def test_off_surface_eval(ctx_factory, use_fmm, do_plot=False):
logging.basicConfig(level=logging.INFO)
cl_ctx = ctx_factory()
queue = cl.CommandQueue(cl_ctx)
# prevent cache 'splosion
from sympy.core.cache import clear_cache
clear_cache()
nelements = 30
target_order = 8
qbx_order = 3
if use_fmm:
fmm_order = qbx_order
else:
fmm_order = False
mesh = make_curve_mesh(partial(ellipse, 3),
np.linspace(0, 1, nelements + 1), target_order)
from pytential.qbx import QBXLayerPotentialSource
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import \
InterpolatoryQuadratureSimplexGroupFactory
pre_density_discr = Discretization(
cl_ctx, mesh, InterpolatoryQuadratureSimplexGroupFactory(target_order))
qbx, _ = QBXLayerPotentialSource(
pre_density_discr,
4 * target_order,
qbx_order,
fmm_order=fmm_order,
).with_refinement()
density_discr = qbx.density_discr
from sumpy.kernel import LaplaceKernel
op = sym.D(LaplaceKernel(2), sym.var("sigma"), qbx_forced_limit=-2)
sigma = density_discr.zeros(queue) + 1
fplot = FieldPlotter(np.zeros(2), extent=0.54, npoints=30)
from pytential.target import PointsTarget
fld_in_vol = bind((qbx, PointsTarget(fplot.points)), op)(queue,
sigma=sigma)
err = cl.clmath.fabs(fld_in_vol - (-1))
linf_err = cl.array.max(err).get()
print("l_inf error:", linf_err)
if do_plot:
fplot.show_scalar_in_matplotlib(fld_in_vol.get())
import matplotlib.pyplot as pt
pt.colorbar()
pt.show()
assert linf_err < 1e-3
def test_off_surface_eval(actx_factory, use_fmm, visualize=False):
logging.basicConfig(level=logging.INFO)
actx = actx_factory()
# prevent cache 'splosion
from sympy.core.cache import clear_cache
clear_cache()
nelements = 30
target_order = 8
qbx_order = 3
if use_fmm:
fmm_order = qbx_order
else:
fmm_order = False
mesh = mgen.make_curve_mesh(partial(mgen.ellipse, 3),
np.linspace(0, 1, nelements + 1), target_order)
from pytential.qbx import QBXLayerPotentialSource
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import \
InterpolatoryQuadratureSimplexGroupFactory
pre_density_discr = Discretization(
actx, mesh, InterpolatoryQuadratureSimplexGroupFactory(target_order))
qbx = QBXLayerPotentialSource(
pre_density_discr,
4 * target_order,
qbx_order,
fmm_order=fmm_order,
)
from pytential.target import PointsTarget
fplot = FieldPlotter(np.zeros(2), extent=0.54, npoints=30)
targets = PointsTarget(actx.freeze(actx.from_numpy(fplot.points)))
places = GeometryCollection((qbx, targets))
density_discr = places.get_discretization(places.auto_source.geometry)
from sumpy.kernel import LaplaceKernel
op = sym.D(LaplaceKernel(2), sym.var("sigma"), qbx_forced_limit=-2)
sigma = density_discr.zeros(actx) + 1
fld_in_vol = bind(places, op)(actx, sigma=sigma)
fld_in_vol_exact = -1
linf_err = actx.to_numpy(
actx.np.linalg.norm(fld_in_vol - fld_in_vol_exact, ord=np.inf))
logger.info("l_inf error: %.12e", linf_err)
if visualize:
fplot.show_scalar_in_matplotlib(actx.to_numpy(fld_in_vol))
import matplotlib.pyplot as pt
pt.colorbar()
pt.show()
assert linf_err < 1e-3
def main():
from sumpy.kernel import ( # noqa: F401
YukawaKernel, HelmholtzKernel, LaplaceKernel)
tctx = t.ToyContext(
cl.create_some_context(),
#LaplaceKernel(2),
YukawaKernel(2),
extra_kernel_kwargs={"lam": 5},
#HelmholtzKernel(2), extra_kernel_kwargs={"k": 0.3},
)
pt_src = t.PointSources(tctx, np.random.rand(2, 50) - 0.5, np.ones(50))
fp = FieldPlotter([3, 0], extent=8)
if 0 and plt is not None:
t.logplot(fp, pt_src, cmap="jet")
plt.colorbar()
plt.show()
mexp = t.multipole_expand(pt_src, [0, 0], 5)
mexp2 = t.multipole_expand(mexp, [0, 0.25]) # noqa: F841
lexp = t.local_expand(mexp, [3, 0])
lexp2 = t.local_expand(lexp, [3, 1], 3)
#diff = mexp - pt_src
#diff = mexp2 - pt_src
diff = lexp2 - pt_src
print(t.l_inf(diff, 1.2, center=lexp2.center))
if 1 and plt is not None:
t.logplot(fp, diff, cmap="jet", vmin=-3, vmax=0)
plt.colorbar()
plt.show()
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 l_inf(psource, radius, center=None, npoints=100, debug=False):
if center is None:
center = psource.center
restr = psource * OneOnBallPotential(psource.toy_ctx, center, radius)
from sumpy.visualization import FieldPlotter
fp = FieldPlotter(center, extent=2 * radius, npoints=npoints)
z = restr.eval(fp.points)
if debug:
fp.show_scalar_in_matplotlib(np.log10(np.abs(z + 1e-15)))
import matplotlib.pyplot as pt
pt.colorbar()
pt.show()
return np.max(np.abs(z))
def l_inf(psource, radius, center=None, npoints=100, debug=False):
if center is None:
center = psource.center
restr = psource * OneOnBallPotential(psource.toy_ctx, center, radius)
from sumpy.visualization import FieldPlotter
fp = FieldPlotter(center, extent=2*radius, npoints=npoints)
z = restr.eval(fp.points)
if debug:
fp.show_scalar_in_matplotlib(
np.log10(np.abs(z + 1e-15)))
import matplotlib.pyplot as pt
pt.colorbar()
pt.show()
return np.max(np.abs(z))
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 main(mesh_name="ellipsoid"):
import logging
logger = logging.getLogger(__name__)
logging.basicConfig(level=logging.WARNING) # INFO for more progress info
cl_ctx = cl.create_some_context()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue)
if mesh_name == "ellipsoid":
cad_file_name = "geometries/ellipsoid.step"
h = 0.6
elif mesh_name == "two-cylinders":
cad_file_name = "geometries/two-cylinders-smooth.step"
h = 0.4
else:
raise ValueError("unknown mesh name: %s" % mesh_name)
from meshmode.mesh.io import generate_gmsh, FileSource
mesh = generate_gmsh(
FileSource(cad_file_name),
2,
order=2,
other_options=["-string",
"Mesh.CharacteristicLengthMax = %g;" % h],
target_unit="MM")
