellipse_aspect == 1:
# {{{ S'
sigma = cl.clmath.cos(mode_nr*angle)
sp_sigma_op = bind(qbx, sym.Sp(0, sym.var("sigma")))
sp_sigma = sp_sigma_op(queue=queue, sigma=sigma)
sp_eigval = 0
sp_sigma_ref = sp_eigval*sigma
sp_err = (
norm(density_discr, queue, sp_sigma - sp_sigma_ref)
/
norm(density_discr, queue, sigma))
sp_eoc_rec.add_data_point(1/nelements, sp_err)
# }}}
print("Errors for S:")
print(s_eoc_rec)
required_order = qbx_order + 1
assert s_eoc_rec.order_estimate() > required_order - 1.5
print("Errors for D:")
print(d_eoc_rec)
required_order = qbx_order
assert d_eoc_rec.order_estimate() > required_order - 1.5
if ellipse_aspect == 1:
print("Errors for S':")
print(sp_eoc_rec)
required_order = qbx_order
assert sp_eoc_rec.order_estimate() > required_order - 1.5
def main():
logging.basicConfig(level=logging.INFO)
nelements = 60
qbx_order = 3
k_fac = 4
k0 = 3*k_fac
k1 = 2.9*k_fac
mesh_order = 10
bdry_quad_order = mesh_order
bdry_ovsmp_quad_order = bdry_quad_order * 4
fmm_order = qbx_order * 2
cl_ctx = cl.create_some_context()
queue = cl.CommandQueue(cl_ctx)
from meshmode.mesh.generation import ellipse, make_curve_mesh
from functools import partial
mesh = make_curve_mesh(
partial(ellipse, 3),
np.linspace(0, 1, nelements+1),
mesh_order)
density_discr = Discretization(
cl_ctx, mesh,
InterpolatoryQuadratureSimplexGroupFactory(bdry_quad_order))
logger.info("%d elements" % mesh.nelements)
# from meshmode.discretization.visualization import make_visualizer
# bdry_vis = make_visualizer(queue, density_discr, 20)
# {{{ solve bvp
from sumpy.kernel import HelmholtzKernel
kernel = HelmholtzKernel(2)
beta = 2.5*k_fac
K0 = np.sqrt(k0**2-beta**2)
K1 = np.sqrt(k1**2-beta**2)
from pytential.symbolic.pde.scalar import DielectricSDRep2DBoundaryOperator
pde_op = DielectricSDRep2DBoundaryOperator(
mode='tm',
k_vacuum=1,
interfaces=((0, 1, sym.DEFAULT_SOURCE),),
domain_k_exprs=(k0, k1),
beta=beta)
op_unknown_sym = pde_op.make_unknown("unknown")
representation0_sym = pde_op.representation(op_unknown_sym, 0)
representation1_sym = pde_op.representation(op_unknown_sym, 1)
from pytential.qbx import QBXLayerPotentialSource
qbx = QBXLayerPotentialSource(
density_discr, fine_order=bdry_ovsmp_quad_order, qbx_order=qbx_order,
fmm_order=fmm_order
)
bound_pde_op = bind(qbx, pde_op.operator(op_unknown_sym))
# in inner domain
sources_1 = make_obj_array(list(np.array([
[-1.5, 0.5]
]).T.copy()))
strengths_1 = np.array([1])
from sumpy.p2p import P2P
pot_p2p = P2P(cl_ctx, [kernel], exclude_self=False)
_, (Einc,) = pot_p2p(queue, density_discr.nodes(), sources_1, [strengths_1],
out_host=False, k=K0)
sqrt_w = bind(density_discr, sym.sqrt_jac_q_weight())(queue)
bvp_rhs = np.zeros(len(pde_op.bcs), dtype=np.object)
for i_bc, terms in enumerate(pde_op.bcs):
for term in terms:
assert term.i_interface == 0
assert term.field_kind == pde_op.field_kind_e
if term.direction == pde_op.dir_none:
bvp_rhs[i_bc] += (
term.coeff_outer * (-Einc)
)
elif term.direction == pde_op.dir_normal:
# no jump in normal derivative
bvp_rhs[i_bc] += 0*Einc
else:
raise NotImplementedError("direction spec in RHS")
bvp_rhs[i_bc] *= sqrt_w
from pytential.solve import gmres
gmres_result = gmres(
bound_pde_op.scipy_op(queue, "unknown", dtype=np.complex128,
domains=[sym.DEFAULT_TARGET]*2, K0=K0, K1=K1),
bvp_rhs, tol=1e-6, progress=True,
hard_failure=True, stall_iterations=0)
# }}}
unknown = gmres_result.solution
# {{{ visualize
from pytential.qbx import QBXLayerPotentialSource
lap_qbx = QBXLayerPotentialSource(
density_discr, fine_order=bdry_ovsmp_quad_order, qbx_order=qbx_order,
fmm_order=qbx_order
)
from sumpy.visualization import FieldPlotter
fplot = FieldPlotter(np.zeros(2), extent=5, npoints=300)
from pytential.target import PointsTarget
fld0 = bind(
(qbx, PointsTarget(fplot.points)),
representation0_sym)(queue, unknown=unknown, K0=K0).get()
fld1 = bind(
(qbx, PointsTarget(fplot.points)),
representation1_sym)(queue, unknown=unknown, K1=K1).get()
ones = cl.array.empty(queue, density_discr.nnodes, np.float64)
dom1_indicator = -bind(
(lap_qbx, PointsTarget(fplot.points)),
sym.D(0, sym.var("sigma")))(
queue, sigma=ones.fill(1)).get()
_, (fld_inc_vol,) = pot_p2p(queue, fplot.points, sources_1, [strengths_1],
out_host=True, k=K0)
#fplot.show_scalar_in_mayavi(fld_in_vol.real, max_val=5)
fplot.write_vtk_file(
"potential.vts",
[
("fld0", fld0),
("fld1", fld1),
("fld_inc_vol", fld_inc_vol),
("fld_total", (
(fld_inc_vol + fld0)*(1-dom1_indicator)
+
fld1*dom1_indicator
)),
("dom1_indicator", dom1_indicator),
]
)
def main():
import logging
logging.basicConfig(level=logging.INFO)
ctx = cl.create_some_context()
queue = cl.CommandQueue(ctx)
mesh = generate_gmsh(
FileSource("circle.step"), 2, order=mesh_order,
force_ambient_dim=2,
other_options=["-string", "Mesh.CharacteristicLengthMax = %g;" % h]
)
logger.info("%d elements" % mesh.nelements)
# {{{ discretizations and connections
vol_discr = Discretization(ctx, mesh,
InterpolatoryQuadratureSimplexGroupFactory(vol_quad_order))
ovsmp_vol_discr = Discretization(ctx, mesh,
InterpolatoryQuadratureSimplexGroupFactory(vol_ovsmp_quad_order))
from meshmode.discretization.connection import (
make_boundary_restriction, make_same_mesh_connection)
bdry_mesh, bdry_discr, bdry_connection = make_boundary_restriction(
queue, vol_discr,
InterpolatoryQuadratureSimplexGroupFactory(bdry_quad_order))
vol_to_ovsmp_vol = make_same_mesh_connection(
queue, ovsmp_vol_discr, vol_discr)
# }}}
# {{{ visualizers
vol_vis = make_visualizer(queue, vol_discr, 20)
bdry_vis = make_visualizer(queue, bdry_discr, 20)
# }}}
vol_x = vol_discr.nodes().with_queue(queue)
ovsmp_vol_x = ovsmp_vol_discr.nodes().with_queue(queue)
rhs = rhs_func(vol_x[0], vol_x[1])
poisson_true_sol = sol_func(vol_x[0], vol_x[1])
vol_vis.write_vtk_file("volume.vtu", [("f", rhs)])
bdry_normals = bind(bdry_discr, p.normal())(queue).as_vector(dtype=object)
bdry_vis.write_vtk_file("boundary.vtu", [
("normals", bdry_normals)
])
bdry_nodes = bdry_discr.nodes().with_queue(queue)
bdry_f = rhs_func(bdry_nodes[0], bdry_nodes[1])
bdry_f_2 = bdry_connection(queue, rhs)
bdry_vis.write_vtk_file("y.vtu", [("f", bdry_f_2)])
if 0:
vol_vis.show_scalar_in_mayavi(rhs, do_show=False)
bdry_vis.show_scalar_in_mayavi(bdry_f - bdry_f_2, line_width=10,
do_show=False)
import mayavi.mlab as mlab
mlab.colorbar()
mlab.show()
# {{{ compute volume potential
from sumpy.qbx import LayerPotential
from sumpy.expansion.local import LineTaylorLocalExpansion
def get_kernel():
from sumpy.symbolic import pymbolic_real_norm_2
from pymbolic.primitives import (make_sym_vector, Variable as var)
r = pymbolic_real_norm_2(make_sym_vector("d", 3))
expr = var("log")(r)
scaling = 1/(2*var("pi"))
from sumpy.kernel import ExpressionKernel
return ExpressionKernel(
dim=3,
expression=expr,
scaling=scaling,
is_complex_valued=False)
laplace_2d_in_3d_kernel = get_kernel()
layer_pot = LayerPotential(ctx, [
LineTaylorLocalExpansion(laplace_2d_in_3d_kernel,
order=vol_qbx_order)])
