def main():
cl_ctx = cl.create_some_context()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue)
dim = 2
nel_1d = 16
from meshmode.mesh.generation import generate_regular_rect_mesh
mesh = generate_regular_rect_mesh(a=(-0.5, ) * dim,
b=(0.5, ) * dim,
n=(nel_1d, ) * dim)
order = 3
if dim == 2:
# no deep meaning here, just a fudge factor
dt = 0.75 / (nel_1d * order**2)
elif dim == 3:
# no deep meaning here, just a fudge factor
dt = 0.45 / (nel_1d * order**2)
else:
raise ValueError("don't have a stable time step guesstimate")
print("%d elements" % mesh.nelements)
from meshmode.discretization.poly_element import \
QuadratureSimplexGroupFactory, \
PolynomialWarpAndBlendGroupFactory
discr = EagerDGDiscretization(
actx,
mesh,
quad_tag_to_group_factory={
QTAG_NONE: PolynomialWarpAndBlendGroupFactory(order),
"vel_prod": QuadratureSimplexGroupFactory(3 * order),
})
# bounded above by 1
c = 0.2 + 0.8 * bump(actx, discr, center=np.zeros(3), width=0.5)
fields = flat_obj_array(bump(
actx,
discr,
), [discr.zeros(actx) for i in range(discr.dim)])
vis = make_visualizer(discr, order + 3 if dim == 2 else order)
def rhs(t, w):
return wave_operator(discr, c=c, w=w)
t = 0
t_final = 3
istep = 0
while t < t_final:
fields = rk4_step(fields, t, dt, rhs)
if istep % 10 == 0:
print(istep, t, discr.norm(fields[0]))
vis.write_vtk_file("fld-wave-eager-var-velocity-%04d.vtu" % istep,
[
("c", c),
("u", fields[0]),
("v", fields[1:]),
])
t += dt
istep += 1
def test_sanity_single_element(ctx_factory, dim, order, visualize=False):
pytest.importorskip("pytential")
cl_ctx = ctx_factory()
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, BTAG_ALL
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], is_conforming=True)
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_face_restriction
bdry_connection = make_face_restriction(
vol_discr, PolynomialWarpAndBlendGroupFactory(order + 3),
BTAG_ALL)
bdry_discr = bdry_connection.to_discr
# }}}
# {{{ 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(dim))(queue).as_vector(dtype=object)
if visualize:
bdry_vis.write_vtk_file("boundary.vtu", [
("bdry_normals", bdry_normals)
])
normal_outward_check = bind(bdry_discr,
sym.normal(dim)
| (sym.nodes(dim) + 0.5*sym.ones_vec(dim)),
)(queue).as_scalar() > 0
assert normal_outward_check.get().all(), normal_outward_check.get()
def test_diffusion_accuracy(actx_factory,
problem,
nsteps,
dt,
scales,
order,
visualize=False):
"""
Checks the accuracy of the diffusion operator by solving the heat equation for a
given problem setup.
"""
actx = actx_factory()
p = problem
sym_x = pmbl.make_sym_vector("x", p.dim)
sym_t = pmbl.var("t")
sym_u = p.get_solution(sym_x, sym_t)
sym_alpha = p.get_alpha(sym_x, sym_t, sym_u)
sym_diffusion_u = sym_diffusion(p.dim, sym_alpha, sym_u)
# In order to support manufactured solutions, we modify the heat equation
# to add a source term f. If the solution is exact, this term should be 0.
sym_f = sym.diff(sym_t)(sym_u) - sym_diffusion_u
from pytools.convergence import EOCRecorder
eoc_rec = EOCRecorder()
for n in scales:
mesh = p.get_mesh(n)
from grudge.eager import EagerDGDiscretization
from meshmode.discretization.poly_element import \
QuadratureSimplexGroupFactory, \
PolynomialWarpAndBlendGroupFactory
discr = EagerDGDiscretization(
actx,
mesh,
discr_tag_to_group_factory={
DISCR_TAG_BASE: PolynomialWarpAndBlendGroupFactory(order),
DISCR_TAG_QUAD: QuadratureSimplexGroupFactory(3 * order),
})
nodes = thaw(actx, discr.nodes())
def get_rhs(t, u):
alpha = p.get_alpha(nodes, t, u)
if isinstance(alpha, DOFArray):
discr_tag = DISCR_TAG_QUAD
else:
discr_tag = DISCR_TAG_BASE
return (
diffusion_operator(discr,
quad_tag=discr_tag,
alpha=alpha,
boundaries=p.get_boundaries(discr, actx, t),
u=u) + _sym_eval(sym_f, x=nodes, t=t))
t = 0.