from meshmode.mesh.processing import perform_flips
# Flip elements--gmsh generates inside-out geometry.
mesh = perform_flips(mesh, np.ones(mesh.nelements))
from meshmode.mesh.processing import find_bounding_box
bbox_min, bbox_max = find_bounding_box(mesh)
bbox_center = 0.5 * (bbox_min + bbox_max)
bbox_size = max(bbox_max - bbox_min) / 2
logger.info("%d elements" % mesh.nelements)
from pytential.qbx import QBXLayerPotentialSource
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import \
InterpolatoryQuadratureSimplexGroupFactory
density_discr = Discretization(
actx, mesh, InterpolatoryQuadratureSimplexGroupFactory(target_order))
qbx = QBXLayerPotentialSource(density_discr,
4 * target_order,
qbx_order,
fmm_order=qbx_order + 3,
target_association_tolerance=0.15)
from pytential.target import PointsTarget
fplot = FieldPlotter(bbox_center, extent=3.5 * bbox_size, npoints=150)
from pytential import GeometryCollection
places = GeometryCollection(
{
"qbx": qbx,
"targets": PointsTarget(fplot.points)
}, auto_where="qbx")
density_discr = places.get_discretization("qbx")
nodes = thaw(actx, density_discr.nodes())
angle = actx.np.arctan2(nodes[1], nodes[0])
if k:
kernel = HelmholtzKernel(3)
else:
kernel = LaplaceKernel(3)
#op = sym.d_dx(sym.S(kernel, sym.var("sigma"), qbx_forced_limit=None))
op = sym.D(kernel, sym.var("sigma"), qbx_forced_limit=None)
#op = sym.S(kernel, sym.var("sigma"), qbx_forced_limit=None)
sigma = actx.np.cos(mode_nr * angle)
if 0:
from meshmode.dof_array import flatten, unflatten
sigma = flatten(0 * angle)
from random import randrange
for i in range(5):
sigma[randrange(len(sigma))] = 1
sigma = unflatten(actx, density_discr, sigma)
if isinstance(kernel, HelmholtzKernel):
for i, elem in np.ndenumerate(sigma):
sigma[i] = elem.astype(np.complex128)
fld_in_vol = actx.to_numpy(
bind(places, op, auto_where=("qbx", "targets"))(actx, sigma=sigma,
k=k))
#fplot.show_scalar_in_mayavi(fld_in_vol.real, max_val=5)
fplot.write_vtk_file("layerpot-3d-potential.vts",
[("potential", fld_in_vol)])
bdry_normals = bind(places, sym.normal(
density_discr.ambient_dim))(actx).as_vector(dtype=object)
from meshmode.discretization.visualization import make_visualizer
bdry_vis = make_visualizer(actx, density_discr, target_order)
bdry_vis.write_vtk_file("layerpot-3d-density.vtu", [
("sigma", sigma),
("bdry_normals", bdry_normals),
])
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 main():
import logging
logging.basicConfig(level=logging.WARNING) # INFO for more progress info
cl_ctx = cl.create_some_context()
queue = cl.CommandQueue(cl_ctx)
from meshmode.mesh.generation import generate_torus
rout = 10
rin = 1
if 1:
base_mesh = generate_torus(rout, rin, 40, 4, mesh_order)
from meshmode.mesh.processing import affine_map, merge_disjoint_meshes
# nx = 1
# ny = 1
nz = 1
dz = 0
meshes = [
affine_map(base_mesh,
A=np.diag([1, 1, 1]),
b=np.array([0, 0, iz * dz])) for iz in range(nz)
]
mesh = merge_disjoint_meshes(meshes, single_group=True)
if 0:
from meshmode.mesh.visualization import draw_curve
draw_curve(mesh)
import matplotlib.pyplot as plt
plt.show()
pre_density_discr = Discretization(
cl_ctx, mesh,
InterpolatoryQuadratureSimplexGroupFactory(bdry_quad_order))
from pytential.qbx import (QBXLayerPotentialSource,
QBXTargetAssociationFailedException)
qbx, _ = QBXLayerPotentialSource(
pre_density_discr,
fine_order=bdry_ovsmp_quad_order,
qbx_order=qbx_order,
fmm_order=fmm_order,
).with_refinement()
density_discr = qbx.density_discr
# {{{ describe bvp
from sumpy.kernel import LaplaceKernel
kernel = LaplaceKernel(3)
cse = sym.cse
sigma_sym = sym.var("sigma")
#sqrt_w = sym.sqrt_jac_q_weight(3)
sqrt_w = 1
inv_sqrt_w_sigma = cse(sigma_sym / sqrt_w)
# -1 for interior Dirichlet
# +1 for exterior Dirichlet
loc_sign = +1
bdry_op_sym = (
loc_sign * 0.5 * sigma_sym + sqrt_w *
(sym.S(kernel, inv_sqrt_w_sigma) + sym.D(kernel, inv_sqrt_w_sigma)))
# }}}
bound_op = bind(qbx, bdry_op_sym)
# {{{ fix rhs and solve
nodes = density_discr.nodes().with_queue(queue)
source = np.array([rout, 0, 0])
def u_incoming_func(x):
# return 1/cl.clmath.sqrt( (x[0] - source[0])**2
# +(x[1] - source[1])**2
# +(x[2] - source[2])**2 )
return 1.0 / la.norm(x.get() - source[:, None], axis=0)
bc = cl.array.to_device(queue, u_incoming_func(nodes))
bvp_rhs = bind(qbx, sqrt_w * sym.var("bc"))(queue, bc=bc)
from pytential.solve import gmres
gmres_result = gmres(bound_op.scipy_op(queue, "sigma", dtype=np.float64),
bvp_rhs,
tol=1e-14,
progress=True,
stall_iterations=0,
hard_failure=True)
sigma = bind(qbx,
sym.var("sigma") / sqrt_w)(queue, sigma=gmres_result.solution)
# }}}
from meshmode.discretization.visualization import make_visualizer
bdry_vis = make_visualizer(queue, density_discr, 20)
bdry_vis.write_vtk_file("laplace.vtu", [
("sigma", sigma),
])
# {{{ postprocess/visualize
repr_kwargs = dict(qbx_forced_limit=None)
representation_sym = (sym.S(kernel, inv_sqrt_w_sigma, **repr_kwargs) +
sym.D(kernel, inv_sqrt_w_sigma, **repr_kwargs))
from sumpy.visualization import FieldPlotter
fplot = FieldPlotter(np.zeros(3), extent=20, npoints=50)
targets = cl.array.to_device(queue, fplot.points)
qbx_stick_out = qbx.copy(target_stick_out_factor=0.2)
try:
fld_in_vol = bind((qbx_stick_out, PointsTarget(targets)),
representation_sym)(queue, sigma=sigma).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-laplace-3d.vts", [
("potential", fld_in_vol),
])
def run_test(cl_ctx, queue):
q_order = 5
qbx_order = q_order
fmm_backend = "sumpy"
mesh = get_ellipse_mesh(20, 40, mesh_order=5)
a = 1
b = 1 / 40
if 0:
from meshmode.mesh.visualization import draw_curve
import matplotlib.pyplot as plt
draw_curve(mesh)
plt.axes().set_aspect('equal')
plt.show()
from pytential.qbx import QBXLayerPotentialSource
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import \
InterpolatoryQuadratureSimplexGroupFactory
pre_density_discr = Discretization(
cl_ctx, mesh, InterpolatoryQuadratureSimplexGroupFactory(q_order))
refiner_extra_kwargs = {
# "_expansion_disturbance_tolerance": 0.05,
"_scaled_max_curvature_threshold": 1,
"maxiter": 10,
}
qbx, _ = QBXLayerPotentialSource(
pre_density_discr,
fine_order=4 * q_order,
qbx_order=qbx_order,
fmm_backend=fmm_backend,
fmm_order=qbx_order + 5,
).with_refinement(**refiner_extra_kwargs)
if 1:
print("%d stage-1 elements after refinement" %
qbx.density_discr.mesh.nelements)
print("%d stage-2 elements after refinement" %
qbx.stage2_density_discr.mesh.nelements)
print("quad stage-2 elements have %d nodes" %
qbx.quad_stage2_density_discr.groups[0].nunit_nodes)
def reference_solu(rvec):
# a harmonic function
x, y = rvec
return 2.1 * x * y + (x**2 - y**2) * 0.5 + x
bvals = reference_solu(qbx.density_discr.nodes().with_queue(queue))
from pytential.symbolic.pde.scalar import DirichletOperator
from sumpy.kernel import LaplaceKernel
from pytential import sym, bind
op = DirichletOperator(LaplaceKernel(2), -1)
bound_op = bind(qbx.copy(target_association_tolerance=0.5),
op.operator(sym.var('sigma')))
rhs = bind(qbx.density_discr, op.prepare_rhs(sym.var("bc")))(queue,
bc=bvals)
from pytential.solve import gmres
gmres_result = gmres(bound_op.scipy_op(queue, "sigma", dtype=np.float64),
rhs,
tol=1e-12,
progress=True,
hard_failure=True,
stall_iterations=50,
no_progress_factor=1.05)
from sumpy.visualization import FieldPlotter
from pytential.target import PointsTarget
pltsize = b * 1.5
fplot = FieldPlotter(np.array([-1 + pltsize * 0.5, 0]),
extent=pltsize * 1.05,
npoints=500)
plt_targets = cl.array.to_device(queue, fplot.points)
interior_pts = (fplot.points[0]**2 / a**2 +