targets = cl.array.zeros(queue, (3,) + vol_x.shape[1:], vol_x.dtype)
targets[:2] = vol_x
center_dist = np.min(
cl.clmath.sqrt(
bind(vol_discr, p.area_element())(queue)).get())
centers = make_obj_array([ci.copy().reshape(vol_discr.nnodes) for ci in targets])
centers[2][:] = center_dist
sources = cl.array.zeros(queue, (3,) + ovsmp_vol_x.shape[1:], ovsmp_vol_x.dtype)
sources[:2] = ovsmp_vol_x
ovsmp_rhs = vol_to_ovsmp_vol(queue, rhs)
ovsmp_vol_weights = bind(ovsmp_vol_discr, p.area_element() * p.QWeight())(queue)
evt, (vol_pot,) = layer_pot(
queue,
targets=targets.reshape(3, vol_discr.nnodes),
centers=centers,
sources=sources.reshape(3, ovsmp_vol_discr.nnodes),
strengths=(
(ovsmp_vol_weights*ovsmp_rhs).reshape(ovsmp_vol_discr.nnodes),)
)
vol_pot_bdry = bdry_connection(queue, vol_pot)
# }}}
# {{{ solve bvp
from sumpy.kernel import LaplaceKernel
from pytential.symbolic.pde.scalar import DirichletOperator
op = DirichletOperator(LaplaceKernel(2), -1, use_l2_weighting=True)
sym_sigma = sym.var("sigma")
op_sigma = op.operator(sym_sigma)
from pytential.qbx import QBXLayerPotentialSource
qbx = QBXLayerPotentialSource(
bdry_discr, fine_order=bdry_ovsmp_quad_order, qbx_order=qbx_order,
fmm_order=fmm_order
)
bound_op = bind(qbx, op_sigma)
poisson_bc = poisson_bc_func(bdry_nodes[0], bdry_nodes[1])
bvp_bc = poisson_bc - vol_pot_bdry
bdry_f = rhs_func(bdry_nodes[0], bdry_nodes[1])
bvp_rhs = bind(bdry_discr, op.prepare_rhs(sym.var("bc")))(queue, bc=bvp_bc)
from pytential.solve import gmres
gmres_result = gmres(
bound_op.scipy_op(queue, "sigma"),
bvp_rhs, tol=1e-14, progress=True,
hard_failure=False)
sigma = gmres_result.solution
print("gmres state:", gmres_result.state)
# }}}
bvp_sol = bind(
(qbx, vol_discr),
op.representation(sym_sigma))(queue, sigma=sigma)
poisson_sol = bvp_sol + vol_pot
poisson_err = poisson_sol-poisson_true_sol
rel_err = (
norm(vol_discr, queue, poisson_err)
/
norm(vol_discr, queue, poisson_true_sol))
bdry_vis.write_vtk_file("poisson-boundary.vtu", [
("vol_pot_bdry", vol_pot_bdry),
("sigma", sigma),
])
vol_vis.write_vtk_file("poisson-volume.vtu", [
("bvp_sol", bvp_sol),
("poisson_sol", poisson_sol),
("poisson_true_sol", poisson_true_sol),
("poisson_err", poisson_err),
("vol_pot", vol_pot),
("rhs", rhs),
])
print("h = %s" % h)
print("mesh_order = %s" % mesh_order)
print("vol_quad_order = %s" % vol_quad_order)
print("vol_ovsmp_quad_order = %s" % vol_ovsmp_quad_order)
print("bdry_quad_order = %s" % bdry_quad_order)
print("bdry_ovsmp_quad_order = %s" % bdry_ovsmp_quad_order)
print("qbx_order = %s" % qbx_order)
print("vol_qbx_order = %s" % vol_qbx_order)
print("fmm_order = %s" % fmm_order)
print()
print("rel err: %g" % rel_err)
def test_refinement_connection(
ctx_getter, refiner_cls, group_factory,
mesh_name, dim, mesh_pars, mesh_order, refine_flags, visualize=False):
from random import seed
seed(13)
# Discretization order
order = 5
cl_ctx = ctx_getter()
queue = cl.CommandQueue(cl_ctx)
from meshmode.discretization import Discretization
from meshmode.discretization.connection import (
make_refinement_connection, check_connection)
from pytools.convergence import EOCRecorder
eoc_rec = EOCRecorder()
for mesh_par in mesh_pars:
# {{{ get mesh
if mesh_name == "circle":
assert dim == 1
h = 1 / mesh_par
mesh = make_curve_mesh(
partial(ellipse, 1), np.linspace(0, 1, mesh_par + 1),
order=mesh_order)
elif mesh_name == "blob":
if mesh_order == 5:
pytest.xfail("https://gitlab.tiker.net/inducer/meshmode/issues/2")
assert dim == 2
mesh = get_blob_mesh(mesh_par, mesh_order)
h = float(mesh_par)
elif mesh_name == "warp":
from meshmode.mesh.generation import generate_warped_rect_mesh
mesh = generate_warped_rect_mesh(dim, order=mesh_order, n=mesh_par)
h = 1/mesh_par
else:
raise ValueError("mesh_name not recognized")
# }}}
from meshmode.mesh.processing import find_bounding_box
mesh_bbox_low, mesh_bbox_high = find_bounding_box(mesh)
mesh_ext = mesh_bbox_high-mesh_bbox_low
def f(x):
result = 1
if mesh_name == "blob":
factor = 15
else:
factor = 9
for iaxis in range(len(x)):
result = result * cl.clmath.sin(factor * (x[iaxis]/mesh_ext[iaxis]))
return result
discr = Discretization(cl_ctx, mesh, group_factory(order))
refiner = refiner_cls(mesh)
flags = refine_flags(mesh)
refiner.refine(flags)
connection = make_refinement_connection(
refiner, discr, group_factory(order))
check_connection(connection)
fine_discr = connection.to_discr
x = discr.nodes().with_queue(queue)
x_fine = fine_discr.nodes().with_queue(queue)
f_coarse = f(x)
f_interp = connection(queue, f_coarse).with_queue(queue)
f_true = f(x_fine).with_queue(queue)
if visualize == "dots":
import matplotlib.pyplot as plt
x = x.get(queue)
err = np.array(np.log10(
1e-16 + np.abs((f_interp - f_true).get(queue))), dtype=float)
import matplotlib.cm as cm
cmap = cm.ScalarMappable(cmap=cm.jet)
cmap.set_array(err)
plt.scatter(x[0], x[1], c=cmap.to_rgba(err), s=20, cmap=cmap)
plt.colorbar(cmap)
plt.show()
elif visualize == "vtk":
from meshmode.discretization.visualization import make_visualizer
fine_vis = make_visualizer(queue, fine_discr, mesh_order)
fine_vis.write_vtk_file(
"refine-fine-%s-%dd-%s.vtu" % (mesh_name, dim, mesh_par), [
("f_interp", f_interp),
("f_true", f_true),
])
import numpy.linalg as la
err = la.norm((f_interp - f_true).get(queue), np.inf)
eoc_rec.add_data_point(h, err)
order_slack = 0.5
if mesh_name == "blob" and order > 1:
order_slack = 1
print(eoc_rec)
assert (
eoc_rec.order_estimate() >= order-order_slack
or eoc_rec.max_error() < 1e-14)
kernel = LaplaceKernel()
#kernel = OneKernel()
mesh = make_curve_mesh(
#lambda t: ellipse(1, t),
starfish,
np.linspace(0, 1, nelements+1),
target_order)
from pytential.qbx import QBXLayerPotentialSource
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import \
InterpolatoryQuadratureSimplexGroupFactory
density_discr = Discretization(
cl_ctx, mesh,
InterpolatoryQuadratureSimplexGroupFactory(target_order))
qbx = QBXLayerPotentialSource(
density_discr, fine_order=2*target_order,
qbx_order=qbx_order, fmm_order=qbx_order)
slow_qbx = QBXLayerPotentialSource(
density_discr, fine_order=2*target_order,
qbx_order=qbx_order, fmm_order=False)
nodes = density_discr.nodes().with_queue(queue)
angle = cl.clmath.atan2(nodes[1], nodes[0])
from pytential import bind, sym
d = sym.Derivative()
def test_sanity_single_element(ctx_getter, dim, order, visualize=False):
pytest.importorskip("pytential")
cl_ctx = ctx_getter()
queue = cl.CommandQueue(cl_ctx)
from modepy.tools import UNIT_VERTICES
vertices = UNIT_VERTICES[dim].T.copy()
center = np.empty(dim, np.float64)
center.fill(-0.5)
import modepy as mp
from meshmode.mesh import SimplexElementGroup, Mesh
mg = SimplexElementGroup(
order=order,
vertex_indices=np.arange(dim+1, dtype=np.int32).reshape(1, -1),
nodes=mp.warp_and_blend_nodes(dim, order).reshape(dim, 1, -1),
dim=dim)
mesh = Mesh(vertices, [mg])
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import \
PolynomialWarpAndBlendGroupFactory
