def p2p(kernels):
if any(knl.is_complex_valued for knl in kernels):
value_dtype = self.complex_dtype
else:
value_dtype = self.real_dtype
from sumpy.p2p import P2P
return P2P(actx.context,
kernels,
exclude_self=False,
value_dtypes=value_dtype)
def get_p2p(self, kernels):
# needs to be separate method for caching
from pytools import any
if any(knl.is_complex_valued for knl in kernels):
value_dtype = self.density_discr.complex_dtype
else:
value_dtype = self.density_discr.real_dtype
from sumpy.p2p import P2P
p2p = P2P(self.cl_context,
kernels, exclude_self=False, value_dtypes=value_dtype)
return p2p
def test_p2p(ctx_factory, exclude_self):
ctx = ctx_factory()
queue = cl.CommandQueue(ctx)
dimensions = 3
n = 5000
from sumpy.p2p import P2P
lknl = LaplaceKernel(dimensions)
knl = P2P(ctx, [lknl, AxisTargetDerivative(0, lknl)],
exclude_self=exclude_self)
targets = np.random.rand(dimensions, n)
sources = targets if exclude_self else np.random.rand(dimensions, n)
strengths = np.ones(n, dtype=np.float64)
extra_kwargs = {}
if exclude_self:
extra_kwargs["target_to_source"] = np.arange(n, dtype=np.int32)
evt, (potential, x_derivative) = knl(queue,
targets,
sources, [strengths],
out_host=True,
**extra_kwargs)
potential_ref = np.empty_like(potential)
targets = targets.T
sources = sources.T
for itarg in range(n):
with np.errstate(divide="ignore"):
invdists = np.sum((targets[itarg] - sources)**2, axis=-1)**-0.5
if exclude_self:
assert np.isinf(invdists[itarg])
invdists[itarg] = 0
potential_ref[itarg] = np.sum(strengths * invdists)
potential_ref *= 1 / (4 * np.pi)
rel_err = la.norm(potential - potential_ref) / la.norm(potential_ref)
print(rel_err)
assert rel_err < 1e-3
def get_true_sol(fspace, kappa, cl_ctx, queue):
"""
Get the ufl expression for the true solution (3D)
or a function with the evaluated solution (2D)
"""
mesh_dim = fspace.mesh().geometric_dimension()
if mesh_dim == 3:
spatial_coord = SpatialCoordinate(fspace.mesh())
x, y, z = spatial_coord # pylint: disable=C0103
norm = sqrt(x**2 + y**2 + z**2)
return Constant(1j / (4 * pi)) / norm * exp(1j * kappa * norm)
if mesh_dim == 2:
# Evaluate true-sol using sumpy
from sumpy.p2p import P2P
from sumpy.kernel import HelmholtzKernel
# https://github.com/inducer/sumpy/blob/900745184d2618bc27a64c847f247e01c2b90b02/examples/curve-pot.py#L87-L88
p2p = P2P(cl_ctx, [HelmholtzKernel(dim=2)],
exclude_self=False,
value_dtypes=np.complex128)
# source is just (0, 0)
sources = np.array([[0.0], [0.0]])
strengths = np.array([[1.0], [1.0]])
# targets are everywhere
targets = np.array([
Function(fspace).interpolate(x_i).dat.data
for x_i in SpatialCoordinate(fspace.mesh())
])
evt, (true_sol_arr, ) = p2p(queue,
targets,
sources,
strengths,
k=kappa)
true_sol = Function(fspace)
true_sol.dat.data[:] = true_sol_arr[:]
return true_sol
raise ValueError("Only meshes of dimension 2, 3 supported")
def get_p2p(self):
from sumpy.p2p import P2P
return P2P(self.cl_context, [self.kernel], exclude_self=False)
def test_translations(ctx_factory, knl, local_expn_class, mpole_expn_class):
logging.basicConfig(level=logging.INFO)
from sympy.core.cache import clear_cache
clear_cache()
ctx = ctx_factory()
queue = cl.CommandQueue(ctx)
np.random.seed(17)
res = 20
nsources = 15
out_kernels = [knl]
extra_kwargs = {}
if isinstance(knl, HelmholtzKernel):
extra_kwargs["k"] = 0.05
if isinstance(knl, StokesletKernel):
extra_kwargs["mu"] = 0.05
# Just to make sure things also work away from the origin
origin = np.array([2, 1, 0][:knl.dim], np.float64)
sources = (0.7 *
(-0.5 + np.random.rand(knl.dim, nsources).astype(np.float64)) +
origin[:, np.newaxis])
strengths = np.ones(nsources, dtype=np.float64) * (1 / nsources)
pconv_verifier_p2m2p = PConvergenceVerifier()
pconv_verifier_p2m2m2p = PConvergenceVerifier()
pconv_verifier_p2m2m2l2p = PConvergenceVerifier()
pconv_verifier_full = PConvergenceVerifier()
from sumpy.visualization import FieldPlotter
eval_offset = np.array([5.5, 0.0, 0][:knl.dim])
centers = (
np.array(
[
# box 0: particles, first mpole here
[0, 0, 0][:knl.dim],
# box 1: second mpole here
np.array([-0.2, 0.1, 0][:knl.dim], np.float64),
# box 2: first local here
eval_offset + np.array([0.3, -0.2, 0][:knl.dim], np.float64),
# box 3: second local and eval here
eval_offset
],
dtype=np.float64) + origin).T.copy()
del eval_offset
from sumpy.expansion import VolumeTaylorExpansionBase
if isinstance(knl, HelmholtzKernel) and \
issubclass(local_expn_class, VolumeTaylorExpansionBase):
# FIXME: Embarrassing--but we run out of memory for higher orders.
orders = [2, 3]
else:
orders = [2, 3, 4]
nboxes = centers.shape[-1]
def eval_at(e2p, source_box_nr, rscale):
e2p_target_boxes = np.array([source_box_nr], dtype=np.int32)