fplot.points[1]**2 / b**2) < 0.99
exact_vals = reference_solu(fplot.points)
out_errs = []
for assotol in [0.05]:
qbx_stick_out = qbx.copy(target_association_tolerance=0.05)
vol_solution = bind((qbx_stick_out, PointsTarget(plt_targets)),
op.representation(sym.var('sigma')))(
queue, sigma=gmres_result.solution).get()
interior_error_linf = (
np.linalg.norm(np.abs(vol_solution - exact_vals)[interior_pts],
ord=np.inf) /
np.linalg.norm(exact_vals[interior_pts], ord=np.inf))
interior_error_l2 = (np.linalg.norm(
np.abs(vol_solution - exact_vals)[interior_pts], ord=2) /
np.linalg.norm(exact_vals[interior_pts], ord=2))
print("\nassotol = %f" % assotol)
print("L_inf Error = %e " % interior_error_linf)
print("L_2 Error = %e " % interior_error_l2)
out_errs.append(
("error-%f" % assotol, np.abs(vol_solution - exact_vals)))
if 1:
fplot.write_vtk_file("results.vts", out_errs)
def main():
logging.basicConfig(level=logging.INFO)
nelements = 60
qbx_order = 3
k_fac = 4
k0 = 3*k_fac
k1 = 2.9*k_fac
mesh_order = 10
bdry_quad_order = mesh_order
bdry_ovsmp_quad_order = bdry_quad_order * 4
fmm_order = qbx_order * 2
cl_ctx = cl.create_some_context()
queue = cl.CommandQueue(cl_ctx)
from meshmode.mesh.generation import ellipse, make_curve_mesh
from functools import partial
mesh = make_curve_mesh(
partial(ellipse, 3),
np.linspace(0, 1, nelements+1),
mesh_order)
density_discr = Discretization(
cl_ctx, mesh,
InterpolatoryQuadratureSimplexGroupFactory(bdry_quad_order))
logger.info("%d elements" % mesh.nelements)
# from meshmode.discretization.visualization import make_visualizer
# bdry_vis = make_visualizer(queue, density_discr, 20)
# {{{ solve bvp
from sumpy.kernel import HelmholtzKernel
kernel = HelmholtzKernel(2)
beta = 2.5*k_fac
K0 = np.sqrt(k0**2-beta**2)
K1 = np.sqrt(k1**2-beta**2)
from pytential.symbolic.pde.scalar import DielectricSDRep2DBoundaryOperator
pde_op = DielectricSDRep2DBoundaryOperator(
mode='tm',
k_vacuum=1,
interfaces=((0, 1, sym.DEFAULT_SOURCE),),
domain_k_exprs=(k0, k1),
beta=beta)
op_unknown_sym = pde_op.make_unknown("unknown")
representation0_sym = pde_op.representation(op_unknown_sym, 0)
representation1_sym = pde_op.representation(op_unknown_sym, 1)
from pytential.qbx import QBXLayerPotentialSource
qbx = QBXLayerPotentialSource(
density_discr, fine_order=bdry_ovsmp_quad_order, qbx_order=qbx_order,
fmm_order=fmm_order
)
bound_pde_op = bind(qbx, pde_op.operator(op_unknown_sym))
# in inner domain
sources_1 = make_obj_array(list(np.array([
[-1.5, 0.5]
]).T.copy()))
strengths_1 = np.array([1])
from sumpy.p2p import P2P
pot_p2p = P2P(cl_ctx, [kernel], exclude_self=False)
_, (Einc,) = pot_p2p(queue, density_discr.nodes(), sources_1, [strengths_1],
out_host=False, k=K0)
sqrt_w = bind(density_discr, sym.sqrt_jac_q_weight())(queue)
bvp_rhs = np.zeros(len(pde_op.bcs), dtype=np.object)
for i_bc, terms in enumerate(pde_op.bcs):
for term in terms:
assert term.i_interface == 0
assert term.field_kind == pde_op.field_kind_e
if term.direction == pde_op.dir_none:
bvp_rhs[i_bc] += (
term.coeff_outer * (-Einc)
)
elif term.direction == pde_op.dir_normal:
# no jump in normal derivative
bvp_rhs[i_bc] += 0*Einc
else:
raise NotImplementedError("direction spec in RHS")
bvp_rhs[i_bc] *= sqrt_w
from pytential.solve import gmres
gmres_result = gmres(
bound_pde_op.scipy_op(queue, "unknown", dtype=np.complex128,
domains=[sym.DEFAULT_TARGET]*2, K0=K0, K1=K1),
bvp_rhs, tol=1e-6, progress=True,
hard_failure=True, stall_iterations=0)
# }}}
unknown = gmres_result.solution
# {{{ visualize
from pytential.qbx import QBXLayerPotentialSource
lap_qbx = QBXLayerPotentialSource(
density_discr, fine_order=bdry_ovsmp_quad_order, qbx_order=qbx_order,
fmm_order=qbx_order
)
from sumpy.visualization import FieldPlotter
fplot = FieldPlotter(np.zeros(2), extent=5, npoints=300)
from pytential.target import PointsTarget
fld0 = bind(
(qbx, PointsTarget(fplot.points)),
representation0_sym)(queue, unknown=unknown, K0=K0).get()
fld1 = bind(
(qbx, PointsTarget(fplot.points)),
representation1_sym)(queue, unknown=unknown, K1=K1).get()
ones = cl.array.empty(queue, density_discr.nnodes, np.float64)
dom1_indicator = -bind(
(lap_qbx, PointsTarget(fplot.points)),
sym.D(0, sym.var("sigma")))(
queue, sigma=ones.fill(1)).get()
_, (fld_inc_vol,) = pot_p2p(queue, fplot.points, sources_1, [strengths_1],
out_host=True, k=K0)
#fplot.show_scalar_in_mayavi(fld_in_vol.real, max_val=5)
fplot.write_vtk_file(
"potential.vts",
[
("fld0", fld0),
("fld1", fld1),
("fld_inc_vol", fld_inc_vol),
("fld_total", (
(fld_inc_vol + fld0)*(1-dom1_indicator)
+
fld1*dom1_indicator
)),
("dom1_indicator", dom1_indicator),
]
)
def main():
# cl.array.to_device(queue, numpy_array)
from meshmode.mesh.io import generate_gmsh, FileSource
mesh = generate_gmsh(
FileSource("ellipsoid.step"),
2,
order=2,
other_options=["-string",
"Mesh.CharacteristicLengthMax = %g;" % h])
from meshmode.mesh.processing import perform_flips
# Flip elements--gmsh generates inside-out geometry.
mesh = perform_flips(mesh, np.ones(mesh.nelements))
print("%d elements" % mesh.nelements)
from meshmode.mesh.processing import find_bounding_box
bbox_min, bbox_max = find_bounding_box(mesh)
bbox_center = 0.5 * (bbox_min + bbox_max)
bbox_size = max(bbox_max - bbox_min) / 2
logger.info("%d elements" % mesh.nelements)
from pytential.qbx import QBXLayerPotentialSource
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import \
InterpolatoryQuadratureSimplexGroupFactory
density_discr = Discretization(
cl_ctx, mesh, InterpolatoryQuadratureSimplexGroupFactory(target_order))
qbx = QBXLayerPotentialSource(density_discr,
4 * target_order,
qbx_order,
fmm_order=qbx_order + 10,
fmm_backend="fmmlib")
from pytential.symbolic.pde.maxwell import MuellerAugmentedMFIEOperator
pde_op = MuellerAugmentedMFIEOperator(
omega=0.4,
epss=[1.4, 1.0],
mus=[1.2, 1.0],
)
from pytential import bind, sym
unk = pde_op.make_unknown("sigma")
sym_operator = pde_op.operator(unk)
sym_rhs = pde_op.rhs(sym.make_sym_vector("Einc", 3),
sym.make_sym_vector("Hinc", 3))
sym_repr = pde_op.representation(0, unk)
if 1:
expr = sym_repr
print(sym.pretty(expr))
print("#" * 80)
from pytential.target import PointsTarget
tgt_points = np.zeros((3, 1))
tgt_points[0, 0] = 100
tgt_points[1, 0] = -200
tgt_points[2, 0] = 300
bound_op = bind((qbx, PointsTarget(tgt_points)), expr)
print(bound_op.code)
if 1:
def green3e(x, y, z, source, strength, k):
# electric field corresponding to dyadic green's function
# due to monochromatic electric dipole located at "source".
# "strength" is the the intensity of the dipole.
# E = (I + Hess)(exp(ikr)/r) dot (strength)
#
dx = x - source[0]
dy = y - source[1]
dz = z - source[2]
rr = np.sqrt(dx**2 + dy**2 + dz**2)
fout = np.exp(1j * k * rr) / rr
evec = fout * strength
qmat = np.zeros((3, 3), dtype=np.complex128)
qmat[0, 0] = (2 * dx**2 - dy**2 - dz**2) * (1 - 1j * k * rr)
qmat[1, 1] = (2 * dy**2 - dz**2 - dx**2) * (1 - 1j * k * rr)
qmat[2, 2] = (2 * dz**2 - dx**2 - dy**2) * (1 - 1j * k * rr)
qmat[0, 0] = qmat[0, 0] + (-k**2 * dx**2 * rr**2)
qmat[1, 1] = qmat[1, 1] + (-k**2 * dy**2 * rr**2)
qmat[2, 2] = qmat[2, 2] + (-k**2 * dz**2 * rr**2)
qmat[0, 1] = (3 - k**2 * rr**2 - 3 * 1j * k * rr) * (dx * dy)
qmat[1, 2] = (3 - k**2 * rr**2 - 3 * 1j * k * rr) * (dy * dz)
qmat[2, 0] = (3 - k**2 * rr**2 - 3 * 1j * k * rr) * (dz * dx)
qmat[1, 0] = qmat[0, 1]
qmat[2, 1] = qmat[1, 2]
qmat[0, 2] = qmat[2, 0]
fout = np.exp(1j * k * rr) / rr**5 / k**2
fvec = fout * np.dot(qmat, strength)
evec = evec + fvec
return evec
def green3m(x, y, z, source, strength, k):