u = p.get_solution(nodes, t)
from mirgecom.integrators import rk4_step
for _ in range(nsteps):
u = rk4_step(u, t, dt, get_rhs)
t += dt
expected_u = p.get_solution(nodes, t)
rel_linf_err = actx.to_numpy(
discr.norm(u - expected_u, np.inf) /
discr.norm(expected_u, np.inf))
eoc_rec.add_data_point(1. / n, rel_linf_err)
if visualize:
from grudge.shortcuts import make_visualizer
vis = make_visualizer(discr, discr.order + 3)
vis.write_vtk_file(
"diffusion_accuracy_{order}_{n}.vtu".format(order=order, n=n),
[
("u", u),
("expected_u", expected_u),
])
print("L^inf error:")
print(eoc_rec)
# Expected convergence rates from Hesthaven/Warburton book
expected_order = order + 1 if order % 2 == 0 else order
assert (eoc_rec.order_estimate() >= expected_order - 0.5
or eoc_rec.max_error() < 1e-11)
def build_connection_from_firedrake(actx, fdrake_fspace, grp_factory=None,
restrict_to_boundary=None):
"""
Create a :class:`FiredrakeConnection` from a :mod:`firedrake`
``"DG"`` function space by creates a corresponding
meshmode discretization and facilitating
transfer of functions to and from :mod:`firedrake`.
:arg actx: A :class:`~meshmode.array_context.ArrayContext`
used to instantiate :attr:`FiredrakeConnection.discr`.
:arg fdrake_fspace: A :mod:`firedrake` ``"DG"``
function space (of class
:class:`~firedrake.functionspaceimpl.WithGeometry`) built on
a mesh which is importable by
:func:`~meshmode.interop.firedrake.mesh.import_firedrake_mesh`.
:arg grp_factory: (optional) If not *None*, should be
a :class:`~meshmode.discretization.poly_element.ElementGroupFactory`
whose group class is a subclass of
:class:`~meshmode.discretization.InterpolatoryElementGroupBase`.
If *None*, and :mod:`recursivenodes` can be imported,
a :class:`~meshmode.discretization.poly_element.\
PolynomialRecursiveNodesGroupFactory` with ``"lgl"`` nodes is used.
Note that :mod:`recursivenodes` may not be importable
as it uses :func:`math.comb`, which is new in Python 3.8.
In the case that :mod:`recursivenodes` cannot be successfully
imported, a :class:`~meshmode.discretization.poly_element.\
PolynomialWarpAndBlendGroupFactory` is used.
:arg restrict_to_boundary: (optional)
If not *None*, then must be a valid boundary marker for
``fdrake_fspace.mesh()``. In this case, creates a
:class:`~meshmode.discretization.Discretization` on a submesh
of ``fdrake_fspace.mesh()`` created from the cells with at least
one vertex on a facet marked with the marker
*restrict_to_boundary*.
"""
# Ensure fdrake_fspace is a function space with appropriate reference
# element.
from firedrake.functionspaceimpl import WithGeometry
if not isinstance(fdrake_fspace, WithGeometry):
raise TypeError("'fdrake_fspace' must be of firedrake type "
"WithGeometry, not '%s'."
% type(fdrake_fspace))
ufl_elt = fdrake_fspace.ufl_element()
if ufl_elt.family() != "Discontinuous Lagrange":
raise ValueError("the 'fdrake_fspace.ufl_element().family()' of "
"must be be "
"'Discontinuous Lagrange', not '%s'."
% ufl_elt.family())
# Make sure grp_factory is the right type if provided, and
# uses an interpolatory class.
if grp_factory is not None:
if not isinstance(grp_factory, ElementGroupFactory):
raise TypeError("'grp_factory' must inherit from "
"meshmode.discretization.ElementGroupFactory,"
"but is instead of type "
"'%s'." % type(grp_factory))
if not issubclass(grp_factory.group_class,
InterpolatoryElementGroupBase):
raise TypeError("'grp_factory.group_class' must inherit from"
"meshmode.discretization."
