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_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 test_unregularized_with_ones_kernel(ctx_factory):
cl_ctx = ctx_factory()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue)
nelements = 10
order = 8
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))
from pytential.unregularized import UnregularizedLayerPotentialSource
lpot_source = UnregularizedLayerPotentialSource(discr)
from pytential.target import PointsTarget
targets = PointsTarget(np.zeros((2, 1), dtype=float))
places = GeometryCollection({
sym.DEFAULT_SOURCE: lpot_source,
sym.DEFAULT_TARGET: lpot_source,
"target_non_self": targets})
from sumpy.kernel import one_kernel_2d
sigma_sym = sym.var("sigma")
op = sym.IntG(one_kernel_2d, sigma_sym, qbx_forced_limit=None)
sigma = discr.zeros(actx) + 1
result_self = bind(places, op,
auto_where=places.auto_where)(
actx, sigma=sigma)
result_nonself = bind(places, op,
auto_where=(places.auto_source, "target_non_self"))(
actx, sigma=sigma)
from meshmode.dof_array import flatten
assert np.allclose(actx.to_numpy(flatten(result_self)), 2 * np.pi)
assert np.allclose(actx.to_numpy(result_nonself), 2 * np.pi)
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_unregularized_off_surface_fmm_vs_direct(ctx_factory):
cl_ctx = ctx_factory()
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_to_fd_idempotency(ctx_factory, mm_mesh, fspace_degree):
"""
Make sure mm->fd->mm and (mm->)->fd->mm->fd are identity
"""
cl_ctx = ctx_factory()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue)
# make sure degree is higher order than mesh
fspace_degree += mm_mesh.groups[0].order
# Make a function space and a function with unique values at each node
factory = InterpolatoryQuadratureSimplexGroupFactory(fspace_degree)
discr = Discretization(actx, mm_mesh, factory)
fdrake_connection = build_connection_to_firedrake(discr)
fdrake_mesh = fdrake_connection.firedrake_fspace().mesh()
dtype = fdrake_mesh.coordinates.dat.data.dtype
mm_unique = discr.zeros(actx, dtype=dtype)
unique_vals = np.arange(np.size(mm_unique[0]), dtype=dtype)
mm_unique[0].set(unique_vals.reshape(mm_unique[0].shape))
mm_unique_copy = DOFArray(actx, (mm_unique[0].copy(), ))
# Test for idempotency mm->fd->mm
fdrake_unique = fdrake_connection.from_meshmode(mm_unique)
fdrake_connection.from_firedrake(fdrake_unique, out=mm_unique_copy)
np.testing.assert_allclose(actx.to_numpy(mm_unique_copy[0]),
actx.to_numpy(mm_unique[0]),
atol=CLOSE_ATOL)
# Test for idempotency (mm->)fd->mm->fd
fdrake_unique_copy = fdrake_connection.from_meshmode(mm_unique_copy)
np.testing.assert_allclose(fdrake_unique_copy.dat.data,
fdrake_unique.dat.data,
atol=CLOSE_ATOL)
class DGDiscretization:
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
@property
def _setup_actx(self):
return self.volume_discr._setup_actx
@property
def array_context(self):
return self.volume_discr.array_context
@property
def dim(self):
return self.volume_discr.dim
# {{{ discretizations/connections
@memoize_method
def boundary_connection(self, boundary_tag):
from meshmode.discretization.connection import make_face_restriction
return make_face_restriction(self.volume_discr._setup_actx,
self.volume_discr,
self.group_factory,
boundary_tag=boundary_tag)
@memoize_method
def interior_faces_connection(self):
from meshmode.discretization.connection import (make_face_restriction,
FACE_RESTR_INTERIOR)
return make_face_restriction(self.volume_discr._setup_actx,
self.volume_discr,
self.group_factory,
FACE_RESTR_INTERIOR,
per_face_groups=False)
@memoize_method
def opposite_face_connection(self):
from meshmode.discretization.connection import \
make_opposite_face_connection
return make_opposite_face_connection(self._setup_actx,
self.interior_faces_connection())
@memoize_method
def all_faces_connection(self):
from meshmode.discretization.connection import (make_face_restriction,
FACE_RESTR_ALL)
return make_face_restriction(self.volume_discr._setup_actx,
self.volume_discr,
self.group_factory,
FACE_RESTR_ALL,
per_face_groups=False)
@memoize_method
def get_to_all_face_embedding(self, where):
from meshmode.discretization.connection import \
make_face_to_all_faces_embedding
faces_conn = self.get_connection("vol", where)
return make_face_to_all_faces_embedding(self._setup_actx, faces_conn,
self.get_discr("all_faces"))
def get_connection(self, src, tgt):
src_tgt = (src, tgt)
if src_tgt == ("vol", "int_faces"):
return self.interior_faces_connection()
elif src_tgt == ("vol", "all_faces"):
return self.all_faces_connection()
elif src_tgt == ("vol", BTAG_ALL):
return self.boundary_connection(tgt)
elif src_tgt == ("int_faces", "all_faces"):
return self.get_to_all_face_embedding(src)
elif src_tgt == (BTAG_ALL, "all_faces"):
return self.get_to_all_face_embedding(src)
else:
raise ValueError(f"locations '{src}'->'{tgt}' not understood")
def interp(self, src, tgt, vec):
if (isinstance(vec, np.ndarray) and vec.dtype.char == "O"
and not isinstance(vec, DOFArray)):
return obj_array_vectorize(lambda el: self.interp(src, tgt, el),
vec)
return self.get_connection(src, tgt)(vec)
def get_discr(self, where):
if where == "vol":
return self.volume_discr
elif where == "all_faces":
return self.all_faces_connection().to_discr
elif where == "int_faces":
return self.interior_faces_connection().to_discr
elif where == BTAG_ALL:
return self.boundary_connection(where).to_discr
else:
raise ValueError(f"location '{where}' not understood")
# }}}
@memoize_method
def parametrization_derivative(self):
return freeze(
parametrization_derivative(self._setup_actx, self.volume_discr))
@memoize_method
def vol_jacobian(self):
[a, b], [c, d] = thaw(self._setup_actx,
self.parametrization_derivative())
return freeze(a * d - b * c)
@memoize_method
def inverse_parametrization_derivative(self):
[a, b], [c, d] = thaw(self._setup_actx,
self.parametrization_derivative())
result = np.zeros((2, 2), dtype=object)
det = a * d - b * c
result[0, 0] = d / det
result[0, 1] = -b / det
result[1, 0] = -c / det
result[1, 1] = a / det
return freeze(result)
def zeros(self, actx):
return self.volume_discr.zeros(actx)
def grad(self, vec):
ipder = self.inverse_parametrization_derivative()
dref = [
self.volume_discr.num_reference_derivative((idim, ), vec)
for idim in range(self.volume_discr.dim)
]
return make_obj_array([
sum(dref_i * ipder_i
for dref_i, ipder_i in zip(dref, ipder[iambient]))
for iambient in range(self.volume_discr.ambient_dim)
])
def div(self, vecs):
return sum(self.grad(vec_i)[i] for i, vec_i in enumerate(vecs))
@memoize_method
def normal(self, where):
bdry_discr = self.get_discr(where)
((a, ), (b, )) = parametrization_derivative(self._setup_actx,
bdry_discr)
nrm = 1 / (a**2 + b**2)**0.5
return freeze(flat_obj_array(b * nrm, -a * nrm))
@memoize_method
def face_jacobian(self, where):
bdry_discr = self.get_discr(where)
((a, ), (b, )) = parametrization_derivative(self._setup_actx,
bdry_discr)
return freeze((a**2 + b**2)**0.5)
@memoize_method
def get_inverse_mass_matrix(self, grp, dtype):
import modepy as mp
matrix = mp.inverse_mass_matrix(grp.basis(), grp.unit_nodes)
actx = self._setup_actx
return actx.freeze(actx.from_numpy(matrix))
def inverse_mass(self, vec):
if (isinstance(vec, np.ndarray) and vec.dtype.char == "O"
and not isinstance(vec, DOFArray)):
return obj_array_vectorize(lambda el: self.inverse_mass(el), vec)
@memoize_in(self, "elwise_linear_knl")
def knl():
return make_loopy_program(
"""{[iel,idof,j]:
0<=iel<nelements and
0<=idof<ndiscr_nodes_out and
0<=j<ndiscr_nodes_in}""",
"result[iel,idof] = sum(j, mat[idof, j] * vec[iel, j])",
name="diff")
discr = self.volume_discr
result = discr.empty_like(vec)
for grp in discr.groups:
matrix = self.get_inverse_mass_matrix(grp, vec.entry_dtype)
vec.array_context.call_loopy(knl(),
mat=matrix,
result=result[grp.index],
vec=vec[grp.index])
return result / self.vol_jacobian()
@memoize_method
def get_local_face_mass_matrix(self, afgrp, volgrp, dtype):
nfaces = volgrp.mesh_el_group.nfaces
assert afgrp.nelements == nfaces * volgrp.nelements
matrix = np.empty((volgrp.nunit_dofs, nfaces, afgrp.nunit_dofs),
dtype=dtype)
from modepy.tools import UNIT_VERTICES
import modepy as mp
for iface, fvi in enumerate(
volgrp.mesh_el_group.face_vertex_indices()):
face_vertices = UNIT_VERTICES[volgrp.dim][np.array(fvi)].T
matrix[:, iface, :] = mp.nodal_face_mass_matrix(
volgrp.basis(), volgrp.unit_nodes, afgrp.unit_nodes,
volgrp.order, face_vertices)
actx = self._setup_actx
return actx.freeze(actx.from_numpy(matrix))
def face_mass(self, vec):
if (isinstance(vec, np.ndarray) and vec.dtype.char == "O"
and not isinstance(vec, DOFArray)):
return obj_array_vectorize(lambda el: self.face_mass(el), vec)
@memoize_in(self, "face_mass_knl")
def knl():
return make_loopy_program(
"""{[iel,idof,f,j]:
0<=iel<nelements and
0<=f<nfaces and
0<=idof<nvol_nodes and
0<=j<nface_nodes}""", "result[iel,idof] = "
"sum(f, sum(j, mat[idof, f, j] * vec[f, iel, j]))",
name="face_mass")
all_faces_conn = self.get_connection("vol", "all_faces")
all_faces_discr = all_faces_conn.to_discr
vol_discr = all_faces_conn.from_discr
result = vol_discr.empty_like(vec)
fj = self.face_jacobian("all_faces")
vec = vec * fj
assert len(all_faces_discr.groups) == len(vol_discr.groups)
for afgrp, volgrp in zip(all_faces_discr.groups, vol_discr.groups):
nfaces = volgrp.mesh_el_group.nfaces
matrix = self.get_local_face_mass_matrix(afgrp, volgrp,
vec.entry_dtype)
vec.array_context.call_loopy(knl(),
mat=matrix,
result=result[volgrp.index],
vec=vec[afgrp.index].reshape(
nfaces, volgrp.nelements,
afgrp.nunit_dofs))
return result
class DiscretizationCollection:
"""A collection of discretizations, defined on the same underlying
:class:`~meshmode.mesh.Mesh`, corresponding to various mesh entities
(volume, interior facets, boundaries) and associated element
groups.