vol_discr = Discretization(cl_ctx, mesh,
PolynomialWarpAndBlendGroupFactory(order+3))
# {{{ volume calculation check
vol_x = vol_discr.nodes().with_queue(queue)
vol_one = vol_x[0].copy()
vol_one.fill(1)
from pytential import norm, integral # noqa
from pytools import factorial
true_vol = 1/factorial(dim) * 2**dim
comp_vol = integral(vol_discr, queue, vol_one)
rel_vol_err = abs(true_vol - comp_vol) / true_vol
assert rel_vol_err < 1e-12
# }}}
# {{{ boundary discretization
from meshmode.discretization.connection import make_boundary_restriction
bdry_mesh, bdry_discr, bdry_connection = make_boundary_restriction(
queue, vol_discr, PolynomialWarpAndBlendGroupFactory(order + 3))
# }}}
# {{{ visualizers
from meshmode.discretization.visualization import make_visualizer
#vol_vis = make_visualizer(queue, vol_discr, 4)
bdry_vis = make_visualizer(queue, bdry_discr, 4)
# }}}
from pytential import bind, sym
bdry_normals = bind(bdry_discr, sym.normal())(queue).as_vector(dtype=object)
if visualize:
bdry_vis.write_vtk_file("boundary.vtu", [
("bdry_normals", bdry_normals)
])
from pytential import bind, sym
normal_outward_check = bind(bdry_discr,
sym.normal()
|
(sym.Nodes() + 0.5*sym.ones_vec(dim)),
)(queue).as_scalar() > 0
assert normal_outward_check.get().all(), normal_outward_check.get()
def test_identities(ctx_getter, zero_op_name, curve_name, curve_f, qbx_order, k):
cl_ctx = ctx_getter()
queue = cl.CommandQueue(cl_ctx)
# prevent cache 'splosion
from sympy.core.cache import clear_cache
clear_cache()
target_order = 7
u_sym = sym.var("u")
grad_u_sym = sym.VectorVariable("grad_u")
dn_u_sym = sym.var("dn_u")
if k == 0:
k_sym = 0
else:
k_sym = "k"
zero_op_table = {
"green":
sym.S(k_sym, dn_u_sym) - sym.D(k_sym, u_sym) - 0.5*u_sym,
"green_grad":
d1.nabla * d1(sym.S(k_sym, dn_u_sym))
- d2.nabla * d2(sym.D(k_sym, u_sym))
- 0.5*grad_u_sym,
# only for k==0:
"zero_calderon":
-sym.Dp(0, sym.S(0, u_sym))
- 0.25*u_sym + sym.Sp(0, sym.Sp(0, u_sym))
}
order_table = {
"green": qbx_order,
"green_grad": qbx_order-1,
"zero_calderon": qbx_order-1,
}
zero_op = zero_op_table[zero_op_name]
from pytools.convergence import EOCRecorder
eoc_rec = EOCRecorder()
for nelements in [30, 50, 70]:
mesh = make_curve_mesh(curve_f,
np.linspace(0, 1, nelements+1),
target_order)
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import \
InterpolatoryQuadratureSimplexGroupFactory
from pytential.qbx import QBXLayerPotentialSource
density_discr = Discretization(
cl_ctx, mesh,
InterpolatoryQuadratureSimplexGroupFactory(target_order))
qbx = QBXLayerPotentialSource(density_discr, 4*target_order,
qbx_order,
# Don't use FMM for now
fmm_order=False)
# {{{ compute values of a solution to the PDE
nodes_host = density_discr.nodes().get(queue)
normal = bind(density_discr, sym.normal())(queue).as_vector(np.object)
normal_host = [normal[0].get(), normal[1].get()]
if k != 0:
angle = 0.3
wave_vec = np.array([np.cos(angle), np.sin(angle)])
u = np.exp(1j*k*np.tensordot(wave_vec, nodes_host, axes=1))
grad_u = 1j*k*wave_vec[:, np.newaxis]*u
else:
center = np.array([3, 1])
diff = nodes_host - center[:, np.newaxis]
dist_squared = np.sum(diff**2, axis=0)
dist = np.sqrt(dist_squared)
u = np.log(dist)
grad_u = diff/dist_squared
dn_u = normal_host[0]*grad_u[0] + normal_host[1]*grad_u[1]
# }}}
u_dev = cl.array.to_device(queue, u)
dn_u_dev = cl.array.to_device(queue, dn_u)
grad_u_dev = cl.array.to_device(queue, grad_u)
key = (qbx_order, curve_name, nelements, zero_op_name)
bound_op = bind(qbx, zero_op)
error = bound_op(
queue, u=u_dev, dn_u=dn_u_dev, grad_u=grad_u_dev, k=k)
if 0:
pt.plot(error)
pt.show()
l2_error_norm = norm(density_discr, queue, error)
print(key, l2_error_norm)
eoc_rec.add_data_point(1/nelements, l2_error_norm)
print(eoc_rec)
tgt_order = order_table[zero_op_name]
assert eoc_rec.order_estimate() > tgt_order - 1.3
def test_boundary_interpolation(ctx_getter, group_factory, boundary_tag,
mesh_name, dim, mesh_pars, per_face_groups):
cl_ctx = ctx_getter()
queue = cl.CommandQueue(cl_ctx)
from meshmode.discretization import Discretization
from meshmode.discretization.connection import (
make_face_restriction, check_connection)
from pytools.convergence import EOCRecorder
eoc_rec = EOCRecorder()
order = 4
def f(x):
return 0.1*cl.clmath.sin(30*x)
for mesh_par in mesh_pars:
# {{{ get mesh
if mesh_name == "blob":
assert dim == 2
h = mesh_par
from meshmode.mesh.io import generate_gmsh, FileSource
print("BEGIN GEN")
mesh = generate_gmsh(
FileSource("blob-2d.step"), 2, order=order,
force_ambient_dim=2,
other_options=[
"-string", "Mesh.CharacteristicLengthMax = %s;" % h]
)
print("END GEN")
elif mesh_name == "warp":
from meshmode.mesh.generation import generate_warped_rect_mesh
mesh = generate_warped_rect_mesh(dim, order=4, n=mesh_par)
h = 1/mesh_par
else:
raise ValueError("mesh_name not recognized")
# }}}
vol_discr = Discretization(cl_ctx, mesh,
group_factory(order))
print("h=%s -> %d elements" % (
h, sum(mgrp.nelements for mgrp in mesh.groups)))
x = vol_discr.nodes()[0].with_queue(queue)
vol_f = f(x)
bdry_connection = make_face_restriction(
vol_discr, group_factory(order),
boundary_tag, per_face_groups=per_face_groups)
check_connection(bdry_connection)
bdry_discr = bdry_connection.to_discr
bdry_x = bdry_discr.nodes()[0].with_queue(queue)
bdry_f = f(bdry_x)
bdry_f_2 = bdry_connection(queue, vol_f)
if mesh_name == "blob" and dim == 2:
mat = bdry_connection.full_resample_matrix(queue).get(queue)
bdry_f_2_by_mat = mat.dot(vol_f.get())
mat_error = la.norm(bdry_f_2.get(queue=queue) - bdry_f_2_by_mat)
assert mat_error < 1e-14, mat_error
err = la.norm((bdry_f-bdry_f_2).get(), np.inf)
eoc_rec.add_data_point(h, err)
print(eoc_rec)
assert (
eoc_rec.order_estimate() >= order-0.5
or eoc_rec.max_error() < 1e-14)
def main():
import logging
logging.basicConfig(level=logging.INFO)
cl_ctx = cl.create_some_context()
queue = cl.CommandQueue(cl_ctx)
from meshmode.mesh.generation import ellipse, make_curve_mesh
from functools import partial
mesh = make_curve_mesh(
partial(ellipse, 3),
np.linspace(0, 1, nelements+1),
mesh_order)
density_discr = Discretization(
cl_ctx, mesh,
InterpolatoryQuadratureSimplexGroupFactory(bdry_quad_order))
from pytential.qbx import QBXLayerPotentialSource
qbx = QBXLayerPotentialSource(
density_discr, fine_order=bdry_ovsmp_quad_order, qbx_order=qbx_order,
fmm_order=fmm_order
)
# {{{ describe bvp
from sumpy.kernel import HelmholtzKernel
kernel = HelmholtzKernel(2)
cse = sym.cse
sigma_sym = sym.var("sigma")
sqrt_w = sym.sqrt_jac_q_weight()
inv_sqrt_w_sigma = cse(sigma_sym/sqrt_w)
# Brakhage-Werner parameter
alpha = 1j
# -1 for interior Dirichlet
# +1 for exterior Dirichlet
loc_sign = -1
bdry_op_sym = (-loc_sign*0.5*sigma_sym
+ sqrt_w*(
alpha*sym.S(kernel, inv_sqrt_w_sigma, k=sym.var("k"))
- sym.D(kernel, inv_sqrt_w_sigma, k=sym.var("k"))
))
# }}}
bound_op = bind(qbx, bdry_op_sym)
# {{{ fix rhs and solve
mode_nr = 3
nodes = density_discr.nodes().with_queue(queue)
angle = cl.clmath.atan2(nodes[1], nodes[0])