# These are indexed by global box numbers.
e2p_box_target_starts = np.array([0, 0, 0, 0], dtype=np.int32)
e2p_box_target_counts_nonchild = np.array([0, 0, 0, 0], dtype=np.int32)
e2p_box_target_counts_nonchild[source_box_nr] = ntargets
evt, (pot, ) = e2p(
queue,
src_expansions=mpoles,
src_base_ibox=0,
target_boxes=e2p_target_boxes,
box_target_starts=e2p_box_target_starts,
box_target_counts_nonchild=e2p_box_target_counts_nonchild,
centers=centers,
targets=targets,
rscale=rscale,
out_host=True,
**extra_kwargs)
return pot
for order in orders:
m_expn = mpole_expn_class(knl, order=order)
l_expn = local_expn_class(knl, order=order)
from sumpy import P2EFromSingleBox, E2PFromSingleBox, P2P, E2EFromCSR
p2m = P2EFromSingleBox(ctx, m_expn)
m2m = E2EFromCSR(ctx, m_expn, m_expn)
m2p = E2PFromSingleBox(ctx, m_expn, out_kernels)
m2l = E2EFromCSR(ctx, m_expn, l_expn)
l2l = E2EFromCSR(ctx, l_expn, l_expn)
l2p = E2PFromSingleBox(ctx, l_expn, out_kernels)
p2p = P2P(ctx, out_kernels, exclude_self=False)
fp = FieldPlotter(centers[:, -1], extent=0.3, npoints=res)
targets = fp.points
# {{{ compute (direct) reference solution
evt, (pot_direct, ) = p2p(queue,
targets,
sources, (strengths, ),
out_host=True,
**extra_kwargs)
# }}}
m1_rscale = 0.5
m2_rscale = 0.25
l1_rscale = 0.5
l2_rscale = 0.25
# {{{ apply P2M
p2m_source_boxes = np.array([0], dtype=np.int32)
# These are indexed by global box numbers.
p2m_box_source_starts = np.array([0, 0, 0, 0], dtype=np.int32)
p2m_box_source_counts_nonchild = np.array([nsources, 0, 0, 0],
dtype=np.int32)
evt, (mpoles, ) = p2m(
queue,
source_boxes=p2m_source_boxes,
box_source_starts=p2m_box_source_starts,
box_source_counts_nonchild=p2m_box_source_counts_nonchild,
centers=centers,
sources=sources,
strengths=(strengths, ),
nboxes=nboxes,
rscale=m1_rscale,
tgt_base_ibox=0,
#flags="print_hl_wrapper",
out_host=True,
**extra_kwargs)
# }}}
ntargets = targets.shape[-1]
pot = eval_at(m2p, 0, m1_rscale)
err = la.norm((pot - pot_direct) / res**2)
err = err / (la.norm(pot_direct) / res**2)
pconv_verifier_p2m2p.add_data_point(order, err)
# {{{ apply M2M
m2m_target_boxes = np.array([1], dtype=np.int32)
m2m_src_box_starts = np.array([0, 1], dtype=np.int32)
m2m_src_box_lists = np.array([0], dtype=np.int32)
evt, (mpoles, ) = m2m(
queue,
src_expansions=mpoles,
src_base_ibox=0,
tgt_base_ibox=0,
ntgt_level_boxes=mpoles.shape[0],
target_boxes=m2m_target_boxes,
src_box_starts=m2m_src_box_starts,
src_box_lists=m2m_src_box_lists,
centers=centers,
src_rscale=m1_rscale,
tgt_rscale=m2_rscale,
#flags="print_hl_cl",
out_host=True,
**extra_kwargs)
# }}}
pot = eval_at(m2p, 1, m2_rscale)
err = la.norm((pot - pot_direct) / res**2)
err = err / (la.norm(pot_direct) / res**2)
pconv_verifier_p2m2m2p.add_data_point(order, err)
# {{{ apply M2L
m2l_target_boxes = np.array([2], dtype=np.int32)
m2l_src_box_starts = np.array([0, 1], dtype=np.int32)
m2l_src_box_lists = np.array([1], dtype=np.int32)
evt, (mpoles, ) = m2l(
queue,
src_expansions=mpoles,
src_base_ibox=0,
tgt_base_ibox=0,
ntgt_level_boxes=mpoles.shape[0],
target_boxes=m2l_target_boxes,
src_box_starts=m2l_src_box_starts,
src_box_lists=m2l_src_box_lists,
centers=centers,
src_rscale=m2_rscale,
tgt_rscale=l1_rscale,
#flags="print_hl_cl",
out_host=True,
**extra_kwargs)
# }}}
pot = eval_at(l2p, 2, l1_rscale)
err = la.norm((pot - pot_direct) / res**2)
err = err / (la.norm(pot_direct) / res**2)
pconv_verifier_p2m2m2l2p.add_data_point(order, err)
# {{{ apply L2L
l2l_target_boxes = np.array([3], dtype=np.int32)
l2l_src_box_starts = np.array([0, 1], dtype=np.int32)
l2l_src_box_lists = np.array([2], dtype=np.int32)
evt, (mpoles, ) = l2l(
queue,
src_expansions=mpoles,
src_base_ibox=0,
tgt_base_ibox=0,
ntgt_level_boxes=mpoles.shape[0],
target_boxes=l2l_target_boxes,
src_box_starts=l2l_src_box_starts,
src_box_lists=l2l_src_box_lists,
centers=centers,
src_rscale=l1_rscale,
tgt_rscale=l2_rscale,
#flags="print_hl_wrapper",
out_host=True,
**extra_kwargs)
# }}}
pot = eval_at(l2p, 3, l2_rscale)
err = la.norm((pot - pot_direct) / res**2)
err = err / (la.norm(pot_direct) / res**2)
pconv_verifier_full.add_data_point(order, err)
for name, verifier in [
("p2m2p", pconv_verifier_p2m2p),
("p2m2m2p", pconv_verifier_p2m2m2p),
("p2m2m2l2p", pconv_verifier_p2m2m2l2p),
("full", pconv_verifier_full),
]:
print(30 * "-")
print(name)
print(30 * "-")
print(verifier)
print(30 * "-")
verifier()
def test_p2e2p(ctx_factory, base_knl, expn_class, order,
with_source_derivative):
#logging.basicConfig(level=logging.INFO)
from sympy.core.cache import clear_cache
clear_cache()
ctx = ctx_factory()
queue = cl.CommandQueue(ctx)
np.random.seed(17)
res = 100
nsources = 100
extra_kwargs = {}
if isinstance(base_knl, HelmholtzKernel):
if base_knl.allow_evanescent:
extra_kwargs["k"] = 0.2 * (0.707 + 0.707j)
else:
extra_kwargs["k"] = 0.2
if isinstance(base_knl, StokesletKernel):
extra_kwargs["mu"] = 0.2
if with_source_derivative:
knl = DirectionalSourceDerivative(base_knl, "dir_vec")
else:
knl = base_knl
out_kernels = [
knl,