.. automethod:: __init__
.. autoattribute:: dim
.. autoattribute:: ambient_dim
.. autoattribute:: mesh
.. autoattribute:: real_dtype
.. autoattribute:: complex_dtype
.. automethod:: discr_from_dd
.. automethod:: connection_from_dds
.. automethod:: empty
.. automethod:: zeros
.. automethod:: nodes
.. automethod:: normal
.. rubric:: Internal functionality
.. automethod:: _base_to_geoderiv_connection
"""
# {{{ constructor
def __init__(
self,
array_context: ArrayContext,
mesh: Mesh,
order=None,
discr_tag_to_group_factory=None,
mpi_communicator=None,
# FIXME: `quad_tag_to_group_factory` is deprecated
quad_tag_to_group_factory=None):
"""
:arg discr_tag_to_group_factory: A mapping from discretization tags
(typically one of: :class:`grudge.dof_desc.DISCR_TAG_BASE`,
:class:`grudge.dof_desc.DISCR_TAG_MODAL`, or
:class:`grudge.dof_desc.DISCR_TAG_QUAD`) to a
:class:`~meshmode.discretization.poly_element.ElementGroupFactory`
indicating with which type of discretization the operations are
to be carried out, or *None* to indicate that operations with this
discretization tag should be carried out with the standard volume
discretization.
"""
if (quad_tag_to_group_factory is not None
and discr_tag_to_group_factory is not None):
raise ValueError(
"Both `quad_tag_to_group_factory` and `discr_tag_to_group_factory` "
"are specified. Use `discr_tag_to_group_factory` instead.")
# FIXME: `quad_tag_to_group_factory` is deprecated
if (quad_tag_to_group_factory is not None
and discr_tag_to_group_factory is None):
warn(
"`quad_tag_to_group_factory` is a deprecated kwarg and will "
"be dropped in version 2022.x. Use `discr_tag_to_group_factory` "
"instead.",
DeprecationWarning,
stacklevel=2)
discr_tag_to_group_factory = quad_tag_to_group_factory
self._setup_actx = array_context.clone()
from meshmode.discretization.poly_element import \
default_simplex_group_factory
if discr_tag_to_group_factory is None:
if order is None:
raise TypeError(
"one of 'order' and 'discr_tag_to_group_factory' must be given"
)
discr_tag_to_group_factory = {
DISCR_TAG_BASE:
default_simplex_group_factory(base_dim=mesh.dim, order=order)
}
else:
if order is not None:
discr_tag_to_group_factory = discr_tag_to_group_factory.copy()
if DISCR_TAG_BASE in discr_tag_to_group_factory:
raise ValueError(
"if 'order' is given, 'discr_tag_to_group_factory' must "
"not have a key of DISCR_TAG_BASE")
discr_tag_to_group_factory[DISCR_TAG_BASE] = \
default_simplex_group_factory(base_dim=mesh.dim, order=order)
# Modal discr should always come from the base discretization
discr_tag_to_group_factory[DISCR_TAG_MODAL] = \
_generate_modal_group_factory(
discr_tag_to_group_factory[DISCR_TAG_BASE]
)
self.discr_tag_to_group_factory = discr_tag_to_group_factory
from meshmode.discretization import Discretization
self._volume_discr = Discretization(
array_context, mesh,
self.group_factory_for_discretization_tag(DISCR_TAG_BASE))
# NOTE: Can be removed when symbolics are completely removed
# {{{ 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
# }}}
@property
def quad_tag_to_group_factory(self):
warn(
"`DiscretizationCollection.quad_tag_to_group_factory` "
"is deprecated and will go away in 2022. Use "
"`DiscretizationCollection.discr_tag_to_group_factory` "
"instead.",
DeprecationWarning,
stacklevel=2)
return self.discr_tag_to_group_factory
def get_management_rank_index(self):
return 0
def is_management_rank(self):
if self.mpi_communicator is None:
return True
else:
return self.mpi_communicator.Get_rank() \
== self.get_management_rank_index()
# {{{ distributed
def _set_up_distributed_communication(self, mpi_communicator,
array_context):
from_dd = DOFDesc("vol", DISCR_TAG_BASE)
boundary_connections = {}
from meshmode.distributed import get_connected_partitions
connected_parts = get_connected_partitions(self._volume_discr.mesh)
if connected_parts:
if mpi_communicator is None:
raise RuntimeError(
"must supply an MPI communicator when using a "
"distributed mesh")
grp_factory = \
self.group_factory_for_discretization_tag(DISCR_TAG_BASE)
local_boundary_connections = {}
for i_remote_part in connected_parts:
local_boundary_connections[
i_remote_part] = self.connection_from_dds(
from_dd,
DOFDesc(BTAG_PARTITION(i_remote_part), DISCR_TAG_BASE))
from meshmode.distributed import MPIBoundaryCommSetupHelper
with MPIBoundaryCommSetupHelper(mpi_communicator, array_context,
local_boundary_connections,
grp_factory) as bdry_setup_helper:
while True:
conns = bdry_setup_helper.complete_some()
if not conns:
break
for i_remote_part, conn in conns.items():
boundary_connections[i_remote_part] = conn
return boundary_connections
def get_distributed_boundary_swap_connection(self, dd):
warn(
"`DiscretizationCollection.get_distributed_boundary_swap_connection` "
"is deprecated and will go away in 2022. Use "
"`DiscretizationCollection.distributed_boundary_swap_connection` "
"instead.",
DeprecationWarning,
stacklevel=2)
return self.distributed_boundary_swap_connection(dd)
def distributed_boundary_swap_connection(self, dd):
"""Provides a mapping from the base volume discretization
to the exterior boundary restriction on a parallel boundary
partition described by *dd*. This connection is used to
communicate across element boundaries in different parallel
partitions during distributed runs.
:arg dd: a :class:`~grudge.dof_desc.DOFDesc`, or a value
convertible to one. The domain tag must be a subclass
of :class:`grudge.dof_desc.DTAG_BOUNDARY` with an
associated :class:`meshmode.mesh.BTAG_PARTITION`
corresponding to a particular communication rank.
"""
if dd.discretization_tag is not DISCR_TAG_BASE:
# FIXME
raise NotImplementedError(
"Distributed communication with discretization tag "
f"{dd.discretization_tag} is not implemented.")
assert isinstance(dd.domain_tag, DTAG_BOUNDARY)
assert isinstance(dd.domain_tag.tag, BTAG_PARTITION)
return self._dist_boundary_connections[dd.domain_tag.tag.part_nr]
# }}}
# {{{ discr_from_dd
@memoize_method
def discr_from_dd(self, dd):
"""Provides a :class:`meshmode.discretization.Discretization`
object from *dd*.
:arg dd: a :class:`~grudge.dof_desc.DOFDesc`, or a value
convertible to one.