"InterpolatoryElementGroupBase, but"
" is instead of type '%s'"
% type(grp_factory.group_class))
# If not provided, make one
else:
degree = ufl_elt.degree()
try:
# recursivenodes is only importable in Python 3.8 since
# it uses :func:`math.comb`, so need to check if it can
# be imported
import recursivenodes # noqa : F401
family = "lgl" # L-G-Legendre
grp_factory = PolynomialRecursiveNodesGroupFactory(degree, family)
except ImportError:
# If cannot be imported, uses warp-and-blend nodes
grp_factory = PolynomialWarpAndBlendGroupFactory(degree)
if restrict_to_boundary is not None:
uniq_markers = fdrake_fspace.mesh().exterior_facets.unique_markers
allowable_bdy_ids = list(uniq_markers) + ["on_boundary"]
# make sure restrict_to_boundary is of correct type
type_check = isinstance(restrict_to_boundary, int)
if not type_check:
is_tuple = isinstance(restrict_to_boundary, tuple)
if is_tuple:
type_check = all([isinstance(x, int) for x in restrict_to_boundary])
else:
type_check = restrict_to_boundary == "on_boundary"
if not type_check:
raise TypeError("restrict_to_boundary must be an int, a tuple"
" of ints, or the string 'on_boundary', not"
f" of type {type(restrict_to_boundary)}")
# convert int to tuple to avoid corner cases
else:
restrict_to_boundary = (restrict_to_boundary,)
# make sure all markers are valid
if restrict_to_boundary != "on_boundary":
for marker in restrict_to_boundary:
if marker not in allowable_bdy_ids:
raise ValueError("'restrict_to_boundary' must be one of"
" the following allowable boundary ids: "
f"{allowable_bdy_ids}, not "
f"'{restrict_to_boundary}'")
# If only converting a portion of the mesh near the boundary, get
# *cells_to_use* as described in
# :func:`meshmode.interop.firedrake.mesh.import_firedrake_mesh`
cells_to_use = _get_cells_to_use(fdrake_fspace.mesh(),
restrict_to_boundary)
# Create to_discr
mm_mesh, orient = import_firedrake_mesh(fdrake_fspace.mesh(),
cells_to_use=cells_to_use)
to_discr = Discretization(actx, mm_mesh, grp_factory)
# get firedrake unit nodes and map onto meshmode reference element
group = to_discr.groups[0]
fd_ref_cell_to_mm = get_affine_reference_simplex_mapping(group.dim,
True)
fd_unit_nodes = get_finat_element_unit_nodes(fdrake_fspace.finat_element)
fd_unit_nodes = fd_ref_cell_to_mm(fd_unit_nodes)
# Flipping negative elements corresponds to reordering the nodes.
# We handle reordering by storing the permutation explicitly as
# a numpy array
# Get the reordering fd->mm.
flip_mat = get_simplex_element_flip_matrix(ufl_elt.degree(),
fd_unit_nodes)
fd_cell_node_list = fdrake_fspace.cell_node_list
if cells_to_use is not None:
fd_cell_node_list = fd_cell_node_list[cells_to_use]
# flip fd_cell_node_list
flipped_cell_node_list = _reorder_nodes(orient,
fd_cell_node_list,
flip_mat,
unflip=False)
assert np.size(np.unique(flipped_cell_node_list)) == \
np.size(flipped_cell_node_list), \
"A firedrake node in a 'DG' space got duplicated"
return FiredrakeConnection(to_discr,
fdrake_fspace,
flipped_cell_node_list)
def test_all_faces_interpolation(ctx_factory, mesh_name, dim, mesh_pars,
per_face_groups):
cl_ctx = ctx_factory()
queue = cl.CommandQueue(cl_ctx)
from meshmode.discretization import Discretization
from meshmode.discretization.connection import (
make_face_restriction, make_face_to_all_faces_embedding,
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,
PolynomialWarpAndBlendGroupFactory(order))
print("h=%s -> %d elements" % (
h, sum(mgrp.nelements for mgrp in mesh.groups)))
all_face_bdry_connection = make_face_restriction(
vol_discr, PolynomialWarpAndBlendGroupFactory(order),
FACE_RESTR_ALL, per_face_groups=per_face_groups)
all_face_bdry_discr = all_face_bdry_connection.to_discr
for ito_grp, ceg in enumerate(all_face_bdry_connection.groups):
for ibatch, batch in enumerate(ceg.batches):
assert np.array_equal(
batch.from_element_indices.get(queue),
np.arange(vol_discr.mesh.nelements))
if per_face_groups:
assert ito_grp == batch.to_element_face
else:
assert ibatch == batch.to_element_face
all_face_x = all_face_bdry_discr.nodes()[0].with_queue(queue)
all_face_f = f(all_face_x)
all_face_f_2 = all_face_bdry_discr.zeros(queue)
for boundary_tag in [
BTAG_ALL,
FACE_RESTR_INTERIOR,
]:
bdry_connection = make_face_restriction(
vol_discr, PolynomialWarpAndBlendGroupFactory(order),
boundary_tag, per_face_groups=per_face_groups)
bdry_discr = bdry_connection.to_discr
bdry_x = bdry_discr.nodes()[0].with_queue(queue)
bdry_f = f(bdry_x)
all_face_embedding = make_face_to_all_faces_embedding(
bdry_connection, all_face_bdry_discr)
check_connection(all_face_embedding)
all_face_f_2 += all_face_embedding(queue, bdry_f)
err = la.norm((all_face_f-all_face_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 test_dof_array_arithmetic_same_as_numpy(actx_factory):
actx = actx_factory()
from meshmode.mesh.generation import generate_regular_rect_mesh
mesh = generate_regular_rect_mesh(
a=(-0.5,)*2, b=(0.5,)*2, n=(3,)*2, order=1)
discr = Discretization(actx, mesh, PolynomialWarpAndBlendGroupFactory(3))
def get_real(ary):
return ary.real
def get_imag(ary):