AxisTargetDerivative(0, knl),
]
expn = expn_class(knl, order=order)
from sumpy import P2EFromSingleBox, E2PFromSingleBox, P2P
p2e = P2EFromSingleBox(ctx, expn, kernels=[knl])
e2p = E2PFromSingleBox(ctx, expn, kernels=out_kernels)
p2p = P2P(ctx, out_kernels, exclude_self=False)
from pytools.convergence import EOCRecorder
eoc_rec_pot = EOCRecorder()
eoc_rec_grad_x = EOCRecorder()
from sumpy.expansion.local import LocalExpansionBase
if issubclass(expn_class, LocalExpansionBase):
h_values = [1 / 5, 1 / 7, 1 / 20]
else:
h_values = [1 / 2, 1 / 3, 1 / 5]
center = np.array([2, 1, 0][:knl.dim], np.float64)
sources = (0.7 *
(-0.5 + np.random.rand(knl.dim, nsources).astype(np.float64)) +
center[:, np.newaxis])
strengths = np.ones(nsources, dtype=np.float64) * (1 / nsources)
source_boxes = np.array([0], dtype=np.int32)
box_source_starts = np.array([0], dtype=np.int32)
box_source_counts_nonchild = np.array([nsources], dtype=np.int32)
extra_source_kwargs = extra_kwargs.copy()
if isinstance(knl, DirectionalSourceDerivative):
alpha = np.linspace(0, 2 * np.pi, nsources, np.float64)
dir_vec = np.vstack([np.cos(alpha), np.sin(alpha)])
extra_source_kwargs["dir_vec"] = dir_vec
from sumpy.visualization import FieldPlotter
for h in h_values:
if issubclass(expn_class, LocalExpansionBase):
loc_center = np.array([5.5, 0.0, 0.0][:knl.dim]) + center
centers = np.array(loc_center,
dtype=np.float64).reshape(knl.dim, 1)
fp = FieldPlotter(loc_center, extent=h, npoints=res)
else:
eval_center = np.array([1 / h, 0.0, 0.0][:knl.dim]) + center
fp = FieldPlotter(eval_center, extent=0.1, npoints=res)
centers = (np.array([0.0, 0.0, 0.0][:knl.dim],
dtype=np.float64).reshape(knl.dim, 1) +
center[:, np.newaxis])
targets = fp.points
rscale = 0.5 # pick something non-1
# {{{ apply p2e
evt, (mpoles, ) = p2e(
queue,
source_boxes=source_boxes,
box_source_starts=box_source_starts,
box_source_counts_nonchild=box_source_counts_nonchild,
centers=centers,
sources=sources,
strengths=(strengths, ),
nboxes=1,
tgt_base_ibox=0,
rscale=rscale,
#flags="print_hl_cl",
out_host=True,
**extra_source_kwargs)
# }}}
# {{{ apply e2p
ntargets = targets.shape[-1]
box_target_starts = np.array([0], dtype=np.int32)
box_target_counts_nonchild = np.array([ntargets], dtype=np.int32)
evt, (
pot,
grad_x,
) = e2p(
queue,
src_expansions=mpoles,
src_base_ibox=0,
target_boxes=source_boxes,
box_target_starts=box_target_starts,
box_target_counts_nonchild=box_target_counts_nonchild,
centers=centers,
targets=targets,
rscale=rscale,
#flags="print_hl_cl",
out_host=True,
**extra_kwargs)
# }}}
# {{{ compute (direct) reference solution
evt, (
pot_direct,
grad_x_direct,
) = p2p(queue,
targets,
sources, (strengths, ),
out_host=True,
**extra_source_kwargs)
err_pot = la.norm((pot - pot_direct) / res**2)
err_grad_x = la.norm((grad_x - grad_x_direct) / res**2)
if 1:
err_pot = err_pot / la.norm((pot_direct) / res**2)
err_grad_x = err_grad_x / la.norm((grad_x_direct) / res**2)
if 0:
import matplotlib.pyplot as pt
from matplotlib.colors import Normalize
pt.subplot(131)
im = fp.show_scalar_in_matplotlib(pot.real)
im.set_norm(Normalize(vmin=-0.1, vmax=0.1))
pt.subplot(132)
im = fp.show_scalar_in_matplotlib(pot_direct.real)
im.set_norm(Normalize(vmin=-0.1, vmax=0.1))
pt.colorbar()
pt.subplot(133)
im = fp.show_scalar_in_matplotlib(
np.log10(1e-15 + np.abs(pot - pot_direct)))
im.set_norm(Normalize(vmin=-6, vmax=1))
pt.colorbar()
pt.show()
# }}}
eoc_rec_pot.add_data_point(h, err_pot)
eoc_rec_grad_x.add_data_point(h, err_grad_x)
print(expn_class, knl, order)
print("POTENTIAL:")
print(eoc_rec_pot)
print("X TARGET DERIVATIVE:")
print(eoc_rec_grad_x)
tgt_order = order + 1
if issubclass(expn_class, LocalExpansionBase):
tgt_order_grad = tgt_order - 1
slack = 0.7
grad_slack = 0.5
else:
tgt_order_grad = tgt_order + 1
slack = 0.5
grad_slack = 1
if order <= 2:
slack += 1
grad_slack += 1
if isinstance(knl, DirectionalSourceDerivative):
slack += 1
grad_slack += 2
if isinstance(base_knl, DirectionalSourceDerivative):
slack += 1
grad_slack += 2
if isinstance(base_knl, HelmholtzKernel):
if base_knl.allow_evanescent:
slack += 0.5
grad_slack += 0.5
if issubclass(expn_class, VolumeTaylorMultipoleExpansionBase):
slack += 0.3
grad_slack += 0.3
assert eoc_rec_pot.order_estimate() > tgt_order - slack
assert eoc_rec_grad_x.order_estimate() > tgt_order_grad - grad_slack
def test_pyfmmlib_fmm(ctx_getter, dims, use_dipoles, helmholtz_k):
logging.basicConfig(level=logging.INFO)
from pytest import importorskip
importorskip("pyfmmlib")
ctx = ctx_getter()
queue = cl.CommandQueue(ctx)
nsources = 3000
ntargets = 1000
dtype = np.float64
sources = p_normal(queue, nsources, dims, dtype, seed=15)
targets = (p_normal(queue, ntargets, dims, dtype, seed=18) +
np.array([2, 0, 0])[:dims])
sources_host = particle_array_to_host(sources)
targets_host = particle_array_to_host(targets)
from boxtree import TreeBuilder
tb = TreeBuilder(ctx)
tree, _ = tb(queue,
sources,
targets=targets,
max_particles_in_box=30,
debug=True)
from boxtree.traversal import FMMTraversalBuilder