# magnetic field corresponding to dyadic green's function
# due to monochromatic electric dipole located at "source".
# "strength" is the the intensity of the dipole.
# H = curl((I + Hess)(exp(ikr)/r) dot (strength)) =
# strength \cross \grad (exp(ikr)/r)
#
dx = x - source[0]
dy = y - source[1]
dz = z - source[2]
rr = np.sqrt(dx**2 + dy**2 + dz**2)
fout = (1 - 1j * k * rr) * np.exp(1j * k * rr) / rr**3
fvec = np.zeros(3, dtype=np.complex128)
fvec[0] = fout * dx
fvec[1] = fout * dy
fvec[2] = fout * dz
hvec = np.cross(strength, fvec)
return hvec
def dipole3e(x, y, z, source, strength, k):
#
# evalaute electric and magnetic field due
# to monochromatic electric dipole located at "source"
# with intensity "strength"
evec = green3e(x, y, z, source, strength, k)
evec = evec * 1j * k
hvec = green3m(x, y, z, source, strength, k)
return evec, hvec
def dipole3m(x, y, z, source, strength, k):
#
# evalaute electric and magnetic field due
# to monochromatic magnetic dipole located at "source"
# with intensity "strength"
evec = green3m(x, y, z, source, strength, k)
hvec = green3e(x, y, z, source, strength, k)
hvec = -hvec * 1j * k
return evec, hvec
def dipole3eall(x, y, z, sources, strengths, k):
ns = len(strengths)
evec = np.zeros(3, dtype=np.complex128)
hvec = np.zeros(3, dtype=np.complex128)
for i in range(ns):
evect, hvect = dipole3e(x, y, z, sources[i], strengths[i], k)
evec = evec + evect
hvec = hvec + hvect
nodes = density_discr.nodes().with_queue(queue).get()
source = [0.01, -0.03, 0.02]
# source = cl.array.to_device(queue,np.zeros(3))
# source[0] = 0.01
# source[1] =-0.03
# source[2] = 0.02
strength = np.ones(3)
# evec = cl.array.to_device(queue,np.zeros((3,len(nodes[0])),dtype=np.complex128))
# hvec = cl.array.to_device(queue,np.zeros((3,len(nodes[0])),dtype=np.complex128))
evec = np.zeros((3, len(nodes[0])), dtype=np.complex128)
hvec = np.zeros((3, len(nodes[0])), dtype=np.complex128)
for i in range(len(nodes[0])):
evec[:, i], hvec[:, i] = dipole3e(nodes[0][i], nodes[1][i],
nodes[2][i], source, strength, k)
print(np.shape(hvec))
print(type(evec))
print(type(hvec))
evec = cl.array.to_device(queue, evec)
hvec = cl.array.to_device(queue, hvec)
bvp_rhs = bind(qbx, sym_rhs)(queue, Einc=evec, Hinc=hvec)
print(np.shape(bvp_rhs))
print(type(bvp_rhs))
# print(bvp_rhs)
1 / -1
bound_op = bind(qbx, sym_operator)
from pytential.solve import gmres
if 0:
gmres_result = gmres(bound_op.scipy_op(queue,
"sigma",
dtype=np.complex128,
k=k),
bvp_rhs,
tol=1e-8,
progress=True,
stall_iterations=0,
hard_failure=True)
sigma = gmres_result.solution
fld_at_tgt = bind((qbx, PointsTarget(tgt_points)),
sym_repr)(queue, sigma=bvp_rhs, k=k)
fld_at_tgt = np.array([fi.get() for fi in fld_at_tgt])
print(fld_at_tgt)
1 / 0
# }}}
#mlab.figure(bgcolor=(1, 1, 1))
if 1:
from meshmode.discretization.visualization import make_visualizer
bdry_vis = make_visualizer(queue, density_discr, target_order)
bdry_normals = bind(density_discr, sym.normal(3))(queue)\
.as_vector(dtype=object)
bdry_vis.write_vtk_file("source.vtu", [
("sigma", sigma),
("bdry_normals", bdry_normals),
])
fplot = FieldPlotter(bbox_center,
extent=2 * bbox_size,
npoints=(150, 150, 1))
qbx_tgt_tol = qbx.copy(target_association_tolerance=0.1)
from pytential.target import PointsTarget
from pytential.qbx import QBXTargetAssociationFailedException
rho_sym = sym.var("rho")
try:
fld_in_vol = bind((qbx_tgt_tol, PointsTarget(fplot.points)),
sym.make_obj_array([
sym.S(pde_op.kernel,
rho_sym,
k=sym.var("k"),
qbx_forced_limit=None),
sym.d_dx(
3,
sym.S(pde_op.kernel,
rho_sym,
k=sym.var("k"),
qbx_forced_limit=None)),
sym.d_dy(
3,
sym.S(pde_op.kernel,
rho_sym,
k=sym.var("k"),
qbx_forced_limit=None)),
sym.d_dz(
3,
sym.S(pde_op.kernel,
rho_sym,
k=sym.var("k"),
qbx_forced_limit=None)),
]))(queue, jt=jt, rho=rho, k=k)
except QBXTargetAssociationFailedException as e:
fplot.write_vtk_file(
"failed-targets.vts",
[("failed_targets", e.failed_target_flags.get(queue))])
raise
fld_in_vol = sym.make_obj_array([fiv.get() for fiv in fld_in_vol])
#fplot.show_scalar_in_mayavi(fld_in_vol.real, max_val=5)
fplot.write_vtk_file("potential.vts", [
("potential", fld_in_vol[0]),
("grad", fld_in_vol[1:]),
])
def main():
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)
target_order = 16
qbx_order = 3
nelements = 60
mode_nr = 0
k = 0
if k:
kernel = HelmholtzKernel(2)
else:
kernel = LaplaceKernel(2)
mesh = make_curve_mesh(
#lambda t: ellipse(1, t),
starfish,
np.linspace(0, 1, nelements + 1),
target_order)
from pytential.qbx import QBXLayerPotentialSource
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import \
InterpolatoryQuadratureSimplexGroupFactory
pre_density_discr = Discretization(
actx, mesh, InterpolatoryQuadratureSimplexGroupFactory(target_order))
unaccel_qbx = QBXLayerPotentialSource(
pre_density_discr,
fine_order=2 * target_order,
qbx_order=qbx_order,
fmm_order=False,
target_association_tolerance=.05,
)
from pytential.target import PointsTarget
fplot = FieldPlotter(np.zeros(2), extent=5, npoints=600)
from pytential import GeometryCollection
places = GeometryCollection({
"unaccel_qbx": unaccel_qbx,
"qbx": unaccel_qbx.copy(fmm_order=10),
"targets": PointsTarget(fplot.points)
})
density_discr = places.get_discretization("unaccel_qbx")
nodes = thaw(actx, density_discr.nodes())
angle = actx.np.arctan2(nodes[1], nodes[0])
from pytential import bind, sym
if k:
kernel_kwargs = {"k": sym.var("k")}
else:
kernel_kwargs = {}
def get_op():
kwargs = dict(qbx_forced_limit=None)
kwargs.update(kernel_kwargs)
# return sym.d_dx(2, sym.S(kernel, sym.var("sigma"), **kwargs))
# return sym.D(kernel, sym.var("sigma"), **kwargs)
return sym.S(kernel, sym.var("sigma"), **kwargs)
op = get_op()
sigma = actx.np.cos(mode_nr * angle)
if isinstance(kernel, HelmholtzKernel):
for i, elem in np.ndenumerate(sigma):
sigma[i] = elem.astype(np.complex128)
fld_in_vol = bind(places, op,
auto_where=("unaccel_qbx", "targets"))(actx,
sigma=sigma,
k=k).get()
fmm_fld_in_vol = bind(places, op,
auto_where=("qbx", "targets"))(actx,
sigma=sigma,
k=k).get()
err = fmm_fld_in_vol - fld_in_vol
try:
import matplotlib
except ImportError:
return
matplotlib.use("Agg")
im = fplot.show_scalar_in_matplotlib(np.log10(np.abs(err) + 1e-17))
from matplotlib.colors import Normalize
im.set_norm(Normalize(vmin=-12, vmax=0))
import matplotlib.pyplot as pt
from matplotlib.ticker import NullFormatter
pt.gca().xaxis.set_major_formatter(NullFormatter())
pt.gca().yaxis.set_major_formatter(NullFormatter())
cb = pt.colorbar(shrink=0.9)
cb.set_label(r"$\log_{10}(\mathrm{Error})$")
pt.savefig("fmm-error-order-%d.pdf" % qbx_order)
angle = cl.clmath.atan2(nodes[1], nodes[0])
from pytential import bind, sym
d = sym.Derivative()
#op = d.nabla[0] * d(sym.S(kernel, sym.var("sigma")))
#op = sym.D(kernel, sym.var("sigma"))
op = sym.S(kernel, sym.var("sigma"))
sigma = cl.clmath.cos(mode_nr*angle)
if isinstance(kernel, HelmholtzKernel):
sigma = sigma.astype(np.complex128)
bound_bdry_op = bind(qbx, op)
fplot = FieldPlotter(np.zeros(2), extent=5, npoints=600)
from pytential.target import PointsTarget
fld_in_vol = bind(
(slow_qbx, PointsTarget(fplot.points)),
op)(queue, sigma=sigma, k=k).get()
fmm_fld_in_vol = bind(
(qbx, PointsTarget(fplot.points)),