"""
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))
# }}}
# {{{ _base_to_geoderiv_connection
@memoize_method
def _has_affine_groups(self):
from modepy.shapes import Simplex
return any(
megrp.is_affine and issubclass(megrp._modepy_shape_cls, Simplex)
for megrp in self._volume_discr.mesh.groups)
@memoize_method
def _base_to_geoderiv_connection(self, dd: DOFDesc):
r"""The "geometry derivatives" discretization for a given *dd* is
typically identical to the one returned by :meth:`discr_from_dd`,
however for affinely-mapped simplicial elements, it will use a
:math:`P^0` discretization having a single DOF per element.
As a result, :class:`~meshmode.dof_array.DOFArray`\ s on this
are broadcast-compatible with the discretizations returned by
:meth:`discr_from_dd`.
This is an internal function, not intended for use outside
:mod:`grudge`.
"""
base_discr = self.discr_from_dd(dd)
if not self._has_affine_groups():
# no benefit to having another discretization that takes
# advantage of affine-ness
from meshmode.discretization.connection import \
IdentityDiscretizationConnection
return IdentityDiscretizationConnection(base_discr)
base_group_factory = self.group_factory_for_discretization_tag(
dd.discretization_tag)
def geo_group_factory(megrp, index):
from modepy.shapes import Simplex
from meshmode.discretization.poly_element import \
PolynomialEquidistantSimplexElementGroup
if megrp.is_affine and issubclass(megrp._modepy_shape_cls,
Simplex):
return PolynomialEquidistantSimplexElementGroup(megrp,
order=0,
index=index)
else:
return base_group_factory(megrp, index)
from meshmode.discretization import Discretization
geo_deriv_discr = Discretization(self._setup_actx, base_discr.mesh,
geo_group_factory)
from meshmode.discretization.connection.same_mesh import \
make_same_mesh_connection
return make_same_mesh_connection(self._setup_actx,
to_discr=geo_deriv_discr,
from_discr=base_discr)
# }}}
# {{{ connection_from_dds
@memoize_method
def connection_from_dds(self, from_dd, to_dd):
"""Provides a mapping (connection) from one discretization to
another, e.g. from the volume to the boundary, or from the
base to the an overintegrated quadrature discretization, or from
a nodal representation to a modal representation.
:arg from_dd: a :class:`~grudge.dof_desc.DOFDesc`, or a value
convertible to one.
:arg to_dd: a :class:`~grudge.dof_desc.DOFDesc`, or a value
convertible to one.
"""
from_dd = as_dofdesc(from_dd)
to_dd = as_dofdesc(to_dd)
to_discr_tag = to_dd.discretization_tag
from_discr_tag = from_dd.discretization_tag
# {{{ mapping between modal and nodal representations
if (from_discr_tag is DISCR_TAG_MODAL
and to_discr_tag is not DISCR_TAG_MODAL):
return self._modal_to_nodal_connection(to_dd)
if (to_discr_tag is DISCR_TAG_MODAL
and from_discr_tag is not DISCR_TAG_MODAL):
return self._nodal_to_modal_connection(from_dd)
# }}}
assert (to_discr_tag is not DISCR_TAG_MODAL
and from_discr_tag is not DISCR_TAG_MODAL)
if (not from_dd.is_volume() and from_discr_tag == to_discr_tag
and to_dd.domain_tag is FACE_RESTR_ALL):
faces_conn = self.connection_from_dds(DOFDesc("vol"),
DOFDesc(from_dd.domain_tag))
from meshmode.discretization.connection import \
make_face_to_all_faces_embedding
return make_face_to_all_faces_embedding(
self._setup_actx, faces_conn, self.discr_from_dd(to_dd),
self.discr_from_dd(from_dd))
# {{{ simplify domain + discr_tag change into chained
if (from_dd.domain_tag != to_dd.domain_tag
and from_discr_tag is DISCR_TAG_BASE
and to_discr_tag is not DISCR_TAG_BASE):
from meshmode.discretization.connection import \
ChainedDiscretizationConnection
intermediate_dd = DOFDesc(to_dd.domain_tag)
return ChainedDiscretizationConnection([
# first change domain
self.connection_from_dds(from_dd, intermediate_dd),
# then go to quad grid
self.connection_from_dds(intermediate_dd, to_dd)
])
# }}}
# {{{ generic to-quad
# DISCR_TAG_MODAL is handled above
if (from_dd.domain_tag == to_dd.domain_tag
and from_discr_tag is DISCR_TAG_BASE
and to_discr_tag is not DISCR_TAG_BASE):
from meshmode.discretization.connection.same_mesh import \
make_same_mesh_connection
return make_same_mesh_connection(self._setup_actx,
self.discr_from_dd(to_dd),
self.discr_from_dd(from_dd))
# }}}
if from_discr_tag is not DISCR_TAG_BASE:
raise ValueError("cannot interpolate *from* a "
"(non-interpolatory) quadrature grid")
assert to_discr_tag is DISCR_TAG_BASE
if from_dd.is_volume():
if to_dd.domain_tag is FACE_RESTR_ALL:
return self._all_faces_volume_connection()
if to_dd.domain_tag is FACE_RESTR_INTERIOR:
return self._interior_faces_connection()
elif to_dd.is_boundary_or_partition_interface():
assert from_discr_tag is DISCR_TAG_BASE
return self._boundary_connection(to_dd.domain_tag.tag)
elif to_dd.is_volume():
from meshmode.discretization.connection import \
make_same_mesh_connection
to_discr = self._discr_tag_volume_discr(to_discr_tag)
from_discr = self._volume_discr
return make_same_mesh_connection(self._setup_actx, to_discr,
from_discr)
else:
raise ValueError("cannot interpolate from volume to: " +
str(to_dd))
else:
raise ValueError("cannot interpolate from: " + str(from_dd))
# }}}
# {{{ group_factory_for_discretization_tag
def group_factory_for_quadrature_tag(self, discretization_tag):
warn(
"`DiscretizationCollection.group_factory_for_quadrature_tag` "
"is deprecated and will go away in 2022. Use "
"`DiscretizationCollection.group_factory_for_discretization_tag` "
"instead.",
DeprecationWarning,
stacklevel=2)
return self.group_factory_for_discretization_tag(discretization_tag)
def group_factory_for_discretization_tag(self, discretization_tag):
"""
OK to override in user code to control mode/node choice.
"""
if discretization_tag is None:
discretization_tag = DISCR_TAG_BASE
return self.discr_tag_to_group_factory[discretization_tag]
# }}}
@memoize_method
def _discr_tag_volume_discr(self, discretization_tag):
assert discretization_tag is not None
# Refuse to re-make the volume discretization
if discretization_tag is DISCR_TAG_BASE:
return self._volume_discr
from meshmode.discretization import Discretization
return Discretization(
self._setup_actx, self._volume_discr.mesh,
self.group_factory_for_discretization_tag(discretization_tag))
@memoize_method
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))
# {{{ connection factories: modal<->nodal
@memoize_method
def _modal_to_nodal_connection(self, to_dd):
"""
:arg to_dd: a :class:`grudge.dof_desc.DOFDesc`
describing the dofs corresponding to the
*to_discr*
"""
from meshmode.discretization.connection import \
ModalToNodalDiscretizationConnection
return ModalToNodalDiscretizationConnection(
from_discr=self._modal_discr(to_dd.domain_tag),
to_discr=self.discr_from_dd(to_dd))
@memoize_method
def _nodal_to_modal_connection(self, from_dd):
"""
:arg from_dd: a :class:`grudge.dof_desc.DOFDesc`
describing the dofs corresponding to the
*from_discr*
"""
from meshmode.discretization.connection import \
NodalToModalDiscretizationConnection
return NodalToModalDiscretizationConnection(
from_discr=self.discr_from_dd(from_dd),
to_discr=self._modal_discr(from_dd.domain_tag))
# }}}
# {{{ connection factories: boundary
@memoize_method
def _boundary_connection(self, boundary_tag):
return make_face_restriction(
self._setup_actx,
self._volume_discr,
self.group_factory_for_discretization_tag(DISCR_TAG_BASE),
boundary_tag=boundary_tag)
# }}}
# {{{ connection factories: interior faces
@memoize_method
def _interior_faces_connection(self):
return make_face_restriction(
self._setup_actx,
self._volume_discr,
self.group_factory_for_discretization_tag(DISCR_TAG_BASE),
FACE_RESTR_INTERIOR,
# FIXME: This will need to change as soon as we support
# pyramids or other elements with non-identical face
# types.
per_face_groups=False)
@memoize_method
def opposite_face_connection(self):
"""Provides a mapping from the base volume discretization
to the exterior boundary restriction on a neighboring element.
This does not take into account parallel partitions.
"""
from meshmode.discretization.connection import \
make_opposite_face_connection
return make_opposite_face_connection(self._setup_actx,
self._interior_faces_connection())
# }}}
# {{{ connection factories: all-faces
@memoize_method
def _all_faces_volume_connection(self):
return make_face_restriction(
self._setup_actx,
self._volume_discr,
self.group_factory_for_discretization_tag(DISCR_TAG_BASE),
FACE_RESTR_ALL,
# FIXME: This will need to change as soon as we support
# pyramids or other elements with non-identical face
# types.
per_face_groups=False)
# }}}
@property
def dim(self):
"""Return the topological dimension."""
return self._volume_discr.dim
@property
def ambient_dim(self):
"""Return the dimension of the ambient space."""
return self._volume_discr.ambient_dim
@property
def real_dtype(self):
"""Return the data type used for real-valued arithmetic."""
return self._volume_discr.real_dtype
@property
def complex_dtype(self):
"""Return the data type used for complex-valued arithmetic."""
return self._volume_discr.complex_dtype
@property
def mesh(self):
"""Return the :class:`meshmode.mesh.Mesh` over which the discretization
collection is built.