tbuild = FMMTraversalBuilder(ctx)
trav, _ = tbuild(queue, tree, debug=True)
trav = trav.get(queue=queue)
from pyopencl.clrandom import PhiloxGenerator
rng = PhiloxGenerator(queue.context, seed=20)
weights = rng.uniform(queue, nsources, dtype=np.float64).get()
#weights = np.ones(nsources)
if use_dipoles:
np.random.seed(13)
dipole_vec = np.random.randn(dims, nsources)
else:
dipole_vec = None
if dims == 2 and helmholtz_k == 0:
base_nterms = 20
else:
base_nterms = 10
def fmm_level_to_nterms(tree, lev):
result = base_nterms
if lev < 3 and helmholtz_k:
# exercise order-varies-by-level capability
result += 5
if use_dipoles:
result += 1
return result
from boxtree.pyfmmlib_integration import FMMLibExpansionWrangler
wrangler = FMMLibExpansionWrangler(trav.tree,
helmholtz_k,
fmm_level_to_nterms=fmm_level_to_nterms,
dipole_vec=dipole_vec)
from boxtree.fmm import drive_fmm
timing_data = {}
pot = drive_fmm(trav, wrangler, weights, timing_data=timing_data)
print(timing_data)
assert timing_data
# {{{ ref fmmlib computation
logger.info("computing direct (reference) result")
import pyfmmlib
fmmlib_routine = getattr(
pyfmmlib, "%spot%s%ddall%s_vec" %
(wrangler.eqn_letter, "fld" if dims == 3 else "grad", dims,
"_dp" if use_dipoles else ""))
kwargs = {}
if dims == 3:
kwargs["iffld"] = False
else:
kwargs["ifgrad"] = False
kwargs["ifhess"] = False
if use_dipoles:
if helmholtz_k == 0 and dims == 2:
kwargs["dipstr"] = -weights * (dipole_vec[0] + 1j * dipole_vec[1])
else:
kwargs["dipstr"] = weights
kwargs["dipvec"] = dipole_vec
else:
kwargs["charge"] = weights
if helmholtz_k:
kwargs["zk"] = helmholtz_k
ref_pot = wrangler.finalize_potentials(
fmmlib_routine(sources=sources_host.T,
targets=targets_host.T,
**kwargs)[0])
rel_err = la.norm(pot - ref_pot, np.inf) / la.norm(ref_pot, np.inf)
logger.info("relative l2 error vs fmmlib direct: %g" % rel_err)
assert rel_err < 1e-5, rel_err
# }}}
# {{{ check against sumpy
try:
import sumpy # noqa
except ImportError:
have_sumpy = False
from warnings import warn
warn("sumpy unavailable: cannot compute independent reference "
"values for pyfmmlib")
else:
have_sumpy = True
if have_sumpy:
from sumpy.kernel import (LaplaceKernel, HelmholtzKernel,
DirectionalSourceDerivative)
from sumpy.p2p import P2P
sumpy_extra_kwargs = {}
if helmholtz_k:
knl = HelmholtzKernel(dims)
sumpy_extra_kwargs["k"] = helmholtz_k
else:
knl = LaplaceKernel(dims)
if use_dipoles:
knl = DirectionalSourceDerivative(knl)
sumpy_extra_kwargs["src_derivative_dir"] = dipole_vec
p2p = P2P(ctx, [knl], exclude_self=False)
evt, (sumpy_ref_pot, ) = p2p(queue,
targets,
sources, [weights],
out_host=True,
**sumpy_extra_kwargs)
sumpy_rel_err = (la.norm(pot - sumpy_ref_pot, np.inf) /
la.norm(sumpy_ref_pot, np.inf))
logger.info("relative l2 error vs sumpy direct: %g" % sumpy_rel_err)
assert sumpy_rel_err < 1e-5, sumpy_rel_err
def main():
logging.basicConfig(level=logging.INFO)
nelements = 60
qbx_order = 3
k_fac = 4
k0 = 3 * k_fac
k1 = 2.9 * k_fac
mesh_order = 10
bdry_quad_order = mesh_order
bdry_ovsmp_quad_order = bdry_quad_order * 4
fmm_order = qbx_order * 2
cl_ctx = cl.create_some_context()
queue = cl.CommandQueue(cl_ctx)
from meshmode.mesh.generation import ellipse, make_curve_mesh
from functools import partial
mesh = make_curve_mesh(partial(ellipse, 3),
np.linspace(0, 1, nelements + 1), mesh_order)
density_discr = Discretization(
cl_ctx, mesh,
InterpolatoryQuadratureSimplexGroupFactory(bdry_quad_order))
logger.info("%d elements" % mesh.nelements)
# from meshmode.discretization.visualization import make_visualizer
# bdry_vis = make_visualizer(queue, density_discr, 20)
# {{{ solve bvp
from sumpy.kernel import HelmholtzKernel
kernel = HelmholtzKernel(2)
beta = 2.5 * k_fac
K0 = np.sqrt(k0**2 - beta**2)
K1 = np.sqrt(k1**2 - beta**2)
from pytential.symbolic.pde.scalar import DielectricSDRep2DBoundaryOperator
pde_op = DielectricSDRep2DBoundaryOperator(
mode='tm',
k_vacuum=1,
interfaces=((0, 1, sym.DEFAULT_SOURCE), ),
domain_k_exprs=(k0, k1),
beta=beta)
op_unknown_sym = pde_op.make_unknown("unknown")
representation0_sym = pde_op.representation(op_unknown_sym, 0)
representation1_sym = pde_op.representation(op_unknown_sym, 1)
from pytential.qbx import QBXLayerPotentialSource
qbx = QBXLayerPotentialSource(density_discr,
fine_order=bdry_ovsmp_quad_order,
qbx_order=qbx_order,
fmm_order=fmm_order)
bound_pde_op = bind(qbx, pde_op.operator(op_unknown_sym))
# in inner domain
sources_1 = make_obj_array(list(np.array([[-1.5, 0.5]]).T.copy()))
strengths_1 = np.array([1])
from sumpy.p2p import P2P
pot_p2p = P2P(cl_ctx, [kernel], exclude_self=False)
_, (Einc, ) = pot_p2p(queue,
density_discr.nodes(),
sources_1, [strengths_1],
out_host=False,
k=K0)
sqrt_w = bind(density_discr, sym.sqrt_jac_q_weight())(queue)
bvp_rhs = np.zeros(len(pde_op.bcs), dtype=object)
for i_bc, terms in enumerate(pde_op.bcs):
for term in terms:
assert term.i_interface == 0
assert term.field_kind == pde_op.field_kind_e
if term.direction == pde_op.dir_none:
bvp_rhs[i_bc] += (term.coeff_outer * (-Einc))
elif term.direction == pde_op.dir_normal:
# no jump in normal derivative
bvp_rhs[i_bc] += 0 * Einc
else:
raise NotImplementedError("direction spec in RHS")
bvp_rhs[i_bc] *= sqrt_w
from pytential.solve import gmres
gmres_result = gmres(bound_pde_op.scipy_op(queue,
"unknown",
dtype=np.complex128,
domains=[sym.DEFAULT_TARGET] *
2,
K0=K0,
K1=K1),
bvp_rhs,
tol=1e-6,
progress=True,
hard_failure=True,
stall_iterations=0)
# }}}
unknown = gmres_result.solution
# {{{ visualize
from pytential.qbx import QBXLayerPotentialSource
lap_qbx = QBXLayerPotentialSource(density_discr,
fine_order=bdry_ovsmp_quad_order,
qbx_order=qbx_order,
fmm_order=qbx_order)
from sumpy.visualization import FieldPlotter
fplot = FieldPlotter(np.zeros(2), extent=5, npoints=300)
from pytential.target import PointsTarget
fld0 = bind((qbx, PointsTarget(fplot.points)),
representation0_sym)(queue, unknown=unknown, K0=K0).get()
fld1 = bind((qbx, PointsTarget(fplot.points)),
representation1_sym)(queue, unknown=unknown, K1=K1).get()
ones = cl.array.empty(queue, density_discr.nnodes, np.float64)
dom1_indicator = -bind(
(lap_qbx, PointsTarget(fplot.points)), sym.D(0, sym.var("sigma")))(
queue, sigma=ones.fill(1)).get()
_, (fld_inc_vol, ) = pot_p2p(queue,
fplot.points,
sources_1, [strengths_1],
out_host=True,
k=K0)
#fplot.show_scalar_in_mayavi(fld_in_vol.real, max_val=5)
fplot.write_vtk_file("potential.vts", [
("fld0", fld0),
("fld1", fld1),
("fld_inc_vol", fld_inc_vol),
("fld_total", ((fld_inc_vol + fld0) *
(1 - dom1_indicator) + fld1 * dom1_indicator)),
("dom1_indicator", dom1_indicator),
])
def test_p2p_direct(ctx_factory, exclude_self, factor, lpot_id):
logging.basicConfig(level=logging.INFO)
ctx = ctx_factory()
queue = cl.CommandQueue(ctx)
ndim = 2
nblks = 10
mode_nr = 25
from sumpy.kernel import LaplaceKernel, DirectionalSourceDerivative
if lpot_id == 1:
lknl = LaplaceKernel(ndim)
elif lpot_id == 2:
lknl = LaplaceKernel(ndim)
lknl = DirectionalSourceDerivative(lknl, dir_vec_name="dsource_vec")
else:
raise ValueError("unknow lpot_id")
from sumpy.p2p import P2P
lpot = P2P(ctx, [lknl], exclude_self=exclude_self)
from sumpy.p2p import P2PMatrixGenerator
mat_gen = P2PMatrixGenerator(ctx, [lknl], exclude_self=exclude_self)
from sumpy.p2p import P2PMatrixBlockGenerator
blk_gen = P2PMatrixBlockGenerator(ctx, [lknl], exclude_self=exclude_self)
for n in [200, 300, 400]:
targets, sources, _, _, sigma = \
_build_geometry(queue, n, mode_nr, target_radius=1.2)
h = 2 * np.pi / n
strengths = (sigma * h, )
tgtindices = _build_block_index(queue, n, nblks, factor)
srcindices = _build_block_index(queue, n, nblks, factor)
index_set = MatrixBlockIndexRanges(ctx, tgtindices, srcindices)
extra_kwargs = {}
if exclude_self:
extra_kwargs["target_to_source"] = \
cl.array.arange(queue, 0, n, dtype=np.int)
if lpot_id == 2:
from pytools.obj_array import make_obj_array
extra_kwargs["dsource_vec"] = \
vector_to_device(queue, make_obj_array(np.ones((ndim, n))))
_, (result_lpot, ) = lpot(queue,
targets=targets,
sources=sources,
strength=strengths,
**extra_kwargs)
result_lpot = result_lpot.get()
_, (mat, ) = mat_gen(queue,
targets=targets,
sources=sources,
**extra_kwargs)
mat = mat.get()
result_mat = mat.dot(strengths[0].get())
_, (blk, ) = blk_gen(queue,
targets=targets,
sources=sources,
index_set=index_set,
**extra_kwargs)
blk = blk.get()
eps = 1.0e-10 * la.norm(result_lpot)
assert la.norm(result_mat - result_lpot) < eps
index_set = index_set.get(queue)
for i in range(index_set.nblocks):
assert la.norm(
index_set.block_take(blk, i) - index_set.take(mat, i)) < eps
def draw_pot_figure(aspect_ratio,
nsrc=100,
novsmp=None,
helmholtz_k=0,
what_operator="S",
what_operator_lpot=None,
order=4,
ovsmp_center_exp=0.66,
force_center_side=None):
import logging
logging.basicConfig(level=logging.INFO)
if novsmp is None:
novsmp = 4 * nsrc
if what_operator_lpot is None:
what_operator_lpot = what_operator
ctx = cl.create_some_context()
queue = cl.CommandQueue(ctx)
# {{{ make plot targets
center = np.asarray([0, 0], dtype=np.float64)
from sumpy.visualization import FieldPlotter
fp = FieldPlotter(center, npoints=1000, extent=6)
# }}}
# {{{ make p2p kernel calculator
from sumpy.p2p import P2P
from sumpy.kernel import LaplaceKernel, HelmholtzKernel
from sumpy.expansion.local import H2DLocalExpansion, LineTaylorLocalExpansion
if helmholtz_k:
if isinstance(helmholtz_k, complex):
knl = HelmholtzKernel(2, allow_evanescent=True)
expn_class = H2DLocalExpansion
knl_kwargs = {"k": helmholtz_k}
else:
knl = HelmholtzKernel(2)
expn_class = H2DLocalExpansion
knl_kwargs = {"k": helmholtz_k}
else:
knl = LaplaceKernel(2)
expn_class = LineTaylorLocalExpansion
knl_kwargs = {}
vol_knl = process_kernel(knl, what_operator)
p2p = P2P(ctx, [vol_knl], exclude_self=False, value_dtypes=np.complex128)
lpot_knl = process_kernel(knl, what_operator_lpot)
from sumpy.qbx import LayerPotential
lpot = LayerPotential(ctx, [expn_class(lpot_knl, order=order)],
value_dtypes=np.complex128)