op)(queue, sigma=sigma, k=k).get()
err = fmm_fld_in_vol-fld_in_vol
im = fplot.show_scalar_in_matplotlib(np.log10(np.abs(err)))
from matplotlib.colors import Normalize
im.set_norm(Normalize(vmin=-6, vmax=0))
def main(mesh_name="torus", 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)
if mesh_name == "torus":
rout = 10
rin = 1
from meshmode.mesh.generation import generate_torus
base_mesh = generate_torus(
rout, rin, 40, 4,
mesh_order)
from meshmode.mesh.processing import affine_map, merge_disjoint_meshes
# nx = 1
# ny = 1
nz = 1
dz = 0
meshes = [
affine_map(
base_mesh,
A=np.diag([1, 1, 1]),
b=np.array([0, 0, iz*dz]))
for iz in range(nz)]
mesh = merge_disjoint_meshes(meshes, single_group=True)
if visualize:
from meshmode.mesh.visualization import draw_curve
draw_curve(mesh)
import matplotlib.pyplot as plt
plt.show()
else:
raise ValueError(f"unknown mesh name: {mesh_name}")
pre_density_discr = Discretization(
actx, mesh,
InterpolatoryQuadratureSimplexGroupFactory(bdry_quad_order))
from pytential.qbx import (
QBXLayerPotentialSource, QBXTargetAssociationFailedException)
qbx = QBXLayerPotentialSource(
pre_density_discr, fine_order=bdry_ovsmp_quad_order, qbx_order=qbx_order,
fmm_order=fmm_order,
)
from sumpy.visualization import FieldPlotter
fplot = FieldPlotter(np.zeros(3), extent=20, npoints=50)
targets = actx.from_numpy(fplot.points)
from pytential import GeometryCollection
places = GeometryCollection({
"qbx": qbx,
"qbx_target_assoc": qbx.copy(target_association_tolerance=0.2),
"targets": PointsTarget(targets)
}, auto_where="qbx")
density_discr = places.get_discretization("qbx")
# {{{ describe bvp
from sumpy.kernel import LaplaceKernel
kernel = LaplaceKernel(3)
sigma_sym = sym.var("sigma")
#sqrt_w = sym.sqrt_jac_q_weight(3)
sqrt_w = 1
inv_sqrt_w_sigma = sym.cse(sigma_sym/sqrt_w)
# -1 for interior Dirichlet
# +1 for exterior Dirichlet
loc_sign = +1
bdry_op_sym = (loc_sign*0.5*sigma_sym
+ sqrt_w*(
sym.S(kernel, inv_sqrt_w_sigma, qbx_forced_limit=+1)
+ sym.D(kernel, inv_sqrt_w_sigma, qbx_forced_limit="avg")
))
# }}}
bound_op = bind(places, bdry_op_sym)
# {{{ fix rhs and solve
from meshmode.dof_array import thaw, flatten, unflatten
nodes = thaw(actx, density_discr.nodes())
source = np.array([rout, 0, 0])
def u_incoming_func(x):
from pytools.obj_array import obj_array_vectorize
x = obj_array_vectorize(actx.to_numpy, flatten(x))
x = np.array(list(x))
# return 1/cl.clmath.sqrt( (x[0] - source[0])**2
# +(x[1] - source[1])**2
# +(x[2] - source[2])**2 )
return 1.0/la.norm(x - source[:, None], axis=0)
bc = unflatten(actx,
density_discr,
actx.from_numpy(u_incoming_func(nodes)))
bvp_rhs = bind(places, sqrt_w*sym.var("bc"))(actx, bc=bc)
from pytential.solve import gmres
gmres_result = gmres(
bound_op.scipy_op(actx, "sigma", dtype=np.float64),
bvp_rhs, tol=1e-14, progress=True,
stall_iterations=0,
hard_failure=True)
sigma = bind(places, sym.var("sigma")/sqrt_w)(
actx, sigma=gmres_result.solution)
# }}}
from meshmode.discretization.visualization import make_visualizer
bdry_vis = make_visualizer(actx, density_discr, 20)
bdry_vis.write_vtk_file("laplace.vtu", [
("sigma", sigma),
])
# {{{ postprocess/visualize
repr_kwargs = dict(
source="qbx_target_assoc",
target="targets",
qbx_forced_limit=None)
representation_sym = (
sym.S(kernel, inv_sqrt_w_sigma, **repr_kwargs)
+ sym.D(kernel, inv_sqrt_w_sigma, **repr_kwargs))
try:
fld_in_vol = actx.to_numpy(
bind(places, representation_sym)(actx, sigma=sigma))
except QBXTargetAssociationFailedException as e:
fplot.write_vtk_file("laplace-dirichlet-3d-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("laplace-dirichlet-3d-potential.vts", [
("potential", fld_in_vol),
])
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)])
def main():
import logging
logging.basicConfig(level=logging.WARNING) # INFO for more progress info
cl_ctx = cl.create_some_context()
queue = cl.CommandQueue(cl_ctx)
target_order = 16
qbx_order = 3
nelements = 60
mode_nr = 0
k = 0
if k:
kernel = HelmholtzKernel(2)
else:
kernel = LaplaceKernel(2)
#kernel = OneKernel()
mesh = make_curve_mesh(
#lambda t: ellipse(1, t),
starfish,
np.linspace(0, 1, nelements + 1),
target_order)
from pytential.qbx import QBXLayerPotentialSource
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import \
InterpolatoryQuadratureSimplexGroupFactory
pre_density_discr = Discretization(
cl_ctx, mesh, InterpolatoryQuadratureSimplexGroupFactory(target_order))
slow_qbx, _ = QBXLayerPotentialSource(
pre_density_discr,
fine_order=2 * target_order,
qbx_order=qbx_order,
fmm_order=False,
target_association_tolerance=.05).with_refinement()
qbx = slow_qbx.copy(fmm_order=10)
density_discr = slow_qbx.density_discr
nodes = density_discr.nodes().with_queue(queue)
angle = cl.clmath.atan2(nodes[1], nodes[0])
from pytential import bind, sym
#op = sym.d_dx(sym.S(kernel, sym.var("sigma")), qbx_forced_limit=None)
#op = sym.D(kernel, sym.var("sigma"), qbx_forced_limit=None)
op = sym.S(kernel, sym.var("sigma"), qbx_forced_limit=None)
sigma = cl.clmath.cos(mode_nr * angle)
if isinstance(kernel, HelmholtzKernel):
sigma = sigma.astype(np.complex128)
fplot = FieldPlotter(np.zeros(2), extent=5, npoints=600)
from pytential.target import PointsTarget
fld_in_vol = bind((slow_qbx, PointsTarget(fplot.points)), op)(queue,
sigma=sigma,
k=k).get()
fmm_fld_in_vol = bind((qbx, PointsTarget(fplot.points)), op)(queue,
sigma=sigma,
k=k).get()
err = fmm_fld_in_vol - fld_in_vol
import matplotlib
matplotlib.use('Agg')
im = fplot.show_scalar_in_matplotlib(np.log10(np.abs(err) + 1e-17))
from matplotlib.colors import Normalize
im.set_norm(Normalize(vmin=-12, vmax=0))
import matplotlib.pyplot as pt
from matplotlib.ticker import NullFormatter
pt.gca().xaxis.set_major_formatter(NullFormatter())
pt.gca().yaxis.set_major_formatter(NullFormatter())
cb = pt.colorbar(shrink=0.9)
cb.set_label(r"$\log_{10}(\mathdefault{Error})$")
pt.savefig("fmm-error-order-%d.pdf" % qbx_order)
def main():
import logging
logging.basicConfig(level=logging.WARNING) # INFO for more progress info
cl_ctx = cl.create_some_context()
queue = cl.CommandQueue(cl_ctx)
target_order = 16
qbx_order = 3
nelements = 60
mode_nr = 0
k = 0
if k:
kernel = HelmholtzKernel(2)
else:
kernel = LaplaceKernel(2)
#kernel = OneKernel()
mesh = make_curve_mesh(
#lambda t: ellipse(1, t),
starfish,
np.linspace(0, 1, nelements+1),
target_order)
from pytential.qbx import QBXLayerPotentialSource
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import \
InterpolatoryQuadratureSimplexGroupFactory
pre_density_discr = Discretization(
cl_ctx, mesh,
InterpolatoryQuadratureSimplexGroupFactory(target_order))
slow_qbx, _ = QBXLayerPotentialSource(
pre_density_discr, fine_order=2*target_order,
qbx_order=qbx_order, fmm_order=False,
target_association_tolerance=.05
).with_refinement()
qbx = slow_qbx.copy(fmm_order=10)
density_discr = slow_qbx.density_discr
nodes = density_discr.nodes().with_queue(queue)
angle = cl.clmath.atan2(nodes[1], nodes[0])
from pytential import bind, sym
#op = sym.d_dx(sym.S(kernel, sym.var("sigma")), qbx_forced_limit=None)
#op = sym.D(kernel, sym.var("sigma"), qbx_forced_limit=None)
op = sym.S(kernel, sym.var("sigma"), qbx_forced_limit=None)
sigma = cl.clmath.cos(mode_nr*angle)