bc = cl.clmath.cos(mode_nr*angle)
bvp_rhs = bind(qbx, sqrt_w*sym.var("bc"))(queue, bc=bc)
from pytential.solve import gmres
gmres_result = gmres(
bound_op.scipy_op(queue, "sigma", k=k),
bvp_rhs, tol=1e-14, progress=True,
stall_iterations=0,
hard_failure=True)
# }}}
# {{{ postprocess/visualize
sigma = gmres_result.solution
representation_sym = (
alpha*sym.S(kernel, inv_sqrt_w_sigma, k=sym.var("k"))
- sym.D(kernel, inv_sqrt_w_sigma, k=sym.var("k")))
from sumpy.visualization import FieldPlotter
fplot = FieldPlotter(np.zeros(2), extent=5, npoints=1500)
from pytential.target import PointsTarget
fld_in_vol = bind(
(qbx, PointsTarget(fplot.points)),
representation_sym)(queue, sigma=sigma, k=k).get()
#fplot.show_scalar_in_mayavi(fld_in_vol.real, max_val=5)
fplot.write_vtk_file(
"potential.vts",
[
("potential", fld_in_vol)
]
)
class QBXLayerPotentialSource(LayerPotentialSource):
"""A source discretization for a QBX layer potential.
.. attribute :: mesh
.. attribute :: groups
.. attribute :: nnodes
.. autoattribute :: nodes
See :ref:`qbxguts` for some information on the inner workings of this.
"""
def __init__(self, density_discr, fine_order, qbx_order, fmm_order,
# FIXME set debug=False once everything works
expansion_getter=None, real_dtype=np.float64, debug=True):
"""
:arg fine_order: The total degree to which the (upsampled)
underlying quadrature is exact.
:arg fmm_order: `False` for direct calculation. ``None`` will set
a reasonable(-ish?) default.
"""
self.fine_density_discr = Discretization(
density_discr.cl_context, density_discr.mesh,
QuadratureSimplexGroupFactory(fine_order), real_dtype)
from meshmode.discretization.connection import make_same_mesh_connection
with cl.CommandQueue(density_discr.cl_context) as queue:
self.resampler = make_same_mesh_connection(
queue,
self.fine_density_discr, density_discr)
if fmm_order is None:
fmm_order = qbx_order + 1
self.qbx_order = qbx_order
self.density_discr = density_discr
self.fmm_order = fmm_order
self.debug = debug
# only used in non-FMM case
if expansion_getter is None:
from sumpy.expansion.local import LineTaylorLocalExpansion
expansion_getter = LineTaylorLocalExpansion
self.expansion_getter = expansion_getter
@property
def ambient_dim(self):
return self.density_discr.ambient_dim
@property
def cl_context(self):
return self.density_discr.cl_context
@property
def real_dtype(self):
return self.density_discr.real_dtype
@property
def complex_dtype(self):
return self.density_discr.complex_dtype
@memoize_method
def centers(self, target_discr, sign):
from pytential import sym, bind
with cl.CommandQueue(self.cl_context) as queue:
return bind(target_discr,
sym.Nodes() + 2*sign*sym.area_element()*sym.normal())(queue) \
.as_vector(np.object)
@memoize_method
def weights_and_area_elements(self):
import pytential.symbolic.primitives as p
from pytential.symbolic.execution import bind
with cl.CommandQueue(self.cl_context) as queue:
# fine_density_discr is not guaranteed to be usable for
# interpolation/differentiation. Use density_discr to find
# area element instead, then upsample that.
area_element = self.resampler(queue,
bind(self.density_discr,
p.area_element())(queue))
qweight = bind(self.fine_density_discr, p.QWeight())(queue)
return (area_element.with_queue(queue)*qweight).with_queue(None)
# {{{ interface with execution
def preprocess_optemplate(self, name, discretizations, expr):
"""
:arg name: The symbolic name for *self*, which the preprocessor
should use to find which expressions it is allowed to modify.
"""
from pytential.symbolic.mappers import QBXPreprocessor
return QBXPreprocessor(name, discretizations)(expr)
def op_group_features(self, expr):
from pytential.symbolic.primitives import IntGdSource
assert not isinstance(expr, IntGdSource)
from sumpy.kernel import AxisTargetDerivativeRemover
result = (
expr.source, expr.density,
AxisTargetDerivativeRemover()(expr.kernel),
)
return result
def exec_layer_potential_insn(self, queue, insn, bound_expr, evaluate):
from pytools.obj_array import with_object_array_or_scalar
from functools import partial
oversample = partial(self.resampler, queue)
def evaluate_wrapper(expr):
value = evaluate(expr)
return with_object_array_or_scalar(oversample, value)
if self.fmm_order is False:
func = self.exec_layer_potential_insn_direct
else:
func = self.exec_layer_potential_insn_fmm
return func(queue, insn, bound_expr, evaluate_wrapper)
# {{{ fmm-based execution
@property
@memoize_method
def qbx_fmm_code_getter(self):
from pytential.qbx.geometry import QBXFMMGeometryCodeGetter
return QBXFMMGeometryCodeGetter(self.cl_context, self.ambient_dim,
debug=self.debug)
@memoize_method
def qbx_fmm_geometry_data(self, target_discrs_and_qbx_sides):
"""
:arg target_discrs_and_qbx_sides:
a tuple of *(discr, qbx_forced_limit)*
tuples, where *discr* is a
:class:`pytential.discretization.Discretization`
or
:class:`pytential.discretization.target.TargetBase`
instance
"""
from pytential.qbx.geometry import QBXFMMGeometryData
return QBXFMMGeometryData(self.qbx_fmm_code_getter,
self, target_discrs_and_qbx_sides, debug=self.debug)
@memoize_method
def expansion_wrangler_code_container(self, base_kernel, out_kernels):
from sumpy.expansion.multipole import VolumeTaylorMultipoleExpansion
from sumpy.expansion.local import VolumeTaylorLocalExpansion
fmm_order = self.fmm_order
# FIXME: Don't hard-code expansion types
from sumpy.kernel import HelmholtzKernel
if (isinstance(base_kernel.get_base_kernel(), HelmholtzKernel)
and base_kernel.dim == 2):
from sumpy.expansion.multipole import H2DMultipoleExpansion
from sumpy.expansion.local import H2DLocalExpansion
mpole_expn_class = H2DMultipoleExpansion
local_expn_class = H2DLocalExpansion
else:
mpole_expn_class = VolumeTaylorMultipoleExpansion
local_expn_class = VolumeTaylorLocalExpansion
fmm_mpole_expn = mpole_expn_class(base_kernel, fmm_order)
fmm_local_expn = local_expn_class(base_kernel, fmm_order)
qbx_local_expn = local_expn_class(
base_kernel, self.qbx_order)
from pytential.qbx.fmm import \
QBXExpansionWranglerCodeContainer
return QBXExpansionWranglerCodeContainer(
self.cl_context, fmm_mpole_expn, fmm_local_expn, qbx_local_expn,
out_kernels)
def exec_layer_potential_insn_fmm(self, queue, insn, bound_expr, evaluate):
# {{{ build list of unique target discretizations used
# map (name, qbx_side) to number in list
tgt_name_and_side_to_number = {}
# list of tuples (discr, qbx_side)
target_discrs_and_qbx_sides = []
for o in insn.outputs:
key = (o.target_name, o.qbx_forced_limit)
if key not in tgt_name_and_side_to_number:
tgt_name_and_side_to_number[key] = \
len(target_discrs_and_qbx_sides)
target_discr = bound_expr.places[o.target_name]
if isinstance(target_discr, LayerPotentialSource):
target_discr = target_discr.density_discr
target_discrs_and_qbx_sides.append(
(target_discr, o.qbx_forced_limit))
target_discrs_and_qbx_sides = tuple(target_discrs_and_qbx_sides)
# }}}
geo_data = self.qbx_fmm_geometry_data(target_discrs_and_qbx_sides)