# }}}
# {{{ set up geometry
# r,a,b match the corresponding letters from G. J. Rodin and O. Steinbach,
# Boundary Element Preconditioners for problems defined on slender domains.
# http://dx.doi.org/10.1137/S1064827500372067
a = 1
b = 1 / aspect_ratio
def map_to_curve(t):
t = t * (2 * np.pi)
x = a * np.cos(t)
y = b * np.sin(t)
w = (np.zeros_like(t) + 1) / len(t)
return x, y, w
from curve import CurveGrid
native_t = np.linspace(0, 1, nsrc, endpoint=False)
native_x, native_y, native_weights = map_to_curve(native_t)
native_curve = CurveGrid(native_x, native_y)
ovsmp_t = np.linspace(0, 1, novsmp, endpoint=False)
ovsmp_x, ovsmp_y, ovsmp_weights = map_to_curve(ovsmp_t)
ovsmp_curve = CurveGrid(ovsmp_x, ovsmp_y)
curve_len = np.sum(ovsmp_weights * ovsmp_curve.speed)
hovsmp = curve_len / novsmp
center_dist = 5 * hovsmp
if force_center_side is not None:
center_side = force_center_side * np.ones(len(native_curve))
else:
center_side = -np.sign(native_curve.mean_curvature)
centers = (native_curve.pos +
center_side[:, np.newaxis] * center_dist * native_curve.normal)
#native_curve.plot()
#pt.show()
volpot_kwargs = knl_kwargs.copy()
lpot_kwargs = knl_kwargs.copy()
if what_operator == "D":
volpot_kwargs["src_derivative_dir"] = native_curve.normal
if what_operator_lpot == "D":
lpot_kwargs["src_derivative_dir"] = ovsmp_curve.normal
if what_operator_lpot == "S'":
lpot_kwargs["tgt_derivative_dir"] = native_curve.normal
# }}}
if 0:
# {{{ build matrix
from fourier import make_fourier_interp_matrix
fim = make_fourier_interp_matrix(novsmp, nsrc)
from sumpy.tools import build_matrix
from scipy.sparse.linalg import LinearOperator
def apply_lpot(x):
xovsmp = np.dot(fim, x)
evt, (y, ) = lpot(queue,
native_curve.pos,
ovsmp_curve.pos,
centers,
[xovsmp * ovsmp_curve.speed * ovsmp_weights],
expansion_radii=np.ones(centers.shape[1]),
**lpot_kwargs)
return y
op = LinearOperator((nsrc, nsrc), apply_lpot)
mat = build_matrix(op, dtype=np.complex128)
w, v = la.eig(mat)
pt.plot(w.real, "o-")
#import sys; sys.exit(0)
return
# }}}
# {{{ compute potentials
mode_nr = 0
density = np.cos(mode_nr * 2 * np.pi * native_t).astype(np.complex128)
ovsmp_density = np.cos(mode_nr * 2 * np.pi * ovsmp_t).astype(np.complex128)
evt, (vol_pot, ) = p2p(queue, fp.points, native_curve.pos,
[native_curve.speed * native_weights * density],
**volpot_kwargs)
evt, (curve_pot, ) = lpot(
queue,
native_curve.pos,
ovsmp_curve.pos,
centers, [ovsmp_density * ovsmp_curve.speed * ovsmp_weights],
expansion_radii=np.ones(centers.shape[1]),
**lpot_kwargs)
# }}}
if 0:
# {{{ plot on-surface potential in 2D
pt.plot(curve_pot, label="pot")
pt.plot(density, label="dens")
pt.legend()
pt.show()
# }}}
fp.write_vtk_file("potential.vts", [("potential", vol_pot.real)])
if 0:
# {{{ 2D false-color plot
pt.clf()
plotval = np.log10(1e-20 + np.abs(vol_pot))
im = fp.show_scalar_in_matplotlib(plotval.real)
from matplotlib.colors import Normalize
im.set_norm(Normalize(vmin=-2, vmax=1))
src = native_curve.pos
pt.plot(src[:, 0], src[:, 1], "o-k")
# close the curve
pt.plot(src[-1::-len(src) + 1, 0], src[-1::-len(src) + 1, 1], "o-k")
#pt.gca().set_aspect("equal", "datalim")
cb = pt.colorbar(shrink=0.9)
cb.set_label(r"$\log_{10}(\mathdefault{Error})$")
#from matplotlib.ticker import NullFormatter
#pt.gca().xaxis.set_major_formatter(NullFormatter())
#pt.gca().yaxis.set_major_formatter(NullFormatter())
fp.set_matplotlib_limits()
# }}}
else:
# {{{ 3D plots
plotval_vol = vol_pot.real
plotval_c = curve_pot.real
scale = 1
if 0:
# crop singularities--doesn't work very well
neighbors = [
np.roll(plotval_vol, 3, 0),
np.roll(plotval_vol, -3, 0),
np.roll(plotval_vol, 6, 0),
np.roll(plotval_vol, -6, 0),
]
avg = np.average(np.abs(plotval_vol))
outlier_flag = sum(np.abs(plotval_vol - nb)
for nb in neighbors) > avg
plotval_vol[outlier_flag] = sum(
nb[outlier_flag] for nb in neighbors) / len(neighbors)
fp.show_scalar_in_mayavi(scale * plotval_vol, max_val=1)
from mayavi import mlab
mlab.colorbar()
if 1:
mlab.points3d(native_curve.pos[0],
native_curve.pos[1],
scale * plotval_c,
scale_factor=0.02)
mlab.show()
def run_dielectric_test(cl_ctx,
queue,
nelements,
qbx_order,
op_class,
mode,
k0=3,
k1=2.9,
mesh_order=10,
bdry_quad_order=None,
bdry_ovsmp_quad_order=None,
use_l2_weighting=False,
fmm_order=None,
visualize=False):
if fmm_order is None:
fmm_order = qbx_order * 2
if bdry_quad_order is None:
bdry_quad_order = mesh_order
if bdry_ovsmp_quad_order is None:
bdry_ovsmp_quad_order = 4 * bdry_quad_order
from meshmode.mesh.generation import ellipse, make_curve_mesh
from functools import partial