return ary.real
import operator
from pytools import generate_nonnegative_integer_tuples_below as gnitb
from random import uniform, randrange
for op_func, n_args, use_integers in [
(operator.add, 2, False),
(operator.sub, 2, False),
(operator.mul, 2, False),
(operator.truediv, 2, False),
(operator.pow, 2, False),
# FIXME pyopencl.Array doesn't do mod.
#(operator.mod, 2, True),
#(operator.mod, 2, False),
#(operator.imod, 2, True),
#(operator.imod, 2, False),
# FIXME: Two outputs
#(divmod, 2, False),
(operator.iadd, 2, False),
(operator.isub, 2, False),
(operator.imul, 2, False),
(operator.itruediv, 2, False),
(operator.and_, 2, True),
(operator.xor, 2, True),
(operator.or_, 2, True),
(operator.iand, 2, True),
(operator.ixor, 2, True),
(operator.ior, 2, True),
(operator.ge, 2, False),
(operator.lt, 2, False),
(operator.gt, 2, False),
(operator.eq, 2, True),
(operator.ne, 2, True),
(operator.pos, 1, False),
(operator.neg, 1, False),
(operator.abs, 1, False),
(get_real, 1, False),
(get_imag, 1, False),
]:
for is_array_flags in gnitb(2, n_args):
if sum(is_array_flags) == 0:
# all scalars, no need to test
continue
if is_array_flags[0] == 0 and op_func in [
operator.iadd, operator.isub,
operator.imul, operator.itruediv,
operator.iand, operator.ixor, operator.ior,
]:
# can't do in place operations with a scalar lhs
continue
args = [
(0.5+np.random.rand(discr.ndofs)
if not use_integers else
np.random.randint(3, 200, discr.ndofs))
if is_array_flag else
(uniform(0.5, 2)
if not use_integers
else randrange(3, 200))
for is_array_flag in is_array_flags]
# {{{ get reference numpy result
# make a copy for the in place operators
ref_args = [
arg.copy() if isinstance(arg, np.ndarray) else arg
for arg in args]
ref_result = op_func(*ref_args)
# }}}
# {{{ test DOFArrays
actx_args = [
unflatten(actx, discr, actx.from_numpy(arg))
if isinstance(arg, np.ndarray) else arg
for arg in args]
actx_result = actx.to_numpy(flatten(op_func(*actx_args)))
assert np.allclose(actx_result, ref_result)