# FIXME Exert more positive control over geo_data attribute lifetimes using
# geo_data.<method>.clear_cache(geo_data).
# FIXME Synthesize "bad centers" around corners and edges that have
# inadequate QBX coverage.
# FIXME don't compute *all* output kernels on all targets--respect that
# some target discretizations may only be asking for derivatives (e.g.)
strengths = (evaluate(insn.density).with_queue(queue)
* self.weights_and_area_elements())
# {{{ get expansion wrangler
base_kernel = None
out_kernels = []
from sumpy.kernel import AxisTargetDerivativeRemover
for knl in insn.kernels:
candidate_base_kernel = AxisTargetDerivativeRemover()(knl)
if base_kernel is None:
base_kernel = candidate_base_kernel
else:
assert base_kernel == candidate_base_kernel
out_kernels = tuple(knl for knl in insn.kernels)
if base_kernel.is_complex_valued or strengths.dtype.kind == "c":
value_dtype = self.complex_dtype
else:
value_dtype = self.real_dtype
# {{{ build extra_kwargs dictionaries
# This contains things like the Helmholtz parameter k or
# the normal directions for double layers.
def reorder_sources(source_array):
if isinstance(source_array, cl.array.Array):
return (source_array
.with_queue(queue)
[geo_data.tree().user_point_source_ids]
.with_queue(None))
else:
return source_array
kernel_extra_kwargs = {}
source_extra_kwargs = {}
from sumpy.tools import gather_arguments, gather_source_arguments
from pytools.obj_array import with_object_array_or_scalar
for func, var_dict in [
(gather_arguments, kernel_extra_kwargs),
(gather_source_arguments, source_extra_kwargs),
]:
for arg in func(out_kernels):
var_dict[arg.name] = with_object_array_or_scalar(
reorder_sources,
evaluate(insn.kernel_arguments[arg.name]))
# }}}
wrangler = self.expansion_wrangler_code_container(
base_kernel, out_kernels).get_wrangler(
queue, geo_data, value_dtype,
source_extra_kwargs=source_extra_kwargs,
kernel_extra_kwargs=kernel_extra_kwargs)
# }}}
#geo_data.plot()
if len(geo_data.global_qbx_centers()) != geo_data.center_info().ncenters:
raise NotImplementedError("geometry has centers requiring local QBX")
from pytential.qbx.geometry import target_state
if (geo_data.user_target_to_center().with_queue(queue)
== target_state.FAILED).get().any():
raise RuntimeError("geometry has failed targets")
# {{{ execute global QBX
from pytential.qbx.fmm import drive_fmm
all_potentials_on_every_tgt = drive_fmm(wrangler, strengths)
# }}}
result = []
for o in insn.outputs:
tgt_side_number = tgt_name_and_side_to_number[
o.target_name, o.qbx_forced_limit]
tgt_slice = slice(*geo_data.target_info().target_discr_starts[
tgt_side_number:tgt_side_number+2])
result.append(
(o.name,
all_potentials_on_every_tgt[o.kernel_index][tgt_slice]))
return result, []
# }}}
# {{{ direct execution
@memoize_method
def get_lpot_applier(self, kernels):
# needs to be separate method for caching
from pytools import any
if any(knl.is_complex_valued for knl in kernels):
value_dtype = self.density_discr.complex_dtype
else:
value_dtype = self.density_discr.real_dtype
from sumpy.qbx import LayerPotential
return LayerPotential(self.cl_context,
[self.expansion_getter(knl, self.qbx_order)
for knl in kernels],
value_dtypes=value_dtype)
@memoize_method
def get_p2p(self, kernels):
# needs to be separate method for caching
from pytools import any
if any(knl.is_complex_valued for knl in kernels):
value_dtype = self.density_discr.complex_dtype
else:
value_dtype = self.density_discr.real_dtype
from sumpy.p2p import P2P
p2p = P2P(self.cl_context,
kernels, exclude_self=False, value_dtypes=value_dtype)
return p2p
def exec_layer_potential_insn_direct(self, queue, insn, bound_expr, evaluate):
lp_applier = self.get_lpot_applier(insn.kernels)
p2p = None
kernel_args = {}
for arg_name, arg_expr in six.iteritems(insn.kernel_arguments):
kernel_args[arg_name] = evaluate(arg_expr)
strengths = (evaluate(insn.density).with_queue(queue)
* self.weights_and_area_elements())
# FIXME: Do this all at once
result = []
for o in insn.outputs:
target_discr = bound_expr.get_discretization(o.target_name)
is_self = self.density_discr is target_discr
if not is_self:
# FIXME: Not sure I understand what case this used to cover...
try:
is_self = target_discr.source_discr is self
except AttributeError:
# apparently not.
pass
if is_self:
# QBXPreprocessor is supposed to have taken care of this
assert o.qbx_forced_limit is not None
assert abs(o.qbx_forced_limit) > 0
evt, output_for_each_kernel = lp_applier(queue, target_discr.nodes(),
self.fine_density_discr.nodes(),
self.centers(target_discr, o.qbx_forced_limit),
[strengths], **kernel_args)
result.append((o.name, output_for_each_kernel[o.kernel_index]))
else:
# yuck, no caching
if p2p is None:
p2p = self.get_p2p(insn.kernels)
evt, output_for_each_kernel = p2p(queue,
target_discr.nodes(), self.fine_density_discr.nodes(),
[strengths], **kernel_args)
result.append((o.name, output_for_each_kernel[o.kernel_index]))
return result, []
def main():
import logging
logger = logging.getLogger(__name__)
logging.basicConfig(level=logging.WARNING) # INFO for more progress info
from meshmode.mesh.io import generate_gmsh, FileSource
mesh = generate_gmsh(
FileSource(cad_file_name), 2, order=2,
other_options=["-string", "Mesh.CharacteristicLengthMax = %g;" % h])
from meshmode.mesh.processing import perform_flips
# Flip elements--gmsh generates inside-out geometry.
mesh = perform_flips(mesh, np.ones(mesh.nelements))
from meshmode.mesh.processing import find_bounding_box
bbox_min, bbox_max = find_bounding_box(mesh)
bbox_center = 0.5*(bbox_min+bbox_max)
bbox_size = max(bbox_max-bbox_min) / 2
logger.info("%d elements" % mesh.nelements)
from pytential.qbx import QBXLayerPotentialSource
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import \
InterpolatoryQuadratureSimplexGroupFactory
density_discr = Discretization(
cl_ctx, mesh, InterpolatoryQuadratureSimplexGroupFactory(target_order))
qbx, _ = QBXLayerPotentialSource(density_discr, 4*target_order, qbx_order,
fmm_order=qbx_order + 3,
target_association_tolerance=0.15).with_refinement()
nodes = density_discr.nodes().with_queue(queue)
angle = cl.clmath.atan2(nodes[1], nodes[0])
from pytential import bind, sym
#op = sym.d_dx(sym.S(kernel, sym.var("sigma"), qbx_forced_limit=None))
op = sym.D(kernel, sym.var("sigma"), qbx_forced_limit=None)
#op = sym.S(kernel, sym.var("sigma"), qbx_forced_limit=None)
sigma = cl.clmath.cos(mode_nr*angle)
if 0:
sigma = 0*angle
from random import randrange
for i in range(5):
sigma[randrange(len(sigma))] = 1
if isinstance(kernel, HelmholtzKernel):
sigma = sigma.astype(np.complex128)
fplot = FieldPlotter(bbox_center, extent=3.5*bbox_size, npoints=150)
from pytential.target import PointsTarget
fld_in_vol = bind(
(qbx, PointsTarget(fplot.points)),
op)(queue, sigma=sigma, k=k).get()
#fplot.show_scalar_in_mayavi(fld_in_vol.real, max_val=5)
fplot.write_vtk_file(
"potential-3d.vts",
[
("potential", fld_in_vol)
]
)
bdry_normals = bind(
density_discr,
sym.normal(density_discr.ambient_dim))(queue).as_vector(dtype=object)
from meshmode.discretization.visualization import make_visualizer
bdry_vis = make_visualizer(queue, density_discr, target_order)
bdry_vis.write_vtk_file("source-3d.vtu", [
("sigma", sigma),
("bdry_normals", bdry_normals),
])
def main():
# cl.array.to_device(queue, numpy_array)
from meshmode.mesh.io import generate_gmsh, FileSource
mesh = generate_gmsh(
FileSource("ellipsoid.step"), 2, order=2,
other_options=["-string", "Mesh.CharacteristicLengthMax = %g;" % h])