if isinstance(kernel, HelmholtzKernel):
sigma = sigma.astype(np.complex128)
fplot = FieldPlotter(np.zeros(2), extent=5, npoints=600)
from pytential.target import PointsTarget
fld_in_vol = bind(
(slow_qbx, PointsTarget(fplot.points)),
op)(queue, sigma=sigma, k=k).get()
fmm_fld_in_vol = bind(
(qbx, PointsTarget(fplot.points)),
op)(queue, sigma=sigma, k=k).get()
err = fmm_fld_in_vol-fld_in_vol
import matplotlib
matplotlib.use('Agg')
im = fplot.show_scalar_in_matplotlib(np.log10(np.abs(err) + 1e-17))
from matplotlib.colors import Normalize
im.set_norm(Normalize(vmin=-12, vmax=0))
import matplotlib.pyplot as pt
from matplotlib.ticker import NullFormatter
pt.gca().xaxis.set_major_formatter(NullFormatter())
pt.gca().yaxis.set_major_formatter(NullFormatter())
cb = pt.colorbar(shrink=0.9)
cb.set_label(r"$\log_{10}(\mathdefault{Error})$")
pt.savefig("fmm-error-order-%d.pdf" % qbx_order)
def main():
import logging
logging.basicConfig(level=logging.INFO)
cl_ctx = cl.create_some_context()
queue = cl.CommandQueue(cl_ctx)
from meshmode.mesh.generation import ellipse, make_curve_mesh
from functools import partial
mesh = make_curve_mesh(
partial(ellipse, 3),
np.linspace(0, 1, nelements+1),
mesh_order)
density_discr = Discretization(
cl_ctx, mesh,
InterpolatoryQuadratureSimplexGroupFactory(bdry_quad_order))
from pytential.qbx import QBXLayerPotentialSource
qbx = QBXLayerPotentialSource(
density_discr, fine_order=bdry_ovsmp_quad_order, qbx_order=qbx_order,
fmm_order=fmm_order
)
# {{{ describe bvp
from sumpy.kernel import HelmholtzKernel
kernel = HelmholtzKernel(2)
cse = sym.cse
sigma_sym = sym.var("sigma")
sqrt_w = sym.sqrt_jac_q_weight()
inv_sqrt_w_sigma = cse(sigma_sym/sqrt_w)
# Brakhage-Werner parameter
alpha = 1j
# -1 for interior Dirichlet
# +1 for exterior Dirichlet
loc_sign = -1
bdry_op_sym = (-loc_sign*0.5*sigma_sym
+ sqrt_w*(
alpha*sym.S(kernel, inv_sqrt_w_sigma, k=sym.var("k"))
- sym.D(kernel, inv_sqrt_w_sigma, k=sym.var("k"))
))
# }}}
bound_op = bind(qbx, bdry_op_sym)
# {{{ fix rhs and solve
mode_nr = 3
nodes = density_discr.nodes().with_queue(queue)
angle = cl.clmath.atan2(nodes[1], nodes[0])
bc = cl.clmath.cos(mode_nr*angle)
bvp_rhs = bind(qbx, sqrt_w*sym.var("bc"))(queue, bc=bc)
from pytential.solve import gmres
gmres_result = gmres(
bound_op.scipy_op(queue, "sigma", k=k),
bvp_rhs, tol=1e-14, progress=True,
stall_iterations=0,
hard_failure=True)
# }}}
# {{{ postprocess/visualize
sigma = gmres_result.solution
representation_sym = (
alpha*sym.S(kernel, inv_sqrt_w_sigma, k=sym.var("k"))
- sym.D(kernel, inv_sqrt_w_sigma, k=sym.var("k")))
from sumpy.visualization import FieldPlotter
fplot = FieldPlotter(np.zeros(2), extent=5, npoints=1500)
from pytential.target import PointsTarget
fld_in_vol = bind(
(qbx, PointsTarget(fplot.points)),
representation_sym)(queue, sigma=sigma, k=k).get()
#fplot.show_scalar_in_mayavi(fld_in_vol.real, max_val=5)
fplot.write_vtk_file(
"potential.vts",
[
("potential", fld_in_vol)
]
)
def main():
import logging
logging.basicConfig(level=logging.INFO)
cl_ctx = cl.create_some_context()
queue = cl.CommandQueue(cl_ctx)
from meshmode.mesh.generation import ellipse, make_curve_mesh
from functools import partial
mesh = make_curve_mesh(
partial(ellipse, 2),
np.linspace(0, 1, nelements+1),
mesh_order)
pre_density_discr = Discretization(
cl_ctx, mesh,
InterpolatoryQuadratureSimplexGroupFactory(bdry_quad_order))
from pytential.qbx import (
QBXLayerPotentialSource, QBXTargetAssociationFailedException)
qbx, _ = QBXLayerPotentialSource(
pre_density_discr, fine_order=bdry_ovsmp_quad_order, qbx_order=qbx_order,
fmm_order=fmm_order,
expansion_disks_in_tree_have_extent=True,
).with_refinement()
density_discr = qbx.density_discr
from pytential.symbolic.pde.cahn_hilliard import CahnHilliardOperator
chop = CahnHilliardOperator(
# FIXME: Constants?
lambda1=1.5,
lambda2=1.25,
c=1)
unk = chop.make_unknown("sigma")
bound_op = bind(qbx, chop.operator(unk))
# {{{ fix rhs and solve
nodes = density_discr.nodes().with_queue(queue)
def g(xvec):
x, y = xvec
return cl.clmath.atan2(y, x)
bc = sym.make_obj_array([
# FIXME: Realistic BC
g(nodes),
-g(nodes),
])
from pytential.solve import gmres
gmres_result = gmres(
bound_op.scipy_op(queue, "sigma", dtype=np.complex128),
bc, tol=1e-8, progress=True,
stall_iterations=0,
hard_failure=True)
# }}}
# {{{ postprocess/visualize
sigma = gmres_result.solution
from sumpy.visualization import FieldPlotter
fplot = FieldPlotter(np.zeros(2), extent=5, npoints=500)
targets = cl.array.to_device(queue, fplot.points)
qbx_stick_out = qbx.copy(target_association_tolerance=0.05)
indicator_qbx = qbx_stick_out.copy(qbx_order=2)
from sumpy.kernel import LaplaceKernel
ones_density = density_discr.zeros(queue)
ones_density.fill(1)
indicator = bind(
(indicator_qbx, PointsTarget(targets)),
sym.D(LaplaceKernel(2), sym.var("sigma")))(
queue, sigma=ones_density).get()
try:
fld_in_vol = bind(
(qbx_stick_out, PointsTarget(targets)),
chop.representation(unk))(queue, sigma=sigma).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.vts",
[
("potential", fld_in_vol),
("indicator", indicator),
]
)
def main():
import logging
logging.basicConfig(level=logging.WARNING) # INFO for more progress info
cl_ctx = cl.create_some_context()
queue = cl.CommandQueue(cl_ctx)
from meshmode.mesh.generation import generate_torus
rout = 10
rin = 1
if 1:
base_mesh = generate_torus(
rout, rin, 40, 4,
mesh_order)
from meshmode.mesh.processing import affine_map, merge_disjoint_meshes
# nx = 1
# ny = 1
nz = 1
dz = 0
meshes = [
affine_map(
base_mesh,
A=np.diag([1, 1, 1]),
b=np.array([0, 0, iz*dz]))
for iz in range(nz)]
mesh = merge_disjoint_meshes(meshes, single_group=True)
if 0:
from meshmode.mesh.visualization import draw_curve
draw_curve(mesh)
import matplotlib.pyplot as plt
plt.show()
pre_density_discr = Discretization(
cl_ctx, mesh,
InterpolatoryQuadratureSimplexGroupFactory(bdry_quad_order))
from pytential.qbx import (
QBXLayerPotentialSource, QBXTargetAssociationFailedException)
qbx, _ = QBXLayerPotentialSource(
pre_density_discr, fine_order=bdry_ovsmp_quad_order, qbx_order=qbx_order,
fmm_order=fmm_order
).with_refinement()
density_discr = qbx.density_discr
# {{{ describe bvp
from sumpy.kernel import LaplaceKernel
kernel = LaplaceKernel(3)
cse = sym.cse
sigma_sym = sym.var("sigma")
#sqrt_w = sym.sqrt_jac_q_weight(3)
sqrt_w = 1
inv_sqrt_w_sigma = cse(sigma_sym/sqrt_w)
# -1 for interior Dirichlet
# +1 for exterior Dirichlet
loc_sign = +1
bdry_op_sym = (loc_sign*0.5*sigma_sym
+ sqrt_w*(
sym.S(kernel, inv_sqrt_w_sigma)
+ sym.D(kernel, inv_sqrt_w_sigma)
))
# }}}
bound_op = bind(qbx, bdry_op_sym)
# {{{ fix rhs and solve
nodes = density_discr.nodes().with_queue(queue)
source = np.array([rout, 0, 0])
def u_incoming_func(x):
# return 1/cl.clmath.sqrt( (x[0] - source[0])**2
# +(x[1] - source[1])**2
# +(x[2] - source[2])**2 )
return 1.0/la.norm(x.get()-source[:, None], axis=0)
bc = cl.array.to_device(queue, u_incoming_func(nodes))
bvp_rhs = bind(qbx, sqrt_w*sym.var("bc"))(queue, bc=bc)
from pytential.solve import gmres
gmres_result = gmres(
bound_op.scipy_op(queue, "sigma", dtype=np.float64),
bvp_rhs, tol=1e-14, progress=True,
stall_iterations=0,
hard_failure=True)