# }}}
# {{{ test object arrays of DOFArrays
# It would be very nice if comparisons on object arrays behaved
# consistently with everything else. Alas, they do not. Instead:
#
# 0.5 < obj_array(DOFArray) -> obj_array([True])
#
# because hey, 0.5 < DOFArray returned something truthy.
if op_func not in [
operator.eq, operator.ne,
operator.le, operator.lt,
operator.ge, operator.gt,
operator.iadd, operator.isub,
operator.imul, operator.itruediv,
operator.iand, operator.ixor, operator.ior,
# All Python objects are real-valued, right?
get_imag,
]:
obj_array_args = [
make_obj_array([arg]) if isinstance(arg, DOFArray) else arg
for arg in actx_args]
obj_array_result = actx.to_numpy(
flatten(op_func(*obj_array_args)[0]))
assert np.allclose(obj_array_result, ref_result)
def main(ctx_factory, dim=2, order=4, product_tag=None, visualize=False):
cl_ctx = ctx_factory()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue)
# {{{ parameters
# sphere radius
radius = 1.0
# sphere resolution
resolution = 64 if dim == 2 else 1
# cfl
dt_factor = 2.0
# final time
final_time = np.pi
# velocity field
sym_x = sym.nodes(dim)
c = make_obj_array([-sym_x[1], sym_x[0], 0.0])[:dim]
# flux
flux_type = "lf"
# }}}
# {{{ discretization
if dim == 2:
from meshmode.mesh.generation import make_curve_mesh, ellipse
mesh = make_curve_mesh(lambda t: radius * ellipse(1.0, t),
np.linspace(0.0, 1.0, resolution + 1), order)
elif dim == 3:
from meshmode.mesh.generation import generate_icosphere
mesh = generate_icosphere(radius,
order=4 * order,
uniform_refinement_rounds=resolution)
else:
raise ValueError("unsupported dimension")
quad_tag_to_group_factory = {}
if product_tag == "none":
product_tag = None
from meshmode.discretization.poly_element import \
PolynomialWarpAndBlendGroupFactory, \
QuadratureSimplexGroupFactory
quad_tag_to_group_factory[sym.QTAG_NONE] = \
PolynomialWarpAndBlendGroupFactory(order)
if product_tag:
quad_tag_to_group_factory[product_tag] = \
QuadratureSimplexGroupFactory(order=4*order)
from grudge import DGDiscretizationWithBoundaries
discr = DGDiscretizationWithBoundaries(
actx, mesh, quad_tag_to_group_factory=quad_tag_to_group_factory)
volume_discr = discr.discr_from_dd(sym.DD_VOLUME)
logger.info("ndofs: %d", volume_discr.ndofs)
logger.info("nelements: %d", volume_discr.mesh.nelements)
# }}}
# {{{ symbolic operators
def f_initial_condition(x):
return x[0]
from grudge.models.advection import SurfaceAdvectionOperator
op = SurfaceAdvectionOperator(c, flux_type=flux_type, quad_tag=product_tag)
bound_op = bind(discr, op.sym_operator())
u0 = bind(discr, f_initial_condition(sym_x))(actx, t=0)
def rhs(t, u):
return bound_op(actx, t=t, u=u)
# check velocity is tangential
sym_normal = sym.surface_normal(dim, dim=dim - 1,
dd=sym.DD_VOLUME).as_vector()
error = bind(discr, sym.norm(2, c.dot(sym_normal)))(actx)
logger.info("u_dot_n: %.5e", error)
# }}}
# {{{ time stepping
# compute time step
h_min = bind(discr, sym.h_max_from_volume(discr.ambient_dim,
dim=discr.dim))(actx)
dt = dt_factor * h_min / order**2
nsteps = int(final_time // dt) + 1
dt = final_time / nsteps + 1.0e-15
logger.info("dt: %.5e", dt)
logger.info("nsteps: %d", nsteps)
from grudge.shortcuts import set_up_rk4
dt_stepper = set_up_rk4("u", dt, u0, rhs)
plot = Plotter(actx, discr, order, visualize=visualize)
norm = bind(discr, sym.norm(2, sym.var("u")))
norm_u = norm(actx, u=u0)
step = 0
event = dt_stepper.StateComputed(0.0, 0, 0, u0)
plot(event, "fld-surface-%04d" % 0)
if visualize and dim == 3:
from grudge.shortcuts import make_visualizer
vis = make_visualizer(discr, vis_order=order)
vis.write_vtk_file("fld-surface-velocity.vtu",
[("u", bind(discr, c)(actx)),
("n", bind(discr, sym_normal)(actx))],
overwrite=True)
df = sym.DOFDesc(sym.FACE_RESTR_INTERIOR)
face_discr = discr.connection_from_dds(sym.DD_VOLUME, df).to_discr
face_normal = bind(
discr, sym.normal(df, face_discr.ambient_dim,
dim=face_discr.dim))(actx)
from meshmode.discretization.visualization import make_visualizer