mesh = make_curve_mesh(partial(ellipse, 3),
np.linspace(0, 1, nelements + 1), mesh_order)
density_discr = Discretization(
cl_ctx, mesh,
InterpolatoryQuadratureSimplexGroupFactory(bdry_quad_order))
logger.info("%d elements" % mesh.nelements)
# from meshmode.discretization.visualization import make_visualizer
# bdry_vis = make_visualizer(queue, density_discr, 20)
# {{{ solve bvp
from sumpy.kernel import HelmholtzKernel, AxisTargetDerivative
kernel = HelmholtzKernel(2)
beta = 2.5
K0 = np.sqrt(k0**2 - beta**2) # noqa
K1 = np.sqrt(k1**2 - beta**2) # noqa
pde_op = op_class(mode,
k_vacuum=1,
interfaces=((0, 1, sym.DEFAULT_SOURCE), ),
domain_k_exprs=(k0, k1),
beta=beta,
use_l2_weighting=use_l2_weighting)
op_unknown_sym = pde_op.make_unknown("unknown")
representation0_sym = pde_op.representation(op_unknown_sym, 0)
representation1_sym = pde_op.representation(op_unknown_sym, 1)
from pytential.qbx import QBXLayerPotentialSource
qbx = QBXLayerPotentialSource(density_discr,
fine_order=bdry_ovsmp_quad_order,
qbx_order=qbx_order,
fmm_order=fmm_order).with_refinement()
#print(sym.pretty(pde_op.operator(op_unknown_sym)))
#1/0
bound_pde_op = bind(qbx, pde_op.operator(op_unknown_sym))
e_factor = float(pde_op.ez_enabled)
h_factor = float(pde_op.hz_enabled)
e_sources_0 = make_obj_array(list(np.array([[0.1, 0.2]]).T.copy()))
e_strengths_0 = np.array([1 * e_factor])
e_sources_1 = make_obj_array(list(np.array([[4, 4]]).T.copy()))
e_strengths_1 = np.array([1 * e_factor])
h_sources_0 = make_obj_array(list(np.array([[0.2, 0.1]]).T.copy()))
h_strengths_0 = np.array([1 * h_factor])
h_sources_1 = make_obj_array(list(np.array([[4, 5]]).T.copy()))
h_strengths_1 = np.array([1 * h_factor])
kernel_grad = [
AxisTargetDerivative(i, kernel)
for i in range(density_discr.ambient_dim)
]
from sumpy.p2p import P2P
pot_p2p = P2P(cl_ctx, [kernel], exclude_self=False)
pot_p2p_grad = P2P(cl_ctx, kernel_grad, exclude_self=False)
normal = bind(density_discr, sym.normal())(queue).as_vector(np.object)
tangent = bind(density_discr,
sym.pseudoscalar() / sym.area_element())(queue).as_vector(
np.object)
_, (E0, ) = pot_p2p(queue,
density_discr.nodes(),
e_sources_0, [e_strengths_0],
out_host=False,
k=K0)
_, (E1, ) = pot_p2p(queue,
density_discr.nodes(),
e_sources_1, [e_strengths_1],
out_host=False,
k=K1)
_, (grad0_E0, grad1_E0) = pot_p2p_grad(queue,
density_discr.nodes(),
e_sources_0, [e_strengths_0],
out_host=False,
k=K0)
_, (grad0_E1, grad1_E1) = pot_p2p_grad(queue,
density_discr.nodes(),
e_sources_1, [e_strengths_1],
out_host=False,
k=K1)
_, (H0, ) = pot_p2p(queue,
density_discr.nodes(),
h_sources_0, [h_strengths_0],
out_host=False,
k=K0)
_, (H1, ) = pot_p2p(queue,
density_discr.nodes(),
h_sources_1, [h_strengths_1],
out_host=False,
k=K1)
_, (grad0_H0, grad1_H0) = pot_p2p_grad(queue,
density_discr.nodes(),
h_sources_0, [h_strengths_0],
out_host=False,
k=K0)
_, (grad0_H1, grad1_H1) = pot_p2p_grad(queue,
density_discr.nodes(),
h_sources_1, [h_strengths_1],
out_host=False,
k=K1)
E0_dntarget = (grad0_E0 * normal[0] + grad1_E0 * normal[1]) # noqa
E1_dntarget = (grad0_E1 * normal[0] + grad1_E1 * normal[1]) # noqa
H0_dntarget = (grad0_H0 * normal[0] + grad1_H0 * normal[1]) # noqa
H1_dntarget = (grad0_H1 * normal[0] + grad1_H1 * normal[1]) # noqa
E0_dttarget = (grad0_E0 * tangent[0] + grad1_E0 * tangent[1]) # noqa
E1_dttarget = (grad0_E1 * tangent[0] + grad1_E1 * tangent[1]) # noqa
H0_dttarget = (grad0_H0 * tangent[0] + grad1_H0 * tangent[1]) # noqa
H1_dttarget = (grad0_H1 * tangent[0] + grad1_H1 * tangent[1]) # noqa
sqrt_w = bind(density_discr, sym.sqrt_jac_q_weight())(queue)
bvp_rhs = np.zeros(len(pde_op.bcs), dtype=np.object)
for i_bc, terms in enumerate(pde_op.bcs):
for term in terms:
assert term.i_interface == 0
if term.field_kind == pde_op.field_kind_e:
if term.direction == pde_op.dir_none:
bvp_rhs[i_bc] += (term.coeff_outer * E0 +
term.coeff_inner * E1)
elif term.direction == pde_op.dir_normal:
bvp_rhs[i_bc] += (term.coeff_outer * E0_dntarget +
term.coeff_inner * E1_dntarget)
elif term.direction == pde_op.dir_tangential:
bvp_rhs[i_bc] += (term.coeff_outer * E0_dttarget +
term.coeff_inner * E1_dttarget)
else:
raise NotImplementedError("direction spec in RHS")
elif term.field_kind == pde_op.field_kind_h:
if term.direction == pde_op.dir_none:
bvp_rhs[i_bc] += (term.coeff_outer * H0 +
term.coeff_inner * H1)
elif term.direction == pde_op.dir_normal:
bvp_rhs[i_bc] += (term.coeff_outer * H0_dntarget +
term.coeff_inner * H1_dntarget)
elif term.direction == pde_op.dir_tangential:
bvp_rhs[i_bc] += (term.coeff_outer * H0_dttarget +