"""
return self._volume_discr.mesh
def empty(self, array_context: ArrayContext, dtype=None):
"""Return an empty :class:`~meshmode.dof_array.DOFArray` defined at
the volume nodes: :class:`grudge.dof_desc.DD_VOLUME`.
:arg array_context: an :class:`~arraycontext.context.ArrayContext`.
:arg dtype: type special value 'c' will result in a
vector of dtype :attr:`complex_dtype`. If
*None* (the default), a real vector will be returned.
"""
return self._volume_discr.empty(array_context, dtype)
def zeros(self, array_context: ArrayContext, dtype=None):
"""Return a zero-initialized :class:`~meshmode.dof_array.DOFArray`
defined at the volume nodes, :class:`grudge.dof_desc.DD_VOLUME`.
:arg array_context: an :class:`~arraycontext.context.ArrayContext`.
:arg dtype: type special value 'c' will result in a
vector of dtype :attr:`complex_dtype`. If
*None* (the default), a real vector will be returned.
"""
return self._volume_discr.zeros(array_context, dtype)
def is_volume_where(self, where):
return where is None or as_dofdesc(where).is_volume()
@property
def order(self):
warn(
"DiscretizationCollection.order is deprecated, "
"consider using the orders of element groups instead. "
"'order' will go away in 2021.",
DeprecationWarning,
stacklevel=2)
from pytools import single_valued
return single_valued(egrp.order for egrp in self._volume_discr.groups)
# {{{ Discretization-specific geometric properties
def nodes(self, dd=None):
r"""Return the nodes of a discretization specified by *dd*.
:arg dd: a :class:`~grudge.dof_desc.DOFDesc`, or a value convertible to one.
Defaults to the base volume discretization.
:returns: an object array of frozen :class:`~meshmode.dof_array.DOFArray`\ s
"""
if dd is None:
dd = DD_VOLUME
return self.discr_from_dd(dd).nodes()
def normal(self, dd):
r"""Get the unit normal to the specified surface discretization, *dd*.
:arg dd: a :class:`~grudge.dof_desc.DOFDesc` as the surface discretization.
:returns: an object array of frozen :class:`~meshmode.dof_array.DOFArray`\ s.
"""
from arraycontext import freeze
from grudge.geometry import normal
return freeze(normal(self._setup_actx, self, dd))
def test_to_fd_transfer(ctx_factory, fspace_degree, mesh_name, mesh_pars, dim):
"""
Make sure creating a function which projects onto
one dimension then transports it is the same
(up to resampling error) as projecting to one
dimension on the transported mesh
"""
# build estimate-of-convergence recorder
from pytools.convergence import EOCRecorder
# dimension projecting onto -> EOCRecorder
eoc_recorders = {d: EOCRecorder() for d in range(dim)}
# make a computing context
cl_ctx = ctx_factory()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue)
# Get each of the refinements of the meshmeshes and record
# conversions errors
for mesh_par in mesh_pars:
if mesh_name in ("blob2d-order1", "blob2d-order4"):
assert dim == 2
from meshmode.mesh.io import read_gmsh
mm_mesh = read_gmsh(f"{mesh_name}-h{mesh_par}.msh",
force_ambient_dim=dim)
h = float(mesh_par)
elif mesh_name == "warp":
from meshmode.mesh.generation import generate_warped_rect_mesh
mm_mesh = generate_warped_rect_mesh(dim, order=4, n=mesh_par)
h = 1 / mesh_par
else:
raise ValueError("mesh_name not recognized")
# Make discr and connect it to firedrake
factory = InterpolatoryQuadratureSimplexGroupFactory(fspace_degree)
discr = Discretization(actx, mm_mesh, factory)
fdrake_connection = build_connection_to_firedrake(discr)
fdrake_fspace = fdrake_connection.firedrake_fspace()
spatial_coord = SpatialCoordinate(fdrake_fspace.mesh())
# get the group's nodes in a numpy array
nodes = discr.nodes()
group_nodes = np.array(
[actx.to_numpy(dof_arr[0]) for dof_arr in nodes])
for d in range(dim):
meshmode_f = discr.zeros(actx)
meshmode_f[0][:] = group_nodes[d, :, :]
# connect to firedrake and evaluate expr in firedrake
fdrake_f = Function(fdrake_fspace).interpolate(spatial_coord[d])
# transport to firedrake and record error
mm2fd_f = fdrake_connection.from_meshmode(meshmode_f)
err = np.max(np.abs(fdrake_f.dat.data - mm2fd_f.dat.data))
eoc_recorders[d].add_data_point(h, err)
# assert that order is correct or error is "low enough"
for d, eoc_rec in eoc_recorders.items():
print("\nvector *x* -> *x[%s]*\n" % d, eoc_rec)
assert (eoc_rec.order_estimate() >= fspace_degree
or eoc_rec.max_error() < 2e-14)
def timing_run(nx, ny, visualize=False):
import logging
logging.basicConfig(level=logging.WARNING) # INFO for more progress info
cl_ctx = cl.create_some_context()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue)
mesh = make_mesh(nx=nx, ny=ny, visualize=visualize)
density_discr = Discretization(
actx, 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)
places = {"qbx": qbx}
if visualize:
from sumpy.visualization import FieldPlotter
fplot = FieldPlotter(np.zeros(2), extent=5, npoints=1500)
targets = PointsTarget(actx.from_numpy(fplot.points))
places.update({
"plot-targets":
targets,
"qbx-indicator":
qbx.copy(target_association_tolerance=0.05,
fmm_level_to_order=lambda lev: 7,
qbx_order=2),
"qbx-target-assoc":
qbx.copy(target_association_tolerance=0.1)
})
from pytential import GeometryCollection
places = GeometryCollection(places, auto_where="qbx")
density_discr = places.get_discretization("qbx")
# {{{ describe bvp
from sumpy.kernel import HelmholtzKernel
kernel = HelmholtzKernel(2)
sigma_sym = sym.var("sigma")
sqrt_w = sym.sqrt_jac_q_weight(2)
inv_sqrt_w_sigma = sym.cse(sigma_sym / sqrt_w)
# Brakhage-Werner parameter
alpha = 1j
# -1 for interior Dirichlet
# +1 for exterior Dirichlet
loc_sign = +1
k_sym = sym.var("k")
S_sym = sym.S(kernel, inv_sqrt_w_sigma, k=k_sym, qbx_forced_limit=+1)
D_sym = sym.D(kernel, inv_sqrt_w_sigma, k=k_sym, qbx_forced_limit="avg")
bdry_op_sym = -loc_sign * 0.5 * sigma_sym + sqrt_w * (alpha * S_sym +
D_sym)
# }}}
bound_op = bind(places, bdry_op_sym)
# {{{ fix rhs and solve
mode_nr = 3
from meshmode.dof_array import thaw
nodes = thaw(actx, density_discr.nodes())
angle = actx.np.arctan2(nodes[1], nodes[0])
sigma = actx.np.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(places, sym_op)
print("FMM WARM-UP RUN 1: %5d elements" % mesh.nelements)
bound_op(actx, sigma=sigma, k=k)
queue.finish()
print("FMM WARM-UP RUN 2: %5d elements" % mesh.nelements)
bound_op(actx, sigma=sigma, k=k)
queue.finish()
from time import time
t_start = time()
bound_op(actx, sigma=sigma, k=k)
actx.queue.finish()
elapsed = time() - t_start
print("FMM TIMING RUN: %5d elements -> %g s" %
(mesh.nelements, elapsed))
if visualize:
ones_density = density_discr.zeros(queue)
ones_density.fill(1)
indicator = bind(places,
sym_op,
auto_where=("qbx-indicator", "plot-targets"))(
queue, sigma=ones_density).get()
try:
fld_in_vol = bind(places,
sym_op,
auto_where=("qbx-target-assoc",
"plot-targets"))(queue,
sigma=sigma,
k=k).get()
except QBXTargetAssociationFailedException as e:
fplot.write_vtk_file("scaling-study-failed-targets.vts", [
("failed", e.failed_target_flags.get(queue)),
])
raise
fplot.write_vtk_file("scaling-study-potential.vts", [
("potential", fld_in_vol),
("indicator", indicator),
])
return (mesh.nelements, elapsed)
class DGDiscretization:
def __init__(self, cl_ctx, 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(cl_ctx, mesh, self.group_factory)
assert self.volume_discr.dim == 2
@property
def cl_context(self):
return self.volume_discr.cl_context
@property
def dim(self):
return self.volume_discr.dim