from meshmode.mesh.processing import perform_flips
# Flip elements--gmsh generates inside-out geometry.
mesh = perform_flips(mesh, np.ones(mesh.nelements))
print("%d elements" % mesh.nelements)
from meshmode.mesh.processing import find_bounding_box
bbox_min, bbox_max = find_bounding_box(mesh)
bbox_center = 0.5*(bbox_min+bbox_max)
bbox_size = max(bbox_max-bbox_min) / 2
logger.info("%d elements" % mesh.nelements)
from pytential.qbx import QBXLayerPotentialSource
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import \
InterpolatoryQuadratureSimplexGroupFactory
density_discr = Discretization(
cl_ctx, mesh, InterpolatoryQuadratureSimplexGroupFactory(target_order))
qbx = QBXLayerPotentialSource(density_discr, 4*target_order, qbx_order,
fmm_order=qbx_order + 10, fmm_backend="fmmlib")
from pytential.symbolic.pde.maxwell import MuellerAugmentedMFIEOperator
pde_op = MuellerAugmentedMFIEOperator(
omega=0.4,
epss=[1.4, 1.0],
mus=[1.2, 1.0],
)
from pytential import bind, sym
unk = pde_op.make_unknown("sigma")
sym_operator = pde_op.operator(unk)
sym_rhs = pde_op.rhs(
sym.make_sym_vector("Einc", 3),
sym.make_sym_vector("Hinc", 3))
sym_repr = pde_op.representation(0, unk)
if 1:
expr = sym_repr
print(sym.pretty(expr))
print("#"*80)
from pytential.target import PointsTarget
tgt_points=np.zeros((3,1))
tgt_points[0,0] = 100
tgt_points[1,0] = -200
tgt_points[2,0] = 300
bound_op = bind((qbx, PointsTarget(tgt_points)), expr)
print(bound_op.code)
if 1:
def green3e(x,y,z,source,strength,k):
# electric field corresponding to dyadic green's function
# due to monochromatic electric dipole located at "source".
# "strength" is the the intensity of the dipole.
# E = (I + Hess)(exp(ikr)/r) dot (strength)
#
dx = x - source[0]
dy = y - source[1]
dz = z - source[2]
rr = np.sqrt(dx**2 + dy**2 + dz**2)
fout = np.exp(1j*k*rr)/rr
evec = fout*strength
qmat = np.zeros((3,3),dtype=np.complex128)
qmat[0,0]=(2*dx**2-dy**2-dz**2)*(1-1j*k*rr)
qmat[1,1]=(2*dy**2-dz**2-dx**2)*(1-1j*k*rr)
qmat[2,2]=(2*dz**2-dx**2-dy**2)*(1-1j*k*rr)
qmat[0,0]=qmat[0,0]+(-k**2*dx**2*rr**2)
qmat[1,1]=qmat[1,1]+(-k**2*dy**2*rr**2)
qmat[2,2]=qmat[2,2]+(-k**2*dz**2*rr**2)
qmat[0,1]=(3-k**2*rr**2-3*1j*k*rr)*(dx*dy)
qmat[1,2]=(3-k**2*rr**2-3*1j*k*rr)*(dy*dz)
qmat[2,0]=(3-k**2*rr**2-3*1j*k*rr)*(dz*dx)
qmat[1,0]=qmat[0,1]
qmat[2,1]=qmat[1,2]
qmat[0,2]=qmat[2,0]
fout=np.exp(1j*k*rr)/rr**5/k**2
fvec = fout*np.dot(qmat,strength)
evec = evec + fvec
return evec
def green3m(x,y,z,source,strength,k):
# magnetic field corresponding to dyadic green's function
# due to monochromatic electric dipole located at "source".
# "strength" is the the intensity of the dipole.
# H = curl((I + Hess)(exp(ikr)/r) dot (strength)) =
# strength \cross \grad (exp(ikr)/r)
#
dx = x - source[0]
dy = y - source[1]
dz = z - source[2]
rr = np.sqrt(dx**2 + dy**2 + dz**2)
fout=(1-1j*k*rr)*np.exp(1j*k*rr)/rr**3
fvec = np.zeros(3,dtype=np.complex128)
fvec[0] = fout*dx
fvec[1] = fout*dy
fvec[2] = fout*dz
hvec = np.cross(strength,fvec)
return hvec
def dipole3e(x,y,z,source,strength,k):
#
# evalaute electric and magnetic field due
# to monochromatic electric dipole located at "source"
# with intensity "strength"
evec = green3e(x,y,z,source,strength,k)
evec = evec*1j*k
hvec = green3m(x,y,z,source,strength,k)
return evec,hvec
def dipole3m(x,y,z,source,strength,k):
#
# evalaute electric and magnetic field due
# to monochromatic magnetic dipole located at "source"
# with intensity "strength"
evec = green3m(x,y,z,source,strength,k)
hvec = green3e(x,y,z,source,strength,k)
hvec = -hvec*1j*k
return evec,hvec
def dipole3eall(x,y,z,sources,strengths,k):
ns = len(strengths)
evec = np.zeros(3,dtype=np.complex128)
hvec = np.zeros(3,dtype=np.complex128)
for i in range(ns):
evect,hvect = dipole3e(x,y,z,sources[i],strengths[i],k)
evec = evec + evect
hvec = hvec + hvect
nodes = density_discr.nodes().with_queue(queue).get()
source = [0.01,-0.03,0.02]
# source = cl.array.to_device(queue,np.zeros(3))
# source[0] = 0.01
# source[1] =-0.03
# source[2] = 0.02
strength = np.ones(3)
# evec = cl.array.to_device(queue,np.zeros((3,len(nodes[0])),dtype=np.complex128))
# hvec = cl.array.to_device(queue,np.zeros((3,len(nodes[0])),dtype=np.complex128))
evec = np.zeros((3,len(nodes[0])),dtype=np.complex128)
hvec = np.zeros((3,len(nodes[0])),dtype=np.complex128)
for i in range(len(nodes[0])):
evec[:,i],hvec[:,i] = dipole3e(nodes[0][i],nodes[1][i],nodes[2][i],source,strength,k)
print(np.shape(hvec))
print(type(evec))
print(type(hvec))
evec = cl.array.to_device(queue,evec)
hvec = cl.array.to_device(queue,hvec)
bvp_rhs = bind(qbx, sym_rhs)(queue,Einc=evec,Hinc=hvec)
print(np.shape(bvp_rhs))
print(type(bvp_rhs))
# print(bvp_rhs)
1/-1
bound_op = bind(qbx, sym_operator)
from pytential.solve import gmres
if 0:
gmres_result = gmres(
bound_op.scipy_op(queue, "sigma", dtype=np.complex128, k=k),
bvp_rhs, tol=1e-8, progress=True,
stall_iterations=0,
hard_failure=True)
sigma = gmres_result.solution
fld_at_tgt = bind((qbx, PointsTarget(tgt_points)), sym_repr)(queue,
sigma=bvp_rhs,k=k)
fld_at_tgt = np.array([
fi.get() for fi in fld_at_tgt
])
print(fld_at_tgt)
1/0
# }}}
#mlab.figure(bgcolor=(1, 1, 1))
if 1:
from meshmode.discretization.visualization import make_visualizer
bdry_vis = make_visualizer(queue, density_discr, target_order)
bdry_normals = bind(density_discr, sym.normal(3))(queue)\
.as_vector(dtype=object)
bdry_vis.write_vtk_file("source.vtu", [
("sigma", sigma),
("bdry_normals", bdry_normals),
])
fplot = FieldPlotter(bbox_center, extent=2*bbox_size, npoints=(150, 150, 1))
qbx_tgt_tol = qbx.copy(target_association_tolerance=0.1)
from pytential.target import PointsTarget
from pytential.qbx import QBXTargetAssociationFailedException
rho_sym = sym.var("rho")
try:
fld_in_vol = bind(
(qbx_tgt_tol, PointsTarget(fplot.points)),
sym.make_obj_array([
sym.S(pde_op.kernel, rho_sym, k=sym.var("k"),
qbx_forced_limit=None),
sym.d_dx(3, sym.S(pde_op.kernel, rho_sym, k=sym.var("k"),
qbx_forced_limit=None)),
sym.d_dy(3, sym.S(pde_op.kernel, rho_sym, k=sym.var("k"),
qbx_forced_limit=None)),
sym.d_dz(3, sym.S(pde_op.kernel, rho_sym, k=sym.var("k"),
qbx_forced_limit=None)),
])
)(queue, jt=jt, rho=rho, k=k)
except QBXTargetAssociationFailedException as e:
fplot.write_vtk_file(
"failed-targets.vts",
[
("failed_targets", e.failed_target_flags.get(queue))
])
raise