vis = make_visualizer(actx, face_discr, vis_order=order)
vis.write_vtk_file("fld-surface-face-normals.vtu",
[("n", face_normal)],
overwrite=True)
for event in dt_stepper.run(t_end=final_time, max_steps=nsteps + 1):
if not isinstance(event, dt_stepper.StateComputed):
continue
step += 1
if step % 10 == 0:
norm_u = norm(actx, u=event.state_component)
plot(event, "fld-surface-%04d" % step)
logger.info("[%04d] t = %.5f |u| = %.5e", step, event.t, norm_u)
plot(event, "fld-surface-%04d" % step)
def _test_mpi_boundary_swap(dim, order, num_groups):
from meshmode.distributed import MPIMeshDistributor, MPIBoundaryCommSetupHelper
from mpi4py import MPI
mpi_comm = MPI.COMM_WORLD
i_local_part = mpi_comm.Get_rank()
num_parts = mpi_comm.Get_size()
mesh_dist = MPIMeshDistributor(mpi_comm)
if mesh_dist.is_mananger_rank():
np.random.seed(42)
from meshmode.mesh.generation import generate_warped_rect_mesh
meshes = [generate_warped_rect_mesh(dim, order=order, n=4)
for _ in range(num_groups)]
if num_groups > 1:
from meshmode.mesh.processing import merge_disjoint_meshes
mesh = merge_disjoint_meshes(meshes)
else:
mesh = meshes[0]
part_per_element = np.random.randint(num_parts, size=mesh.nelements)
local_mesh = mesh_dist.send_mesh_parts(mesh, part_per_element, num_parts)
else:
local_mesh = mesh_dist.receive_mesh_part()
group_factory = PolynomialWarpAndBlendGroupFactory(order)
cl_ctx = cl.create_some_context()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue)
from meshmode.discretization import Discretization
vol_discr = Discretization(actx, local_mesh, group_factory)
from meshmode.distributed import get_connected_partitions
connected_parts = get_connected_partitions(local_mesh)
assert i_local_part not in connected_parts
bdry_setup_helpers = {}
local_bdry_conns = {}
from meshmode.discretization.connection import make_face_restriction
from meshmode.mesh import BTAG_PARTITION
for i_remote_part in connected_parts:
local_bdry_conns[i_remote_part] = make_face_restriction(
actx, vol_discr, group_factory, BTAG_PARTITION(i_remote_part))
setup_helper = bdry_setup_helpers[i_remote_part] = \
MPIBoundaryCommSetupHelper(
mpi_comm, actx, local_bdry_conns[i_remote_part],
i_remote_part, bdry_grp_factory=group_factory)
setup_helper.post_sends()
remote_to_local_bdry_conns = {}
from meshmode.discretization.connection import check_connection
while bdry_setup_helpers:
for i_remote_part, setup_helper in bdry_setup_helpers.items():
if setup_helper.is_setup_ready():
assert bdry_setup_helpers.pop(i_remote_part) is setup_helper
conn = setup_helper.complete_setup()
check_connection(actx, conn)
remote_to_local_bdry_conns[i_remote_part] = conn
break
# FIXME: Not ideal, busy-waits
_test_data_transfer(mpi_comm,
actx,
local_bdry_conns,
remote_to_local_bdry_conns,
connected_parts)
logger.debug("Rank %d exiting", i_local_part)
def build_kernel_exterior_normalizer_table(self,
cl_ctx,
queue,
pool=None,
ncpus=None,
mesh_order=5,
quad_order=10,
mesh_size=0.03,
remove_tmp_files=True,
**kwargs):
r"""Build the kernel exterior normalizer table for fractional Laplacians.
An exterior normalizer for kernel :math:`G(r)` and target
:math:`x` is defined as
.. math::
\int_{B^c} G(\lVert x - y \rVert) dy
where :math:`B` is the source box :math:`[0, source_box_extent]^dim`.
"""
logger.warn("this method is currently under construction.")
if not self.inverse_droste:
raise ValueError()
if ncpus is None:
import multiprocessing
ncpus = multiprocessing.cpu_count()
if pool is None:
from multiprocessing import Pool
pool = Pool(ncpus)
def fl_scaling(k, s):
# scaling constant
from scipy.special import gamma
return (2**(2 * s) * s * gamma(s + k / 2)) / (np.pi**(k / 2) *
gamma(1 - s))
# Directly compute and return in 1D
if self.dim == 1:
s = self.integral_knl.s
targets = np.array(self.q_points).reshape(-1)
r1 = targets
r2 = self.source_box_extent - targets
self.kernel_exterior_normalizers = 1 / (2 * s) * (
1 / r1**(2 * s) + 1 / r2**(2 * s)) * fl_scaling(k=self.dim,