sigma = bind(qbx, sym.var("sigma")/sqrt_w)(queue, sigma=gmres_result.solution)
# }}}
from meshmode.discretization.visualization import make_visualizer
bdry_vis = make_visualizer(queue, density_discr, 20)
bdry_vis.write_vtk_file("laplace.vtu", [
("sigma", sigma),
])
# {{{ postprocess/visualize
repr_kwargs = dict(qbx_forced_limit=None)
representation_sym = (
sym.S(kernel, inv_sqrt_w_sigma, **repr_kwargs)
+ sym.D(kernel, inv_sqrt_w_sigma, **repr_kwargs))
from sumpy.visualization import FieldPlotter
fplot = FieldPlotter(np.zeros(3), extent=20, npoints=50)
targets = cl.array.to_device(queue, fplot.points)
qbx_stick_out = qbx.copy(target_stick_out_factor=0.2)
try:
fld_in_vol = bind(
(qbx_stick_out, PointsTarget(targets)),
representation_sym)(queue, sigma=sigma).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-laplace-3d.vts",
[
("potential", fld_in_vol),
]
)
def main(curve_fn=starfish, visualize=True):
import logging
logging.basicConfig(level=logging.WARNING) # INFO for more progress info
import pyopencl as cl
cl_ctx = cl.create_some_context()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue, force_device_scalars=True)
from meshmode.mesh.generation import make_curve_mesh
mesh = make_curve_mesh(
curve_fn,
np.linspace(0, 1, nelements+1),
target_order)
from pytential.qbx import QBXLayerPotentialSource
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import \
InterpolatoryQuadratureSimplexGroupFactory
pre_density_discr = Discretization(
actx, mesh, InterpolatoryQuadratureSimplexGroupFactory(target_order))
qbx = QBXLayerPotentialSource(
pre_density_discr, 4*target_order, qbx_order,
fmm_order=qbx_order+3,
target_association_tolerance=0.005,
#fmm_backend="fmmlib",
)
from pytential.target import PointsTarget
fplot = FieldPlotter(np.zeros(2), extent=5, npoints=1000)
targets_dev = actx.from_numpy(fplot.points)
from pytential import GeometryCollection
places = GeometryCollection({
"qbx": qbx,
"targets": PointsTarget(targets_dev),
}, auto_where="qbx")
density_discr = places.get_discretization("qbx")
nodes = thaw(density_discr.nodes(), actx)
angle = actx.np.arctan2(nodes[1], nodes[0])
if k:
kernel = HelmholtzKernel(2)
kernel_kwargs = {"k": sym.var("k")}
else:
kernel = LaplaceKernel(2)
kernel_kwargs = {}
def op(**kwargs):
kwargs.update(kernel_kwargs)
#op = sym.d_dx(sym.S(kernel, sym.var("sigma"), **kwargs))
return sym.D(kernel, sym.var("sigma"), **kwargs)
#op = sym.S(kernel, sym.var("sigma"), qbx_forced_limit=None, **kwargs)
if 0:
from random import randrange
sigma = actx.zeros(density_discr.ndofs, angle.entry_dtype)
for _ in range(5):
sigma[randrange(len(sigma))] = 1
from arraycontext import unflatten
sigma = unflatten(angle, sigma, actx)
else:
sigma = actx.np.cos(mode_nr*angle)
if isinstance(kernel, HelmholtzKernel):
for i, elem in np.ndenumerate(sigma):
sigma[i] = elem.astype(np.complex128)
bound_bdry_op = bind(places, op())
if visualize:
fld_in_vol = actx.to_numpy(
bind(places, op(
source="qbx",
target="targets",
qbx_forced_limit=None))(actx, sigma=sigma, k=k))
if enable_mayavi:
fplot.show_scalar_in_mayavi(fld_in_vol.real, max_val=5)
else:
fplot.write_vtk_file("layerpot-potential.vts", [
("potential", fld_in_vol)
])
if 0:
apply_op = bound_bdry_op.scipy_op(actx, "sigma", np.float64, k=k)
from sumpy.tools import build_matrix
mat = build_matrix(apply_op)
import matplotlib.pyplot as pt
pt.imshow(mat)
pt.colorbar()
pt.show()
if enable_mayavi:
# {{{ plot boundary field
from arraycontext import flatten
fld_on_bdry = actx.to_numpy(
flatten(bound_bdry_op(actx, sigma=sigma, k=k), actx))
nodes_host = actx.to_numpy(
flatten(density_discr.nodes(), actx)
).reshape(density_discr.ambient_dim, -1)
mlab.points3d(nodes_host[0], nodes_host[1],
fld_on_bdry.real, scale_factor=0.03)
mlab.colorbar()
mlab.show()
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 main():
import logging
logging.basicConfig(level=logging.WARNING) # INFO for more progress info
cl_ctx = cl.create_some_context()
queue = cl.CommandQueue(cl_ctx)
from meshmode.mesh.generation import ( # noqa
make_curve_mesh, starfish, ellipse, drop)
mesh = make_curve_mesh(
#lambda t: ellipse(1, t),
starfish,
np.linspace(0, 1, nelements + 1),
target_order)
from pytential.qbx import QBXLayerPotentialSource
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import \
InterpolatoryQuadratureSimplexGroupFactory
pre_density_discr = Discretization(
cl_ctx, mesh, InterpolatoryQuadratureSimplexGroupFactory(target_order))
qbx, _ = QBXLayerPotentialSource(
pre_density_discr,
4 * target_order,
qbx_order,
fmm_order=qbx_order + 3,
target_association_tolerance=0.005).with_refinement()
density_discr = qbx.density_discr
nodes = density_discr.nodes().with_queue(queue)
angle = cl.clmath.atan2(nodes[1], nodes[0])
def op(**kwargs):
kwargs.update(kernel_kwargs)
#op = sym.d_dx(sym.S(kernel, sym.var("sigma"), **kwargs))
return sym.D(kernel, sym.var("sigma"), **kwargs)
#op = sym.S(kernel, sym.var("sigma"), qbx_forced_limit=None, **kwargs)
sigma = cl.clmath.cos(mode_nr * angle)
if 0:
sigma = 0 * angle
from random import randrange
for i in range(5):
sigma[randrange(len(sigma))] = 1
if isinstance(kernel, HelmholtzKernel):
sigma = sigma.astype(np.complex128)
bound_bdry_op = bind(qbx, op())
#mlab.figure(bgcolor=(1, 1, 1))
if 1:
fplot = FieldPlotter(np.zeros(2), extent=5, npoints=1000)
from pytential.target import PointsTarget
targets_dev = cl.array.to_device(queue, fplot.points)
fld_in_vol = bind((qbx, PointsTarget(targets_dev)),
op(qbx_forced_limit=None))(queue, sigma=sigma,
k=k).get()
if enable_mayavi:
fplot.show_scalar_in_mayavi(fld_in_vol.real, max_val=5)
else:
fplot.write_vtk_file("potential-2d.vts",
[("potential", fld_in_vol)])
if 0:
def apply_op(density):
return bound_bdry_op(queue,
sigma=cl.array.to_device(queue, density),
k=k).get()
from sumpy.tools import build_matrix
n = len(sigma)
mat = build_matrix(apply_op, dtype=np.float64, shape=(n, n))
import matplotlib.pyplot as pt
pt.imshow(mat)
pt.colorbar()
pt.show()
if enable_mayavi:
# {{{ plot boundary field
fld_on_bdry = bound_bdry_op(queue, sigma=sigma, k=k).get()
nodes_host = density_discr.nodes().get(queue=queue)
mlab.points3d(nodes_host[0],
nodes_host[1],
fld_on_bdry.real,
scale_factor=0.03)
# }}}
if enable_mayavi:
mlab.colorbar()
mlab.show()
def main():
import logging
logging.basicConfig(level=logging.WARNING) # INFO for more progress info
cl_ctx = cl.create_some_context()
queue = cl.CommandQueue(cl_ctx)
from meshmode.mesh.generation import ( # noqa
make_curve_mesh, starfish, ellipse, drop)
mesh = make_curve_mesh(
#lambda t: ellipse(1, t),
starfish,
np.linspace(0, 1, nelements+1),
target_order)
from pytential.qbx import QBXLayerPotentialSource
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import \
InterpolatoryQuadratureSimplexGroupFactory
pre_density_discr = Discretization(
cl_ctx, mesh, InterpolatoryQuadratureSimplexGroupFactory(target_order))
qbx, _ = QBXLayerPotentialSource(pre_density_discr, 4*target_order, qbx_order,
fmm_order=qbx_order+3,
target_association_tolerance=0.005).with_refinement()
density_discr = qbx.density_discr
nodes = density_discr.nodes().with_queue(queue)
angle = cl.clmath.atan2(nodes[1], nodes[0])
def op(**kwargs):
kwargs.update(kernel_kwargs)
#op = sym.d_dx(sym.S(kernel, sym.var("sigma"), **kwargs))