# {{{ discretizations/connections
@memoize_method
def boundary_connection(self, boundary_tag):
from meshmode.discretization.connection import make_face_restriction
return make_face_restriction(self.volume_discr,
self.group_factory,
boundary_tag=boundary_tag)
@memoize_method
def interior_faces_connection(self):
from meshmode.discretization.connection import (make_face_restriction,
FACE_RESTR_INTERIOR)
return make_face_restriction(self.volume_discr,
self.group_factory,
FACE_RESTR_INTERIOR,
per_face_groups=False)
@memoize_method
def opposite_face_connection(self):
from meshmode.discretization.connection import \
make_opposite_face_connection
return make_opposite_face_connection(self.interior_faces_connection())
@memoize_method
def all_faces_connection(self):
from meshmode.discretization.connection import (make_face_restriction,
FACE_RESTR_ALL)
return make_face_restriction(self.volume_discr,
self.group_factory,
FACE_RESTR_ALL,
per_face_groups=False)
@memoize_method
def get_to_all_face_embedding(self, where):
from meshmode.discretization.connection import \
make_face_to_all_faces_embedding
faces_conn = self.get_connection("vol", where)
return make_face_to_all_faces_embedding(faces_conn,
self.get_discr("all_faces"))
def get_connection(self, src, tgt):
src_tgt = (src, tgt)
if src_tgt == ("vol", "int_faces"):
return self.interior_faces_connection()
elif src_tgt == ("vol", "all_faces"):
return self.all_faces_connection()
elif src_tgt == ("vol", BTAG_ALL):
return self.boundary_connection(tgt)
elif src_tgt == ("int_faces", "all_faces"):
return self.get_to_all_face_embedding(src)
elif src_tgt == (BTAG_ALL, "all_faces"):
return self.get_to_all_face_embedding(src)
else:
raise ValueError(f"locations '{src}'->'{tgt}' not understood")
def interp(self, src, tgt, vec):
if is_obj_array(vec):
return with_object_array_or_scalar(
lambda el: self.interp(src, tgt, el), vec)
return self.get_connection(src, tgt)(vec.queue, vec)
def get_discr(self, where):
if where == "vol":
return self.volume_discr
elif where == "all_faces":
return self.all_faces_connection().to_discr
elif where == "int_faces":
return self.interior_faces_connection().to_discr
elif where == BTAG_ALL:
return self.boundary_connection(where).to_discr
else:
raise ValueError(f"location '{where}' not understood")
# }}}
@memoize_method
def parametrization_derivative(self):
with cl.CommandQueue(self.cl_context) as queue:
return without_queue(
parametrization_derivative(queue, self.volume_discr))
@memoize_method
def vol_jacobian(self):
with cl.CommandQueue(self.cl_context) as queue:
[a, b], [c, d] = with_queue(queue,
self.parametrization_derivative())
return (a * d - b * c).with_queue(None)
@memoize_method
def inverse_parametrization_derivative(self):
with cl.CommandQueue(self.cl_context) as queue:
[a, b], [c, d] = with_queue(queue,
self.parametrization_derivative())
result = np.zeros((2, 2), dtype=object)
det = a * d - b * c
result[0, 0] = d / det
result[0, 1] = -b / det
result[1, 0] = -c / det
result[1, 1] = a / det
return without_queue(result)
def zeros(self, queue):
return self.volume_discr.zeros(queue)
def grad(self, vec):
ipder = self.inverse_parametrization_derivative()
queue = vec.queue
dref = [
self.volume_discr.num_reference_derivative(queue, (idim, ),
vec).with_queue(queue)
for idim in range(self.volume_discr.dim)
]
return make_obj_array([
sum(dref_i * ipder_i
for dref_i, ipder_i in zip(dref, ipder[iambient]))
for iambient in range(self.volume_discr.ambient_dim)
])
def div(self, vecs):
return sum(self.grad(vec_i)[i] for i, vec_i in enumerate(vecs))
@memoize_method
def normal(self, where):
bdry_discr = self.get_discr(where)
with cl.CommandQueue(self.cl_context) as queue:
((a, ),
(b, )) = with_queue(queue,
parametrization_derivative(queue, bdry_discr))
nrm = 1 / (a**2 + b**2)**0.5
return without_queue(join_fields(b * nrm, -a * nrm))
@memoize_method
def face_jacobian(self, where):
bdry_discr = self.get_discr(where)
with cl.CommandQueue(self.cl_context) as queue:
((a, ),
(b, )) = with_queue(queue,
parametrization_derivative(queue, bdry_discr))
return ((a**2 + b**2)**0.5).with_queue(None)
@memoize_method
def get_inverse_mass_matrix(self, grp, dtype):
import modepy as mp
matrix = mp.inverse_mass_matrix(grp.basis(), grp.unit_nodes)
with cl.CommandQueue(self.cl_context) as queue:
return (cla.to_device(queue, matrix).with_queue(None))
def inverse_mass(self, vec):
if is_obj_array(vec):
return with_object_array_or_scalar(
lambda el: self.inverse_mass(el), vec)
@memoize_in(self, "elwise_linear_knl")
def knl():
knl = lp.make_kernel("""{[k,i,j]:
0<=k<nelements and
0<=i<ndiscr_nodes_out and
0<=j<ndiscr_nodes_in}""",
"result[k,i] = sum(j, mat[i, j] * vec[k, j])",
default_offset=lp.auto,
name="diff")
knl = lp.split_iname(knl, "i", 16, inner_tag="l.0")
return lp.tag_inames(knl, dict(k="g.0"))
discr = self.volume_discr
result = discr.empty(queue=vec.queue, dtype=vec.dtype)
for grp in discr.groups:
matrix = self.get_inverse_mass_matrix(grp, vec.dtype)
knl()(vec.queue,
mat=matrix,
result=grp.view(result),
vec=grp.view(vec))
return result / self.vol_jacobian()
@memoize_method
def get_local_face_mass_matrix(self, afgrp, volgrp, dtype):
nfaces = volgrp.mesh_el_group.nfaces
assert afgrp.nelements == nfaces * volgrp.nelements
matrix = np.empty((volgrp.nunit_nodes, nfaces, afgrp.nunit_nodes),
dtype=dtype)
from modepy.tools import UNIT_VERTICES
import modepy as mp
for iface, fvi in enumerate(
volgrp.mesh_el_group.face_vertex_indices()):
face_vertices = UNIT_VERTICES[volgrp.dim][np.array(fvi)].T
matrix[:, iface, :] = mp.nodal_face_mass_matrix(
volgrp.basis(), volgrp.unit_nodes, afgrp.unit_nodes,
volgrp.order, face_vertices)
with cl.CommandQueue(self.cl_context) as queue:
return (cla.to_device(queue, matrix).with_queue(None))
def face_mass(self, vec):
if is_obj_array(vec):
return with_object_array_or_scalar(lambda el: self.face_mass(el),
vec)
@memoize_in(self, "face_mass_knl")
def knl():
knl = lp.make_kernel(
"""{[k,i,f,j]:
0<=k<nelements and
0<=f<nfaces and
0<=i<nvol_nodes and
0<=j<nface_nodes}""",
"result[k,i] = sum(f, sum(j, mat[i, f, j] * vec[f, k, j]))",
default_offset=lp.auto,
name="face_mass")
knl = lp.split_iname(knl, "i", 16, inner_tag="l.0")
return lp.tag_inames(knl, dict(k="g.0"))
all_faces_conn = self.get_connection("vol", "all_faces")
all_faces_discr = all_faces_conn.to_discr
vol_discr = all_faces_conn.from_discr
result = vol_discr.empty(queue=vec.queue, dtype=vec.dtype)
fj = self.face_jacobian("all_faces")
vec = vec * fj
assert len(all_faces_discr.groups) == len(vol_discr.groups)
for afgrp, volgrp in zip(all_faces_discr.groups, vol_discr.groups):
nfaces = volgrp.mesh_el_group.nfaces
matrix = self.get_local_face_mass_matrix(afgrp, volgrp, vec.dtype)
input_view = afgrp.view(vec).reshape(nfaces, volgrp.nelements,
afgrp.nunit_nodes)
knl()(vec.queue,
mat=matrix,
result=volgrp.view(result),
vec=input_view)
return result
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)
]
)
class DGDiscretizationWithBoundaries(DiscretizationBase):
"""
.. automethod :: discr_from_dd
.. automethod :: connection_from_dds
.. autoattribute :: cl_context
.. autoattribute :: dim
.. autoattribute :: ambient_dim
.. autoattribute :: mesh
.. automethod :: empty
.. automethod :: zeros
"""
def __init__(self,
cl_ctx,
mesh,
order,
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.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.