s=s)
return
from meshmode.array_context import PyOpenCLArrayContext
from meshmode.dof_array import thaw, flatten
from meshmode.mesh.io import read_gmsh
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import \
PolynomialWarpAndBlendGroupFactory
# {{{ gmsh processing
import gmsh
gmsh.initialize()
gmsh.option.setNumber("General.Terminal", 1)
# meshmode does not support other versions
gmsh.option.setNumber("Mesh.MshFileVersion", 2)
gmsh.option.setNumber("Mesh.CharacteristicLengthMax", mesh_size)
gmsh.option.setNumber("Mesh.ElementOrder", mesh_order)
if mesh_order > 1:
gmsh.option.setNumber("Mesh.CharacteristicLengthFromCurvature", 1)
# radius of source box
hs = self.source_box_extent / 2
# radius of bouding sphere
r = hs * np.sqrt(self.dim)
logger.debug("r_inner = %f, r_outer = %f" % (hs, r))
if self.dim == 2:
tag_box = gmsh.model.occ.addRectangle(x=0,
y=0,
z=0,
dx=2 * hs,
dy=2 * hs,
tag=-1)
elif self.dim == 3:
tag_box = gmsh.model.occ.addBox(x=0,
y=0,
z=0,
dx=2 * hs,
dy=2 * hs,
dz=2 * hs,
tag=-1)
else:
raise NotImplementedError()
if self.dim == 2:
tag_ball = gmsh.model.occ.addDisk(xc=hs,
yc=hs,
zc=0,
rx=r,
ry=r,
tag=-1)
elif self.dim == 3:
tag_sphere = gmsh.model.occ.addSphere(xc=hs,
yc=hs,
zc=hs,
radius=r,
tag=-1)
tag_ball = gmsh.model.occ.addVolume([tag_sphere], tag=-1)
else:
raise NotImplementedError()
dimtags_ints, dimtags_map_ints = gmsh.model.occ.cut(
objectDimTags=[(self.dim, tag_ball)],
toolDimTags=[(self.dim, tag_box)],
tag=-1,
removeObject=True,
removeTool=True)
gmsh.model.occ.synchronize()
gmsh.model.mesh.generate(self.dim)
from tempfile import mkdtemp
from os.path import join
temp_dir = mkdtemp(prefix="tmp_volumential_nft")
msh_filename = join(temp_dir, 'chinese_lucky_coin.msh')
gmsh.write(msh_filename)
gmsh.finalize()
mesh = read_gmsh(msh_filename)
if remove_tmp_files:
import shutil
shutil.rmtree(temp_dir)
# }}} End gmsh processing
arr_ctx = PyOpenCLArrayContext(queue)
discr = Discretization(
arr_ctx, mesh,
PolynomialWarpAndBlendGroupFactory(order=quad_order))
from pytential import bind, sym
# {{{ optional checks
if 1:
if self.dim == 2:
arerr = np.abs((np.pi * r**2 - (2 * hs)**2) -
bind(discr, sym.integral(self.dim, self.dim, 1))
(queue)) / (np.pi * r**2 - (2 * hs)**2)
if arerr > 1e-12:
log_to = logger.warn
else:
log_to = logger.debug
log_to("the numerical error when computing the measure of a "
"unit ball is %e" % arerr)
elif self.dim == 3:
arerr = np.abs((4 / 3 * np.pi * r**3 - (2 * hs)**3) -
bind(discr, sym.integral(self.dim, self.dim, 1))
(queue)) / (4 / 3 * np.pi * r**3 - (2 * hs)**3)
if arerr > 1e-12:
log_to = logger.warn
else:
log_to = logger.debug
logger.warn(
"The numerical error when computing the measure of a "
"unit ball is %e" % arerr)
# }}} End optional checks
# {{{ kernel evaluation
# TODO: take advantage of symmetry if this is too slow
from volumential.droste import InverseDrosteReduced
# only for getting kernel evaluation related stuff
drf = InverseDrosteReduced(self.integral_knl,
self.quad_order,
self.interaction_case_vecs,
n_brick_quad_points=0,
knl_symmetry_tags=[],
auto_windowing=False)
# uses "dist[dim]", assigned to "knl_val"
knl_insns = drf.get_sumpy_kernel_insns()
eval_kernel_insns = [
insn.copy(within_inames=insn.within_inames | frozenset(["iqpt"]))
for insn in knl_insns
]
from sumpy.symbolic import SympyToPymbolicMapper
sympy_conv = SympyToPymbolicMapper()
scaling_assignment = lp.Assignment(
id=None,
assignee="knl_scaling",
expression=sympy_conv(
self.integral_knl.get_global_scaling_const()),
temp_var_type=lp.Optional(),
)
extra_kernel_kwarg_types = ()
if "extra_kernel_kwarg_types" in kwargs:
extra_kernel_kwarg_types = kwargs["extra_kernel_kwarg_types"]
lpknl = lp.make_kernel( # NOQA
"{ [iqpt, iaxis]: 0<=iqpt<n_q_points and 0<=iaxis<dim }",
[
"""
for iqpt
for iaxis
<> dist[iaxis] = (quad_points[iaxis, iqpt]
- target_point[iaxis])
end
end
"""
] + eval_kernel_insns + [scaling_assignment] + [
"""
for iqpt
result[iqpt] = knl_val * knl_scaling
end