term.coeff_inner * H1_dttarget)
else:
raise NotImplementedError("direction spec in RHS")
if use_l2_weighting:
bvp_rhs[i_bc] *= sqrt_w
scipy_op = bound_pde_op.scipy_op(queue,
"unknown",
domains=[sym.DEFAULT_TARGET] *
len(pde_op.bcs),
K0=K0,
K1=K1,
dtype=np.complex128)
if mode == "tem" or op_class is SRep:
from sumpy.tools import vector_from_device, vector_to_device
from pytential.solve import lu
unknown = lu(scipy_op, vector_from_device(queue, bvp_rhs))
unknown = vector_to_device(queue, unknown)
else:
from pytential.solve import gmres
gmres_result = gmres(scipy_op,
bvp_rhs,
tol=1e-14,
progress=True,
hard_failure=True,
stall_iterations=0)
unknown = gmres_result.solution
# }}}
targets_0 = make_obj_array(
list(np.array([[3.2 + t, -4] for t in [0, 0.5, 1]]).T.copy()))
targets_1 = make_obj_array(
list(np.array([[t * -0.3, t * -0.2] for t in [0, 0.5, 1]]).T.copy()))
from pytential.target import PointsTarget
from sumpy.tools import vector_from_device
F0_tgt = vector_from_device(
queue,
bind( # noqa
(qbx, PointsTarget(targets_0)),
representation0_sym)(queue, unknown=unknown, K0=K0, K1=K1))
F1_tgt = vector_from_device(
queue,
bind( # noqa
(qbx, PointsTarget(targets_1)),
representation1_sym)(queue, unknown=unknown, K0=K0, K1=K1))
_, (E0_tgt_true, ) = pot_p2p(queue,
targets_0,
e_sources_0, [e_strengths_0],
out_host=True,
k=K0)
_, (E1_tgt_true, ) = pot_p2p(queue,
targets_1,
e_sources_1, [e_strengths_1],
out_host=True,
k=K1)
_, (H0_tgt_true, ) = pot_p2p(queue,
targets_0,
h_sources_0, [h_strengths_0],
out_host=True,
k=K0)
_, (H1_tgt_true, ) = pot_p2p(queue,
targets_1,
h_sources_1, [h_strengths_1],
out_host=True,
k=K1)
err_F0_total = 0 # noqa
err_F1_total = 0 # noqa
i_field = 0
def vec_norm(ary):
return la.norm(ary.reshape(-1))
def field_kind_to_string(field_kind):
return {pde_op.field_kind_e: "E", pde_op.field_kind_h: "H"}[field_kind]
for field_kind in pde_op.field_kinds:
if not pde_op.is_field_present(field_kind):
continue
if field_kind == pde_op.field_kind_e:
F0_tgt_true = E0_tgt_true # noqa
F1_tgt_true = E1_tgt_true # noqa
elif field_kind == pde_op.field_kind_h:
F0_tgt_true = H0_tgt_true # noqa
F1_tgt_true = H1_tgt_true # noqa
else:
assert False
abs_err_F0 = vec_norm(F0_tgt[i_field] - F0_tgt_true) # noqa
abs_err_F1 = vec_norm(F1_tgt[i_field] - F1_tgt_true) # noqa
rel_err_F0 = abs_err_F0 / vec_norm(F0_tgt_true) # noqa
rel_err_F1 = abs_err_F1 / vec_norm(F1_tgt_true) # noqa
err_F0_total = max(rel_err_F0, err_F0_total) # noqa
err_F1_total = max(rel_err_F1, err_F1_total) # noqa
print("Abs Err %s0" % field_kind_to_string(field_kind), abs_err_F0)
print("Abs Err %s1" % field_kind_to_string(field_kind), abs_err_F1)
print("Rel Err %s0" % field_kind_to_string(field_kind), rel_err_F0)
print("Rel Err %s1" % field_kind_to_string(field_kind), rel_err_F1)
i_field += 1
if visualize:
from sumpy.visualization import FieldPlotter
fplot = FieldPlotter(np.zeros(2), extent=5, npoints=300)
from pytential.target import PointsTarget
fld0 = bind((qbx, PointsTarget(fplot.points)),
representation0_sym)(queue, unknown=unknown, K0=K0)
fld1 = bind((qbx, PointsTarget(fplot.points)),
representation1_sym)(queue, unknown=unknown, K1=K1)
comp_fields = []
i_field = 0
for field_kind in pde_op.field_kinds:
if not pde_op.is_field_present(field_kind):
continue
fld_str = field_kind_to_string(field_kind)
comp_fields.extend([
("%s_fld0" % fld_str, fld0[i_field].get()),
("%s_fld1" % fld_str, fld1[i_field].get()),
])
i_field += 0
low_order_qbx = QBXLayerPotentialSource(
density_discr,
fine_order=bdry_ovsmp_quad_order,
qbx_order=2,
fmm_order=3).with_refinement()
from sumpy.kernel import LaplaceKernel
from pytential.target import PointsTarget
ones = (cl.array.empty(queue, (density_discr.nnodes, ),
dtype=np.float64).fill(1))
ind_func = -bind(
(low_order_qbx, PointsTarget(fplot.points)),
sym.D(LaplaceKernel(2), sym.var("u")))(queue, u=ones).get()
_, (e_fld0_true, ) = pot_p2p(queue,
fplot.points,
e_sources_0, [e_strengths_0],
out_host=True,
k=K0)
_, (e_fld1_true, ) = pot_p2p(queue,
fplot.points,
e_sources_1, [e_strengths_1],
out_host=True,
k=K1)
_, (h_fld0_true, ) = pot_p2p(queue,
fplot.points,
h_sources_0, [h_strengths_0],
out_host=True,
k=K0)
_, (h_fld1_true, ) = pot_p2p(queue,
fplot.points,
h_sources_1, [h_strengths_1],
out_host=True,
k=K1)
#fplot.show_scalar_in_mayavi(fld_in_vol.real, max_val=5)
fplot.write_vtk_file("potential-n%d.vts" % nelements, [
("e_fld0_true", e_fld0_true),
("e_fld1_true", e_fld1_true),
("h_fld0_true", h_fld0_true),
("h_fld1_true", h_fld1_true),
("ind", ind_func),
] + comp_fields)
return err_F0_total, err_F1_total