"""
if quad_tag_to_group_factory is None:
quad_tag_to_group_factory = {}
self.order = order
self.quad_tag_to_group_factory = quad_tag_to_group_factory
from meshmode.discretization import Discretization
self._volume_discr = Discretization(
cl_ctx, 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 = {}
# }}}
with cl.CommandQueue(cl_ctx) as queue:
self._dist_boundary_connections = \
self._set_up_distributed_communication(mpi_communicator, queue)
self.mpi_communicator = mpi_communicator
def get_management_rank_index(self):
return 0
def is_management_rank(self):
if self.mpi_communicator is None:
return True
else:
return self.mpi_communicator.Get_rank() \
== self._get_management_rank_index()
def _set_up_distributed_communication(self, mpi_communicator, queue):
from_dd = sym.DOFDesc("vol", sym.QTAG_NONE)
from meshmode.distributed import get_connected_partitions
connected_parts = get_connected_partitions(self._volume_discr.mesh)
if mpi_communicator is None and connected_parts:
raise RuntimeError("must supply an MPI communicator when using a "
"distributed mesh")
grp_factory = self.group_factory_for_quadrature_tag(sym.QTAG_NONE)
setup_helpers = {}
boundary_connections = {}
from meshmode.distributed import MPIBoundaryCommSetupHelper
for i_remote_part in connected_parts:
conn = self.connection_from_dds(
from_dd,
sym.DOFDesc(sym.BTAG_PARTITION(i_remote_part), sym.QTAG_NONE))
setup_helper = setup_helpers[
i_remote_part] = MPIBoundaryCommSetupHelper(
mpi_communicator, queue, conn, i_remote_part, grp_factory)
setup_helper.post_sends()
for i_remote_part, setup_helper in six.iteritems(setup_helpers):
boundary_connections[i_remote_part] = setup_helper.complete_setup()
return boundary_connections
def get_distributed_boundary_swap_connection(self, dd):
if dd.quadrature_tag != sym.QTAG_NONE:
# FIXME
raise NotImplementedError(
"Distributed communication with quadrature")
assert isinstance(dd.domain_tag, sym.BTAG_PARTITION)
return self._dist_boundary_connections[dd.domain_tag.part_nr]
@memoize_method
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))
@memoize_method
def connection_from_dds(self, from_dd, to_dd):
from_dd = sym.as_dofdesc(from_dd)
to_dd = sym.as_dofdesc(to_dd)
to_qtag = to_dd.quadrature_tag
if (not from_dd.is_volume()
and from_dd.quadrature_tag == to_dd.quadrature_tag
and to_dd.domain_tag is sym.FACE_RESTR_ALL):
faces_conn = self.connection_from_dds(
sym.DOFDesc("vol"), sym.DOFDesc(from_dd.domain_tag))
from meshmode.discretization.connection import \
make_face_to_all_faces_embedding
return make_face_to_all_faces_embedding(
faces_conn, self.discr_from_dd(to_dd),
self.discr_from_dd(from_dd))
# {{{ simplify domain + qtag change into chained
if (from_dd.domain_tag != to_dd.domain_tag
and from_dd.quadrature_tag is sym.QTAG_NONE
and to_dd.quadrature_tag is not sym.QTAG_NONE):
from meshmode.discretization.connection import \
ChainedDiscretizationConnection
intermediate_dd = sym.DOFDesc(to_dd.domain_tag)
return ChainedDiscretizationConnection([
# first change domain
self.connection_from_dds(from_dd, intermediate_dd),
# then go to quad grid
self.connection_from_dds(intermediate_dd, to_dd)
])
# }}}
# {{{ generic to-quad
if (from_dd.domain_tag == to_dd.domain_tag
and from_dd.quadrature_tag is sym.QTAG_NONE
and to_dd.quadrature_tag is not sym.QTAG_NONE):
from meshmode.discretization.connection.same_mesh import \
make_same_mesh_connection
return make_same_mesh_connection(self.discr_from_dd(to_dd),
self.discr_from_dd(from_dd))
# }}}
if from_dd.quadrature_tag is not sym.QTAG_NONE:
raise ValueError("cannot interpolate *from* a "
"(non-interpolatory) quadrature grid")
assert to_qtag is sym.QTAG_NONE
if from_dd.is_volume():
if to_dd.domain_tag is sym.FACE_RESTR_ALL:
return self._all_faces_volume_connection()
if to_dd.domain_tag is sym.FACE_RESTR_INTERIOR:
return self._interior_faces_connection()
elif to_dd.is_boundary():
assert from_dd.quadrature_tag is sym.QTAG_NONE
return self._boundary_connection(to_dd.domain_tag)
elif to_dd.is_volume():
from meshmode.discretization.connection import \
make_same_mesh_connection
to_discr = self._quad_volume_discr(to_dd.quadrature_tag)
from_discr = self._volume_discr
return make_same_mesh_connection(to_discr, from_discr)
else:
raise ValueError("cannot interpolate from volume to: " +
str(to_dd))
else:
raise ValueError("cannot interpolate from: " + str(from_dd))
def group_factory_for_quadrature_tag(self, quadrature_tag):
"""
OK to override in user code to control mode/node choice.
"""
if quadrature_tag is None:
quadrature_tag = sym.QTAG_NONE
from meshmode.discretization.poly_element import \
PolynomialWarpAndBlendGroupFactory
if quadrature_tag is not sym.QTAG_NONE:
return self.quad_tag_to_group_factory[quadrature_tag]
else:
return PolynomialWarpAndBlendGroupFactory(order=self.order)
@memoize_method
def _quad_volume_discr(self, quadrature_tag):
from meshmode.discretization import Discretization
return Discretization(
self._volume_discr.cl_context, self._volume_discr.mesh,
self.group_factory_for_quadrature_tag(quadrature_tag))
# {{{ boundary
@memoize_method
def _boundary_connection(self, boundary_tag):
from meshmode.discretization.connection import make_face_restriction
return make_face_restriction(self._volume_discr,
self.group_factory_for_quadrature_tag(
sym.QTAG_NONE),
boundary_tag=boundary_tag)
# }}}
# {{{ interior faces
@memoize_method
def _interior_faces_connection(self):
from meshmode.discretization.connection import (make_face_restriction,
FACE_RESTR_INTERIOR)
return make_face_restriction(
self._volume_discr,
self.group_factory_for_quadrature_tag(sym.QTAG_NONE),
FACE_RESTR_INTERIOR,
# FIXME: This will need to change as soon as we support
# pyramids or other elements with non-identical face
# types.
per_face_groups=False)
@memoize_method
def opposite_face_connection(self):
from meshmode.discretization.connection import \
make_opposite_face_connection
return make_opposite_face_connection(self._interior_faces_connection())
# }}}
# {{{ all-faces
@memoize_method
def _all_faces_volume_connection(self):
from meshmode.discretization.connection import (make_face_restriction,
FACE_RESTR_ALL)
return make_face_restriction(
self._volume_discr,
self.group_factory_for_quadrature_tag(sym.QTAG_NONE),
FACE_RESTR_ALL,
# FIXME: This will need to change as soon as we support
# pyramids or other elements with non-identical face
# types.
per_face_groups=False)
# }}}
@property
def cl_context(self):
return self._volume_discr.cl_context
@property
def dim(self):
return self._volume_discr.dim
@property
def ambient_dim(self):
return self._volume_discr.ambient_dim
@property
def real_dtype(self):
return self._volume_discr.real_dtype
@property
def complex_dtype(self):
return self._volume_discr.complex_dtype
@property
def mesh(self):
return self._volume_discr.mesh
def empty(self, queue=None, dtype=None, extra_dims=None, allocator=None):
return self._volume_discr.empty(queue,
dtype,
extra_dims=extra_dims,
allocator=allocator)
def zeros(self, queue, dtype=None, extra_dims=None, allocator=None):
return self._volume_discr.zeros(queue,
dtype,
extra_dims=extra_dims,
allocator=allocator)
def is_volume_where(self, where):
from grudge import sym
return (where is None or where == sym.VTAG_ALL)
class DGDiscretization:
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
@property
def _setup_actx(self):
return self.volume_discr._setup_actx
@property
def dim(self):
return self.volume_discr.dim
# {{{ discretizations/connections
@memoize_method
def boundary_connection(self, boundary_tag):
from meshmode.discretization.connection import make_face_restriction
return make_face_restriction(self.volume_discr._setup_actx,
self.volume_discr,
self.group_factory,
boundary_tag=boundary_tag)
@memoize_method
def interior_faces_connection(self):
from meshmode.discretization.connection import (make_face_restriction,
FACE_RESTR_INTERIOR)
return make_face_restriction(self.volume_discr._setup_actx,
self.volume_discr,
self.group_factory,
FACE_RESTR_INTERIOR,
per_face_groups=False)
@memoize_method
def opposite_face_connection(self):
from meshmode.discretization.connection import \
make_opposite_face_connection
return make_opposite_face_connection(self._setup_actx,
self.interior_faces_connection())
@memoize_method
def all_faces_connection(self):
from meshmode.discretization.connection import (make_face_restriction,
FACE_RESTR_ALL)
return make_face_restriction(self.volume_discr._setup_actx,
self.volume_discr,
self.group_factory,
FACE_RESTR_ALL,
per_face_groups=False)
@memoize_method
def get_to_all_face_embedding(self, where):
from meshmode.discretization.connection import \
make_face_to_all_faces_embedding
faces_conn = self.get_connection("vol", where)
return make_face_to_all_faces_embedding(self._setup_actx, faces_conn,
self.get_discr("all_faces"))
def get_connection(self, src, tgt):
src_tgt = (src, tgt)
if src_tgt == ("vol", "int_faces"):
return self.interior_faces_connection()
elif src_tgt == ("vol", "all_faces"):
return self.all_faces_connection()
elif src_tgt == ("vol", BTAG_ALL):
return self.boundary_connection(tgt)
elif src_tgt == ("int_faces", "all_faces"):
return self.get_to_all_face_embedding(src)