"""
],
[
lp.ValueArg("dim, n_q_points", np.int32),
lp.GlobalArg("quad_points", np.float64, "dim, n_q_points"),
lp.GlobalArg("target_point", np.float64, "dim")
] + list(extra_kernel_kwarg_types) + [
"...",
],
name="eval_kernel_lucky_coin",
lang_version=(2018, 2),
)
lpknl = lp.fix_parameters(lpknl, dim=self.dim)
lpknl = lp.set_options(lpknl, write_cl=False)
lpknl = lp.set_options(lpknl, return_dict=True)
# }}} End kernel evaluation
node_coords = flatten(thaw(arr_ctx, discr.nodes()))
nodes = cl.array.to_device(
queue, np.vstack([crd.get() for crd in node_coords]))
int_vals = []
for target in self.q_points:
evt, res = lpknl(queue, quad_points=nodes, target_point=target)
knl_vals = res['result']
integ = bind(
discr, sym.integral(self.dim, self.dim,
sym.var("integrand")))(queue,
integrand=knl_vals)
queue.finish()
int_vals.append(integ)
int_vals_coins = np.array(int_vals)
int_vals_inf = np.zeros(self.n_q_points)
# {{{ integrate over the exterior of the ball
if self.dim == 2:
def rho_0(theta, target, radius):
rho_x = np.linalg.norm(target, ord=2)
return (-1 * rho_x * np.cos(theta) +
np.sqrt(radius**2 - rho_x**2 * (np.sin(theta)**2)))
def ext_inf_integrand(theta, s, target, radius):
_rho_0 = rho_0(theta, target=target, radius=radius)
return _rho_0**(-2 * s)
def compute_ext_inf_integral(target, s, radius):
# target: target point
# s: fractional order
# radius: radius of the circle
import scipy.integrate as sint
val, _ = sint.quadrature(partial(ext_inf_integrand,
s=s,
target=target,
radius=radius),
a=0,
b=2 * np.pi)
return val * (1 / (2 * s)) * fl_scaling(k=self.dim, s=s)
if 1:
# optional test
target = [0, 0]
s = 0.5
radius = 1
scaling = fl_scaling(k=self.dim, s=s)
val = compute_ext_inf_integral(target, s, radius)
test_err = np.abs(val - radius**(-2 * s) * 2 * np.pi *
(1 /
(2 * s)) * scaling) / (radius**(-2 * s) *
2 * np.pi *
(1 /
(2 * s)) * scaling)
if test_err > 1e-12:
logger.warn("Error evaluating at origin = %f" % test_err)
for tid, target in enumerate(self.q_points):
# The formula assumes that the source box is centered at origin
int_vals_inf[tid] = compute_ext_inf_integral(
target=target - hs, s=self.integral_knl.s, radius=r)
elif self.dim == 3:
# FIXME
raise NotImplementedError("3D not yet implemented.")
else:
raise NotImplementedError("Unsupported dimension")
# }}} End integrate over the exterior of the ball
self.kernel_exterior_normalizers = int_vals_coins + int_vals_inf
return
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
def drive_test_from_meshmode_interpolation(cl_ctx,
queue,
dim,
degree,
nel_1d,
n_levels,
q_order,
a=-0.5,
b=0.5,
seed=0,
test_case='exact'):
"""
meshmode mesh control: nel_1d, degree
volumential mesh control: n_levels, q_order
"""
mesh = generate_regular_rect_mesh(a=(a, ) * dim,
b=(b, ) * dim,
n=(nel_1d, ) * dim)
arr_ctx = PyOpenCLArrayContext(queue)
group_factory = PolynomialWarpAndBlendGroupFactory(order=degree)
discr = Discretization(arr_ctx, mesh, group_factory)
bbox_fac = BoundingBoxFactory(dim=dim)
boxfmm_fac = BoxFMMGeometryFactory(cl_ctx,
dim=dim,
order=q_order,
nlevels=n_levels,
bbox_getter=bbox_fac,
expand_to_hold_mesh=mesh,
mesh_padding_factor=0.)
boxgeo = boxfmm_fac(queue)
lookup_fac = ElementsToSourcesLookupBuilder(cl_ctx,
tree=boxgeo.tree,
discr=discr)
lookup, evt = lookup_fac(queue)
if test_case == 'exact':
# algebraically exact interpolation
func = random_polynomial_func(dim, degree, seed)
elif test_case == 'non-exact':
if dim == 2:
def func(pts):
x, y = pts
return np.sin(x + y) * x
elif dim == 3:
def func(pts):
x, y, z = pts
return np.sin(x + y * z) * x
else:
raise ValueError()
else:
raise ValueError()
dof_vec = eval_func_on_discr_nodes(queue, discr, func)
res = interpolate_from_meshmode(queue, dof_vec, lookup).get(queue)
tree = boxgeo.tree.get(queue)
ref = func(np.vstack(tree.sources))
if test_case == 'exact':
return np.allclose(ref, res)
resid = np.linalg.norm(ref - res, ord=np.inf)
return resid
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)