fld_in_vol = sym.make_obj_array(
[fiv.get() for fiv in fld_in_vol])
#fplot.show_scalar_in_mayavi(fld_in_vol.real, max_val=5)
fplot.write_vtk_file(
"potential.vts",
[
("potential", fld_in_vol[0]),
("grad", fld_in_vol[1:]),
]
)
def run_dielectric_test(cl_ctx, queue, nelements, qbx_order,
op_class, mode,
k0=3, k1=2.9, mesh_order=10,
bdry_quad_order=None, bdry_ovsmp_quad_order=None,
use_l2_weighting=False,
fmm_order=None, visualize=False):
if fmm_order is None:
fmm_order = qbx_order * 2
if bdry_quad_order is None:
bdry_quad_order = mesh_order
if bdry_ovsmp_quad_order is None:
bdry_ovsmp_quad_order = 4*bdry_quad_order
from meshmode.mesh.generation import ellipse, make_curve_mesh
from functools import partial
mesh = make_curve_mesh(
partial(ellipse, 3),
np.linspace(0, 1, nelements+1),
mesh_order)
density_discr = Discretization(
cl_ctx, mesh,
InterpolatoryQuadratureSimplexGroupFactory(bdry_quad_order))
logger.info("%d elements" % mesh.nelements)
# from meshmode.discretization.visualization import make_visualizer
# bdry_vis = make_visualizer(queue, density_discr, 20)
# {{{ solve bvp
from sumpy.kernel import HelmholtzKernel, AxisTargetDerivative
kernel = HelmholtzKernel(2)
beta = 2.5
K0 = np.sqrt(k0**2-beta**2) # noqa
K1 = np.sqrt(k1**2-beta**2) # noqa
pde_op = op_class(
mode,
k_vacuum=1,
interfaces=((0, 1, sym.DEFAULT_SOURCE),),
domain_k_exprs=(k0, k1),
beta=beta,
use_l2_weighting=use_l2_weighting)
op_unknown_sym = pde_op.make_unknown("unknown")
representation0_sym = pde_op.representation(op_unknown_sym, 0)
representation1_sym = pde_op.representation(op_unknown_sym, 1)
from pytential.qbx import QBXLayerPotentialSource
qbx = QBXLayerPotentialSource(
density_discr, fine_order=bdry_ovsmp_quad_order, qbx_order=qbx_order,
fmm_order=fmm_order
).with_refinement()
#print(sym.pretty(pde_op.operator(op_unknown_sym)))
#1/0
bound_pde_op = bind(qbx, pde_op.operator(op_unknown_sym))
e_factor = float(pde_op.ez_enabled)
h_factor = float(pde_op.hz_enabled)
e_sources_0 = make_obj_array(list(np.array([
[0.1, 0.2]
]).T.copy()))
e_strengths_0 = np.array([1*e_factor])
e_sources_1 = make_obj_array(list(np.array([
[4, 4]
]).T.copy()))
e_strengths_1 = np.array([1*e_factor])
h_sources_0 = make_obj_array(list(np.array([
[0.2, 0.1]
]).T.copy()))
h_strengths_0 = np.array([1*h_factor])
h_sources_1 = make_obj_array(list(np.array([
[4, 5]
]).T.copy()))
h_strengths_1 = np.array([1*h_factor])
kernel_grad = [
AxisTargetDerivative(i, kernel) for i in range(density_discr.ambient_dim)]
from sumpy.p2p import P2P
pot_p2p = P2P(cl_ctx, [kernel], exclude_self=False)
pot_p2p_grad = P2P(cl_ctx, kernel_grad, exclude_self=False)
normal = bind(density_discr, sym.normal())(queue).as_vector(np.object)
tangent = bind(
density_discr,
sym.pseudoscalar()/sym.area_element())(queue).as_vector(np.object)
_, (E0,) = pot_p2p(queue, density_discr.nodes(), e_sources_0, [e_strengths_0],
out_host=False, k=K0)
_, (E1,) = pot_p2p(queue, density_discr.nodes(), e_sources_1, [e_strengths_1],
out_host=False, k=K1)
_, (grad0_E0, grad1_E0) = pot_p2p_grad(
queue, density_discr.nodes(), e_sources_0, [e_strengths_0],
out_host=False, k=K0)
_, (grad0_E1, grad1_E1) = pot_p2p_grad(
queue, density_discr.nodes(), e_sources_1, [e_strengths_1],
out_host=False, k=K1)
_, (H0,) = pot_p2p(queue, density_discr.nodes(), h_sources_0, [h_strengths_0],
out_host=False, k=K0)
_, (H1,) = pot_p2p(queue, density_discr.nodes(), h_sources_1, [h_strengths_1],
out_host=False, k=K1)
_, (grad0_H0, grad1_H0) = pot_p2p_grad(
queue, density_discr.nodes(), h_sources_0, [h_strengths_0],
out_host=False, k=K0)
_, (grad0_H1, grad1_H1) = pot_p2p_grad(
queue, density_discr.nodes(), h_sources_1, [h_strengths_1],
out_host=False, k=K1)
E0_dntarget = (grad0_E0*normal[0] + grad1_E0*normal[1]) # noqa
E1_dntarget = (grad0_E1*normal[0] + grad1_E1*normal[1]) # noqa
H0_dntarget = (grad0_H0*normal[0] + grad1_H0*normal[1]) # noqa
H1_dntarget = (grad0_H1*normal[0] + grad1_H1*normal[1]) # noqa
E0_dttarget = (grad0_E0*tangent[0] + grad1_E0*tangent[1]) # noqa
E1_dttarget = (grad0_E1*tangent[0] + grad1_E1*tangent[1]) # noqa
H0_dttarget = (grad0_H0*tangent[0] + grad1_H0*tangent[1]) # noqa
H1_dttarget = (grad0_H1*tangent[0] + grad1_H1*tangent[1]) # noqa
sqrt_w = bind(density_discr, sym.sqrt_jac_q_weight())(queue)
bvp_rhs = np.zeros(len(pde_op.bcs), dtype=np.object)
for i_bc, terms in enumerate(pde_op.bcs):
for term in terms:
assert term.i_interface == 0
if term.field_kind == pde_op.field_kind_e:
if term.direction == pde_op.dir_none:
bvp_rhs[i_bc] += (
term.coeff_outer * E0
+ term.coeff_inner * E1)
elif term.direction == pde_op.dir_normal:
bvp_rhs[i_bc] += (
term.coeff_outer * E0_dntarget
+ term.coeff_inner * E1_dntarget)
elif term.direction == pde_op.dir_tangential:
bvp_rhs[i_bc] += (
term.coeff_outer * E0_dttarget
+ term.coeff_inner * E1_dttarget)
else:
raise NotImplementedError("direction spec in RHS")
elif term.field_kind == pde_op.field_kind_h:
if term.direction == pde_op.dir_none:
bvp_rhs[i_bc] += (
term.coeff_outer * H0
+ term.coeff_inner * H1)
elif term.direction == pde_op.dir_normal:
bvp_rhs[i_bc] += (
term.coeff_outer * H0_dntarget
+ term.coeff_inner * H1_dntarget)
elif term.direction == pde_op.dir_tangential:
bvp_rhs[i_bc] += (
term.coeff_outer * H0_dttarget
+ term.coeff_inner * H1_dttarget)
else:
raise NotImplementedError("direction spec in RHS")
if use_l2_weighting:
bvp_rhs[i_bc] *= sqrt_w
scipy_op = bound_pde_op.scipy_op(queue, "unknown",
domains=[sym.DEFAULT_TARGET]*len(pde_op.bcs), K0=K0, K1=K1,
dtype=np.complex128)
if mode == "tem" or op_class is SRep:
from sumpy.tools import vector_from_device, vector_to_device
from pytential.solve import lu
unknown = lu(scipy_op, vector_from_device(queue, bvp_rhs))
unknown = vector_to_device(queue, unknown)
else:
from pytential.solve import gmres
gmres_result = gmres(scipy_op,
bvp_rhs, tol=1e-14, progress=True,
hard_failure=True, stall_iterations=0)
unknown = gmres_result.solution
# }}}
targets_0 = make_obj_array(list(np.array([
[3.2 + t, -4]
for t in [0, 0.5, 1]
]).T.copy()))
targets_1 = make_obj_array(list(np.array([
[t*-0.3, t*-0.2]
for t in [0, 0.5, 1]
]).T.copy()))
from pytential.target import PointsTarget
from sumpy.tools import vector_from_device
F0_tgt = vector_from_device(queue, bind( # noqa
(qbx, PointsTarget(targets_0)),
representation0_sym)(queue, unknown=unknown, K0=K0, K1=K1))