elif src_tgt == (BTAG_ALL, "all_faces"):
return self.get_to_all_face_embedding(src)
else:
raise ValueError(f"locations '{src}'->'{tgt}' not understood")
def interp(self, src, tgt, vec):
return self.get_connection(src, tgt)(vec)
def get_discr(self, where):
if where == "vol":
return self.volume_discr
elif where == "all_faces":
return self.all_faces_connection().to_discr
elif where == "int_faces":
return self.interior_faces_connection().to_discr
elif where == BTAG_ALL:
return self.boundary_connection(where).to_discr
else:
raise ValueError(f"location '{where}' not understood")
# }}}
@memoize_method
def parametrization_derivative(self):
return freeze(
parametrization_derivative(self._setup_actx, self.volume_discr))
@memoize_method
def vol_jacobian(self):
[a, b], [c, d] = thaw(self.parametrization_derivative(),
self._setup_actx)
return freeze(a * d - b * c)
@memoize_method
def inverse_parametrization_derivative(self):
[a, b], [c, d] = thaw(self.parametrization_derivative(),
self._setup_actx)
result = np.zeros((2, 2), dtype=object)
det = a * d - b * c
result[0, 0] = d / det
result[0, 1] = -b / det
result[1, 0] = -c / det
result[1, 1] = a / det
return freeze(result)
def zeros(self, actx):
return self.volume_discr.zeros(actx)
def grad(self, vec):
ipder = thaw(self.inverse_parametrization_derivative(),
vec.array_context)
from meshmode.discretization import num_reference_derivative
dref = [
num_reference_derivative(self.volume_discr, (idim, ), vec)
for idim in range(self.volume_discr.dim)
]
return make_obj_array([
sum(dref_i * ipder_i
for dref_i, ipder_i in zip(dref, ipder[iambient]))
for iambient in range(self.volume_discr.ambient_dim)
])
def div(self, vecs):
return sum(self.grad(vec_i)[i] for i, vec_i in enumerate(vecs))
@memoize_method
def normal(self, where):
bdry_discr = self.get_discr(where)
((a, ), (b, )) = parametrization_derivative(self._setup_actx,
bdry_discr)
nrm = 1 / (a**2 + b**2)**0.5
return freeze(flat_obj_array(b * nrm, -a * nrm))
@memoize_method
def face_jacobian(self, where):
bdry_discr = self.get_discr(where)
((a, ), (b, )) = parametrization_derivative(self._setup_actx,
bdry_discr)
return freeze((a**2 + b**2)**0.5)
@memoize_method
def get_inverse_mass_matrix(self, grp, dtype):
import modepy as mp
matrix = mp.inverse_mass_matrix(grp.basis_obj().functions,
grp.unit_nodes)
actx = self._setup_actx
return actx.freeze(actx.from_numpy(matrix))
def inverse_mass(self, vec):
if not isinstance(vec, DOFArray):
return map_array_container(self.inverse_mass, vec)
actx = vec.array_context
dtype = vec.entry_dtype
discr = self.volume_discr
return DOFArray(
actx,
data=tuple(
actx.einsum("ij,ej->ei",
self.get_inverse_mass_matrix(grp, dtype),
vec_i,
arg_names=("mass_inv_mat", "vec"),
tagged=(FirstAxisIsElementsTag(), ))
for grp, vec_i in zip(discr.groups, vec))) / thaw(
self.vol_jacobian(), actx)
@memoize_method
def get_local_face_mass_matrix(self, afgrp, volgrp, dtype):
nfaces = volgrp.mesh_el_group.nfaces
assert afgrp.nelements == nfaces * volgrp.nelements
matrix = np.empty((volgrp.nunit_dofs, nfaces, afgrp.nunit_dofs),
dtype=dtype)
import modepy as mp
shape = mp.Simplex(volgrp.dim)
unit_vertices = mp.unit_vertices_for_shape(shape).T
for face in mp.faces_for_shape(shape):
face_vertices = unit_vertices[np.array(
face.volume_vertex_indices)].T
matrix[:, face.face_index, :] = mp.nodal_face_mass_matrix(
volgrp.basis_obj().functions, volgrp.unit_nodes,
afgrp.unit_nodes, volgrp.order, face_vertices)
actx = self._setup_actx
return actx.freeze(actx.from_numpy(matrix))
def face_mass(self, vec):
if not isinstance(vec, DOFArray):
return map_array_container(self.face_mass, vec)
actx = vec.array_context
dtype = vec.entry_dtype
@memoize_in(self, "face_mass_knl")
def knl():
return make_loopy_program(
"""{[iel,idof,f,j]:
0<=iel<nelements and
0<=f<nfaces and
0<=idof<nvol_nodes and
0<=j<nface_nodes}""", "result[iel,idof] = "
"sum(f, sum(j, mat[idof, f, j] * vec[f, iel, j]))",
name="face_mass")
all_faces_conn = self.get_connection("vol", "all_faces")
all_faces_discr = all_faces_conn.to_discr
vol_discr = all_faces_conn.from_discr
fj = thaw(self.face_jacobian("all_faces"), vec.array_context)
vec = vec * fj
assert len(all_faces_discr.groups) == len(vol_discr.groups)
return DOFArray(
actx,
data=tuple(
actx.call_loopy(
knl(),
mat=self.get_local_face_mass_matrix(afgrp, volgrp, dtype),
vec=vec_i.reshape(volgrp.mesh_el_group.nfaces, volgrp.
nelements, afgrp.nunit_dofs))["result"]
for afgrp, volgrp, vec_i in zip(all_faces_discr.groups,
vol_discr.groups, vec)))
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)])
class DiscretizationCollection:
"""
.. automethod :: __init__
.. automethod :: discr_from_dd
.. automethod :: connection_from_dds
.. autoattribute :: dim
.. autoattribute :: ambient_dim
.. autoattribute :: mesh
.. automethod :: empty
.. automethod :: zeros
"""
def __init__(
self,
array_context,
mesh,
order=None,
discr_tag_to_group_factory=None,
mpi_communicator=None,
# FIXME: `quad_tag_to_group_factory` is deprecated
quad_tag_to_group_factory=None):
"""
:param discr_tag_to_group_factory: A mapping from discretization tags
(typically one of: :class:`grudge.dof_desc.DISCR_TAG_BASE`,
:class:`grudge.dof_desc.DISCR_TAG_MODAL`, or
:class:`grudge.dof_desc.DISCR_TAG_QUAD`) to a
:class:`~meshmode.discretization.poly_element.ElementGroupFactory`
indicating with which type of discretization the operations are
to be carried out, or *None* to indicate that operations with this
discretization tag should be carried out with the standard volume
discretization.
"""
if (quad_tag_to_group_factory is not None
and discr_tag_to_group_factory is not None):
raise ValueError(
"Both `quad_tag_to_group_factory` and `discr_tag_to_group_factory` "
"are specified. Use `discr_tag_to_group_factory` instead.")
# FIXME: `quad_tag_to_group_factory` is deprecated
if (quad_tag_to_group_factory is not None
and discr_tag_to_group_factory is None):
warn(
"`quad_tag_to_group_factory` is a deprecated kwarg and will "
"be dropped in version 2022.x. Use `discr_tag_to_group_factory` "
"instead.",
DeprecationWarning,
stacklevel=2)
discr_tag_to_group_factory = quad_tag_to_group_factory
self._setup_actx = array_context
from meshmode.discretization.poly_element import \
PolynomialWarpAndBlendGroupFactory
if discr_tag_to_group_factory is None:
if order is None:
raise TypeError(
"one of 'order' and 'discr_tag_to_group_factory' must be given"
)
discr_tag_to_group_factory = {
DISCR_TAG_BASE: PolynomialWarpAndBlendGroupFactory(order=order)
}
else:
if order is not None:
discr_tag_to_group_factory = discr_tag_to_group_factory.copy()
if DISCR_TAG_BASE in discr_tag_to_group_factory:
raise ValueError(
"if 'order' is given, 'discr_tag_to_group_factory' must "
"not have a key of DISCR_TAG_BASE")
discr_tag_to_group_factory[DISCR_TAG_BASE] = \
PolynomialWarpAndBlendGroupFactory(order=order)
# Modal discr should always comes from the base discretization
discr_tag_to_group_factory[DISCR_TAG_MODAL] = \
_generate_modal_group_factory(
discr_tag_to_group_factory[DISCR_TAG_BASE]
)
self.discr_tag_to_group_factory = discr_tag_to_group_factory
from meshmode.discretization import Discretization
self._volume_discr = Discretization(
array_context, mesh,
self.group_factory_for_discretization_tag(DISCR_TAG_BASE))
# {{{ 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
@property
def quad_tag_to_group_factory(self):
warn(
"`DiscretizationCollection.quad_tag_to_group_factory` "
"is deprecated and will go away in 2022. Use "
"`DiscretizationCollection.discr_tag_to_group_factory` "
"instead.",
DeprecationWarning,
stacklevel=2)
return self.discr_tag_to_group_factory
def get_management_rank_index(self):
return 0
def is_management_rank(self):
if self.mpi_communicator is None:
return True
else:
return self.mpi_communicator.Get_rank() \
== self.get_management_rank_index()
def _set_up_distributed_communication(self, mpi_communicator,
array_context):
from_dd = DOFDesc("vol", DISCR_TAG_BASE)
boundary_connections = {}
from meshmode.distributed import get_connected_partitions
connected_parts = get_connected_partitions(self._volume_discr.mesh)
if connected_parts:
if mpi_communicator is None:
raise RuntimeError(
"must supply an MPI communicator when using a "
"distributed mesh")
grp_factory = \
self.group_factory_for_discretization_tag(DISCR_TAG_BASE)
local_boundary_connections = {}
for i_remote_part in connected_parts:
local_boundary_connections[
i_remote_part] = self.connection_from_dds(
from_dd,
DOFDesc(BTAG_PARTITION(i_remote_part), DISCR_TAG_BASE))
from meshmode.distributed import MPIBoundaryCommSetupHelper
with MPIBoundaryCommSetupHelper(mpi_communicator, array_context,
local_boundary_connections,
grp_factory) as bdry_setup_helper:
while True:
conns = bdry_setup_helper.complete_some()
if not conns:
break
for i_remote_part, conn in conns.items():
boundary_connections[i_remote_part] = conn
return boundary_connections
def get_distributed_boundary_swap_connection(self, dd):
if dd.discretization_tag is not DISCR_TAG_BASE:
# FIXME
raise NotImplementedError(
"Distributed communication with discretization tag "
f"{dd.discretization_tag} is not implemented.")
assert isinstance(dd.domain_tag, DTAG_BOUNDARY)
assert isinstance(dd.domain_tag.tag, BTAG_PARTITION)
return self._dist_boundary_connections[dd.domain_tag.tag.part_nr]
@memoize_method
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))
@memoize_method
def connection_from_dds(self, from_dd, to_dd):
from_dd = as_dofdesc(from_dd)
to_dd = as_dofdesc(to_dd)
to_discr_tag = to_dd.discretization_tag
from_discr_tag = from_dd.discretization_tag
# {{{ mapping between modal and nodal representations
if (from_discr_tag is DISCR_TAG_MODAL
and to_discr_tag is not DISCR_TAG_MODAL):
return self._modal_to_nodal_connection(to_dd)
if (to_discr_tag is DISCR_TAG_MODAL
and from_discr_tag is not DISCR_TAG_MODAL):
return self._nodal_to_modal_connection(from_dd)
# }}}
assert (to_discr_tag is not DISCR_TAG_MODAL
and from_discr_tag is not DISCR_TAG_MODAL)
if (not from_dd.is_volume() and from_discr_tag == to_discr_tag
and to_dd.domain_tag is FACE_RESTR_ALL):
faces_conn = self.connection_from_dds(DOFDesc("vol"),
DOFDesc(from_dd.domain_tag))
from meshmode.discretization.connection import \
make_face_to_all_faces_embedding
return make_face_to_all_faces_embedding(
self._setup_actx, faces_conn, self.discr_from_dd(to_dd),
self.discr_from_dd(from_dd))
# {{{ simplify domain + discr_tag change into chained
if (from_dd.domain_tag != to_dd.domain_tag
and from_discr_tag is DISCR_TAG_BASE
and to_discr_tag is not DISCR_TAG_BASE):
from meshmode.discretization.connection import \
ChainedDiscretizationConnection
intermediate_dd = DOFDesc(to_dd.domain_tag)
return ChainedDiscretizationConnection([
# first change domain
self.connection_from_dds(from_dd, intermediate_dd),
# then go to quad grid
self.connection_from_dds(intermediate_dd, to_dd)
])
# }}}
# {{{ generic to-quad
# DISCR_TAG_MODAL is handled above
if (from_dd.domain_tag == to_dd.domain_tag
and from_discr_tag is DISCR_TAG_BASE
and to_discr_tag is not DISCR_TAG_BASE):
from meshmode.discretization.connection.same_mesh import \
make_same_mesh_connection
return make_same_mesh_connection(self._setup_actx,
self.discr_from_dd(to_dd),
self.discr_from_dd(from_dd))
# }}}
if from_discr_tag is not DISCR_TAG_BASE:
raise ValueError("cannot interpolate *from* a "
"(non-interpolatory) quadrature grid")
assert to_discr_tag is DISCR_TAG_BASE
if from_dd.is_volume():
if to_dd.domain_tag is FACE_RESTR_ALL:
return self._all_faces_volume_connection()
if to_dd.domain_tag is FACE_RESTR_INTERIOR:
return self._interior_faces_connection()
elif to_dd.is_boundary_or_partition_interface():
assert from_discr_tag is DISCR_TAG_BASE
return self._boundary_connection(to_dd.domain_tag.tag)
elif to_dd.is_volume():
from meshmode.discretization.connection import \
make_same_mesh_connection
to_discr = self._discr_tag_volume_discr(to_discr_tag)
from_discr = self._volume_discr
return make_same_mesh_connection(self._setup_actx, to_discr,
from_discr)
else:
raise ValueError("cannot interpolate from volume to: " +
str(to_dd))
else:
raise ValueError("cannot interpolate from: " + str(from_dd))
def group_factory_for_quadrature_tag(self, discretization_tag):
warn(
"`DiscretizationCollection.group_factory_for_quadrature_tag` "
"is deprecated and will go away in 2022. Use "
"`DiscretizationCollection.group_factory_for_discretization_tag` "
"instead.",
DeprecationWarning,
stacklevel=2)
return self.group_factory_for_discretization_tag(discretization_tag)
def group_factory_for_discretization_tag(self, discretization_tag):
"""
OK to override in user code to control mode/node choice.
"""
if discretization_tag is None:
discretization_tag = DISCR_TAG_BASE
return self.discr_tag_to_group_factory[discretization_tag]
@memoize_method
def _discr_tag_volume_discr(self, discretization_tag):
from meshmode.discretization import Discretization
return Discretization(
self._setup_actx, self._volume_discr.mesh,
self.group_factory_for_discretization_tag(discretization_tag))
# {{{ modal to nodal connections
@memoize_method
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))
@memoize_method
def _modal_to_nodal_connection(self, to_dd):
"""
:arg to_dd: a :class:`grudge.dof_desc.DOFDesc`
describing the dofs corresponding to the
*to_discr*
"""
from meshmode.discretization.connection import \
ModalToNodalDiscretizationConnection
return ModalToNodalDiscretizationConnection(
from_discr=self._modal_discr(to_dd.domain_tag),
to_discr=self.discr_from_dd(to_dd))
@memoize_method
def _nodal_to_modal_connection(self, from_dd):
"""
:arg from_dd: a :class:`grudge.dof_desc.DOFDesc`
describing the dofs corresponding to the
*from_discr*
"""
from meshmode.discretization.connection import \
NodalToModalDiscretizationConnection
return NodalToModalDiscretizationConnection(
from_discr=self.discr_from_dd(from_dd),
to_discr=self._modal_discr(from_dd.domain_tag))
# }}}
# {{{ boundary
@memoize_method
def _boundary_connection(self, boundary_tag):
return make_face_restriction(
self._setup_actx,
self._volume_discr,
self.group_factory_for_discretization_tag(DISCR_TAG_BASE),
boundary_tag=boundary_tag)
# }}}
# {{{ interior faces
@memoize_method
def _interior_faces_connection(self):
return make_face_restriction(
self._setup_actx,
self._volume_discr,
self.group_factory_for_discretization_tag(DISCR_TAG_BASE),
FACE_RESTR_INTERIOR,
# FIXME: This will need to change as soon as we support
# pyramids or other elements with non-identical face
# types.
per_face_groups=False)
@memoize_method
def opposite_face_connection(self):
from meshmode.discretization.connection import \
make_opposite_face_connection
return make_opposite_face_connection(self._setup_actx,
self._interior_faces_connection())
# }}}
# {{{ all-faces
@memoize_method
def _all_faces_volume_connection(self):
return make_face_restriction(
self._setup_actx,
self._volume_discr,
self.group_factory_for_discretization_tag(DISCR_TAG_BASE),
FACE_RESTR_ALL,
# FIXME: This will need to change as soon as we support
# pyramids or other elements with non-identical face
# types.
per_face_groups=False)
# }}}
@property
def dim(self):
return self._volume_discr.dim
@property
def ambient_dim(self):
return self._volume_discr.ambient_dim
@property
def real_dtype(self):
return self._volume_discr.real_dtype
@property
def complex_dtype(self):
return self._volume_discr.complex_dtype
@property
def mesh(self):
return self._volume_discr.mesh
def empty(self, array_context: ArrayContext, dtype=None):
return self._volume_discr.empty(array_context, dtype)
def zeros(self, array_context: ArrayContext, dtype=None):
return self._volume_discr.zeros(array_context, dtype)
def is_volume_where(self, where):
return where is None or as_dofdesc(where).is_volume()
@property
def order(self):
warn(
"DiscretizationCollection.order is deprecated, "
"consider using the orders of element groups instead. "
"'order' will go away in 2021.",
DeprecationWarning,
stacklevel=2)
from pytools import single_valued
return single_valued(egrp.order for egrp in self._volume_discr.groups)