F1_tgt = vector_from_device(queue, bind( # noqa
(qbx, PointsTarget(targets_1)),
representation1_sym)(queue, unknown=unknown, K0=K0, K1=K1))
_, (E0_tgt_true,) = pot_p2p(queue, targets_0, e_sources_0, [e_strengths_0],
out_host=True, k=K0)
_, (E1_tgt_true,) = pot_p2p(queue, targets_1, e_sources_1, [e_strengths_1],
out_host=True, k=K1)
_, (H0_tgt_true,) = pot_p2p(queue, targets_0, h_sources_0, [h_strengths_0],
out_host=True, k=K0)
_, (H1_tgt_true,) = pot_p2p(queue, targets_1, h_sources_1, [h_strengths_1],
out_host=True, k=K1)
err_F0_total = 0 # noqa
err_F1_total = 0 # noqa
i_field = 0
def vec_norm(ary):
return la.norm(ary.reshape(-1))
def field_kind_to_string(field_kind):
return {pde_op.field_kind_e: "E", pde_op.field_kind_h: "H"}[field_kind]
for field_kind in pde_op.field_kinds:
if not pde_op.is_field_present(field_kind):
continue
if field_kind == pde_op.field_kind_e:
F0_tgt_true = E0_tgt_true # noqa
F1_tgt_true = E1_tgt_true # noqa
elif field_kind == pde_op.field_kind_h:
F0_tgt_true = H0_tgt_true # noqa
F1_tgt_true = H1_tgt_true # noqa
else:
assert False
abs_err_F0 = vec_norm(F0_tgt[i_field] - F0_tgt_true) # noqa
abs_err_F1 = vec_norm(F1_tgt[i_field] - F1_tgt_true) # noqa
rel_err_F0 = abs_err_F0/vec_norm(F0_tgt_true) # noqa
rel_err_F1 = abs_err_F1/vec_norm(F1_tgt_true) # noqa
err_F0_total = max(rel_err_F0, err_F0_total) # noqa
err_F1_total = max(rel_err_F1, err_F1_total) # noqa
print("Abs Err %s0" % field_kind_to_string(field_kind), abs_err_F0)
print("Abs Err %s1" % field_kind_to_string(field_kind), abs_err_F1)
print("Rel Err %s0" % field_kind_to_string(field_kind), rel_err_F0)
print("Rel Err %s1" % field_kind_to_string(field_kind), rel_err_F1)
i_field += 1
if visualize:
from sumpy.visualization import FieldPlotter
fplot = FieldPlotter(np.zeros(2), extent=5, npoints=300)
from pytential.target import PointsTarget
fld0 = bind(
(qbx, PointsTarget(fplot.points)),
representation0_sym)(queue, unknown=unknown, K0=K0)
fld1 = bind(
(qbx, PointsTarget(fplot.points)),
representation1_sym)(queue, unknown=unknown, K1=K1)
comp_fields = []
i_field = 0
for field_kind in pde_op.field_kinds:
if not pde_op.is_field_present(field_kind):
continue
fld_str = field_kind_to_string(field_kind)
comp_fields.extend([
("%s_fld0" % fld_str, fld0[i_field].get()),
("%s_fld1" % fld_str, fld1[i_field].get()),
])
i_field += 0
low_order_qbx = QBXLayerPotentialSource(
density_discr, fine_order=bdry_ovsmp_quad_order, qbx_order=2,
fmm_order=3).with_refinement()
from sumpy.kernel import LaplaceKernel
from pytential.target import PointsTarget
ones = (cl.array.empty(queue, (density_discr.nnodes,), dtype=np.float64)
.fill(1))
ind_func = - bind((low_order_qbx, PointsTarget(fplot.points)),
sym.D(LaplaceKernel(2), sym.var("u")))(
queue, u=ones).get()
_, (e_fld0_true,) = pot_p2p(
queue, fplot.points, e_sources_0, [e_strengths_0],
out_host=True, k=K0)
_, (e_fld1_true,) = pot_p2p(
queue, fplot.points, e_sources_1, [e_strengths_1],
out_host=True, k=K1)
_, (h_fld0_true,) = pot_p2p(
queue, fplot.points, h_sources_0, [h_strengths_0],
out_host=True, k=K0)
_, (h_fld1_true,) = pot_p2p(
queue, fplot.points, h_sources_1, [h_strengths_1],
out_host=True, k=K1)
#fplot.show_scalar_in_mayavi(fld_in_vol.real, max_val=5)
fplot.write_vtk_file(
"potential-n%d.vts" % nelements,
[
("e_fld0_true", e_fld0_true),
("e_fld1_true", e_fld1_true),
("h_fld0_true", h_fld0_true),
("h_fld1_true", h_fld1_true),
("ind", ind_func),
] + comp_fields
)
return err_F0_total, err_F1_total
def test_sanity_balls(ctx_getter, src_file, dim, mesh_order,
visualize=False):
pytest.importorskip("pytential")
logging.basicConfig(level=logging.INFO)
ctx = ctx_getter()
queue = cl.CommandQueue(ctx)
from pytools.convergence import EOCRecorder
vol_eoc_rec = EOCRecorder()
surf_eoc_rec = EOCRecorder()
# overkill
quad_order = mesh_order
from pytential import bind, sym
for h in [0.2, 0.14, 0.1]:
from meshmode.mesh.io import generate_gmsh, FileSource
mesh = generate_gmsh(
FileSource(src_file), dim, order=mesh_order,
other_options=["-string", "Mesh.CharacteristicLengthMax = %g;" % h],
force_ambient_dim=dim)
logger.info("%d elements" % mesh.nelements)
# {{{ discretizations and connections
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import \
InterpolatoryQuadratureSimplexGroupFactory
vol_discr = Discretization(ctx, mesh,
InterpolatoryQuadratureSimplexGroupFactory(quad_order))
from meshmode.discretization.connection import make_boundary_restriction
bdry_mesh, bdry_discr, bdry_connection = make_boundary_restriction(
queue, vol_discr,
InterpolatoryQuadratureSimplexGroupFactory(quad_order))
# }}}
# {{{ visualizers
from meshmode.discretization.visualization import make_visualizer
vol_vis = make_visualizer(queue, vol_discr, 20)
bdry_vis = make_visualizer(queue, bdry_discr, 20)
# }}}
from math import gamma
true_surf = 2*np.pi**(dim/2)/gamma(dim/2)
true_vol = true_surf/dim
vol_x = vol_discr.nodes().with_queue(queue)
vol_one = vol_x[0].copy()
vol_one.fill(1)
from pytential import norm, integral # noqa
comp_vol = integral(vol_discr, queue, vol_one)
rel_vol_err = abs(true_vol - comp_vol) / true_vol
vol_eoc_rec.add_data_point(h, rel_vol_err)
print("VOL", true_vol, comp_vol)
bdry_x = bdry_discr.nodes().with_queue(queue)
bdry_one_exact = bdry_x[0].copy()
bdry_one_exact.fill(1)
bdry_one = bdry_connection(queue, vol_one).with_queue(queue)
intp_err = norm(bdry_discr, queue, bdry_one-bdry_one_exact)
assert intp_err < 1e-14
comp_surf = integral(bdry_discr, queue, bdry_one)
rel_surf_err = abs(true_surf - comp_surf) / true_surf
surf_eoc_rec.add_data_point(h, rel_surf_err)
print("SURF", true_surf, comp_surf)
if visualize:
vol_vis.write_vtk_file("volume-h=%g.vtu" % h, [
("f", vol_one),
("area_el", bind(vol_discr, sym.area_element())(queue)),
])
bdry_vis.write_vtk_file("boundary-h=%g.vtu" % h, [("f", bdry_one)])
# {{{ check normals point outward
normal_outward_check = bind(bdry_discr,
sym.normal() | sym.Nodes(),
)(queue).as_scalar() > 0
assert normal_outward_check.get().all(), normal_outward_check.get()
# }}}
print("---------------------------------")
print("VOLUME")
print("---------------------------------")
print(vol_eoc_rec)
assert vol_eoc_rec.order_estimate() >= mesh_order
print("---------------------------------")
print("SURFACE")
print("---------------------------------")
print(surf_eoc_rec)
assert surf_eoc_rec.order_estimate() >= mesh_order