return sym.D(kernel, sym.var("sigma"), **kwargs)
#op = sym.S(kernel, sym.var("sigma"), qbx_forced_limit=None, **kwargs)
sigma = cl.clmath.cos(mode_nr*angle)
if 0:
sigma = 0*angle
from random import randrange
for i in range(5):
sigma[randrange(len(sigma))] = 1
if isinstance(kernel, HelmholtzKernel):
sigma = sigma.astype(np.complex128)
bound_bdry_op = bind(qbx, op())
#mlab.figure(bgcolor=(1, 1, 1))
if 1:
fplot = FieldPlotter(np.zeros(2), extent=5, npoints=1000)
from pytential.target import PointsTarget
targets_dev = cl.array.to_device(queue, fplot.points)
fld_in_vol = bind(
(qbx, PointsTarget(targets_dev)),
op(qbx_forced_limit=None))(queue, sigma=sigma, k=k).get()
if enable_mayavi:
fplot.show_scalar_in_mayavi(fld_in_vol.real, max_val=5)
else:
fplot.write_vtk_file(
"potential-2d.vts",
[
("potential", fld_in_vol)
]
)
if 0:
def apply_op(density):
return bound_bdry_op(
queue, sigma=cl.array.to_device(queue, density), k=k).get()
from sumpy.tools import build_matrix
n = len(sigma)
mat = build_matrix(apply_op, dtype=np.float64, shape=(n, n))
import matplotlib.pyplot as pt
pt.imshow(mat)
pt.colorbar()
pt.show()
if enable_mayavi:
# {{{ plot boundary field
fld_on_bdry = bound_bdry_op(queue, sigma=sigma, k=k).get()
nodes_host = density_discr.nodes().get(queue=queue)
mlab.points3d(nodes_host[0], nodes_host[1],
fld_on_bdry.real, scale_factor=0.03)
# }}}
if enable_mayavi:
mlab.colorbar()
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
def test_off_surface_eval(ctx_getter, use_fmm, do_plot=False):
logging.basicConfig(level=logging.INFO)
cl_ctx = ctx_getter()
queue = cl.CommandQueue(cl_ctx)
# prevent cache 'splosion
from sympy.core.cache import clear_cache
clear_cache()
nelements = 30
target_order = 8
qbx_order = 3
if use_fmm:
fmm_order = qbx_order
else:
fmm_order = False
mesh = make_curve_mesh(partial(ellipse, 3),
np.linspace(0, 1, nelements+1),
target_order)
from pytential.qbx import QBXLayerPotentialSource
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import \
InterpolatoryQuadratureSimplexGroupFactory
pre_density_discr = Discretization(
cl_ctx, mesh, InterpolatoryQuadratureSimplexGroupFactory(target_order))
qbx, _ = QBXLayerPotentialSource(
pre_density_discr,
4*target_order,
qbx_order,
fmm_order=fmm_order,
).with_refinement()
density_discr = qbx.density_discr
from sumpy.kernel import LaplaceKernel
op = sym.D(LaplaceKernel(2), sym.var("sigma"), qbx_forced_limit=-2)
sigma = density_discr.zeros(queue) + 1
fplot = FieldPlotter(np.zeros(2), extent=0.54, npoints=30)
from pytential.target import PointsTarget
fld_in_vol = bind(
(qbx, PointsTarget(fplot.points)),
op)(queue, sigma=sigma)
err = cl.clmath.fabs(fld_in_vol - (-1))
linf_err = cl.array.max(err).get()
print("l_inf error:", linf_err)
if do_plot:
fplot.show_scalar_in_matplotlib(fld_in_vol.get())
import matplotlib.pyplot as pt
pt.colorbar()
pt.show()
assert linf_err < 1e-3
#op = sym.S(kernel, sym.var("sigma"))
sigma = cl.clmath.cos(mode_nr*angle)
if 0:
sigma = 0*angle
from random import randrange
for i in range(5):
sigma[randrange(len(sigma))] = 1
if isinstance(kernel, HelmholtzKernel):
sigma = sigma.astype(np.complex128)
bound_bdry_op = bind(qbx, op)
#mlab.figure(bgcolor=(1, 1, 1))
if 1:
fplot = FieldPlotter(np.zeros(2), extent=5, npoints=1500)
from pytential.target import PointsTarget
fld_in_vol = bind(
(qbx, PointsTarget(fplot.points)),
op)(queue, sigma=sigma, k=k).get()
#fplot.show_scalar_in_mayavi(fld_in_vol.real, max_val=5)
fplot.write_vtk_file(
"potential.vts",
[
("potential", fld_in_vol)
]
)
if 0:
def apply_op(density):
def main():
import logging
logging.basicConfig(level=logging.WARNING) # INFO for more progress info
cl_ctx = cl.create_some_context()
queue = cl.CommandQueue(cl_ctx)
from meshmode.mesh.generation import ellipse, make_curve_mesh
from functools import partial
if 0:
mesh = make_curve_mesh(
partial(ellipse, 1),
np.linspace(0, 1, nelements+1),
mesh_order)
else:
base_mesh = make_curve_mesh(
partial(ellipse, 1),
np.linspace(0, 1, nelements+1),
mesh_order)
from meshmode.mesh.processing import affine_map, merge_disjoint_meshes
nx = 2
ny = 2
dx = 2 / nx
meshes = [
affine_map(
base_mesh,
A=np.diag([dx*0.25, dx*0.25]),
b=np.array([dx*(ix-nx/2), dx*(iy-ny/2)]))
for ix in range(nx)
for iy in range(ny)]
mesh = merge_disjoint_meshes(meshes, single_group=True)
if 0:
from meshmode.mesh.visualization import draw_curve
draw_curve(mesh)
import matplotlib.pyplot as plt
plt.show()
pre_density_discr = Discretization(
cl_ctx, mesh,
InterpolatoryQuadratureSimplexGroupFactory(bdry_quad_order))
from pytential.qbx import (
QBXLayerPotentialSource, QBXTargetAssociationFailedException)
qbx, _ = QBXLayerPotentialSource(
pre_density_discr, fine_order=bdry_ovsmp_quad_order, qbx_order=qbx_order,
fmm_order=fmm_order
).with_refinement()
density_discr = qbx.density_discr
# {{{ describe bvp
from sumpy.kernel import LaplaceKernel, 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"),
qbx_forced_limit=+1)
- sym.D(kernel, inv_sqrt_w_sigma, k=sym.var("k"),
qbx_forced_limit="avg")
))
# }}}
bound_op = bind(qbx, bdry_op_sym)
# {{{ fix rhs and solve
nodes = density_discr.nodes().with_queue(queue)
k_vec = np.array([2, 1])
k_vec = k * k_vec / la.norm(k_vec, 2)
def u_incoming_func(x):
return cl.clmath.exp(
1j * (x[0] * k_vec[0] + x[1] * k_vec[1]))
bc = -u_incoming_func(nodes)
bvp_rhs = bind(qbx, sqrt_w*sym.var("bc"))(queue, bc=bc)
from pytential.solve import gmres
gmres_result = gmres(
bound_op.scipy_op(queue, "sigma", dtype=np.complex128, k=k),
bvp_rhs, tol=1e-8, progress=True,
stall_iterations=0,
hard_failure=True)
# }}}
# {{{ postprocess/visualize
sigma = gmres_result.solution
repr_kwargs = dict(k=sym.var("k"), qbx_forced_limit=None)
representation_sym = (
alpha*sym.S(kernel, inv_sqrt_w_sigma, **repr_kwargs)
- sym.D(kernel, inv_sqrt_w_sigma, **repr_kwargs))
from sumpy.visualization import FieldPlotter
fplot = FieldPlotter(np.zeros(2), extent=5, npoints=500)
targets = cl.array.to_device(queue, fplot.points)
u_incoming = u_incoming_func(targets)
qbx_stick_out = qbx.copy(target_association_tolerance=0.05)
ones_density = density_discr.zeros(queue)
ones_density.fill(1)
indicator = bind(
(qbx_stick_out, PointsTarget(targets)),
sym.D(LaplaceKernel(2), sym.var("sigma"), qbx_forced_limit=None))(
queue, sigma=ones_density).get()
try:
fld_in_vol = bind(
(qbx_stick_out, PointsTarget(targets)),
representation_sym)(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-helm.vts",
[
("potential", fld_in_vol),
("indicator", indicator),
("u_incoming", u_incoming.get()),
]
)
def run_exterior_stokes_2d(ctx_factory,
nelements,
mesh_order=4,
target_order=4,
qbx_order=4,
fmm_order=10,
mu=1,
circle_rad=1.5,
do_plot=False):
# This program tests an exterior Stokes flow in 2D using the
# compound representation given in Hsiao & Kress,
# ``On an integral equation for the two-dimensional exterior Stokes problem,''
# Applied Numerical Mathematics 1 (1985).
logging.basicConfig(level=logging.INFO)
cl_ctx = cl.create_some_context()
queue = cl.CommandQueue(cl_ctx)
ovsmp_target_order = 4 * target_order
from meshmode.mesh.generation import ( # noqa
make_curve_mesh, starfish, ellipse, drop)
mesh = make_curve_mesh(lambda t: circle_rad * ellipse(1, t),
np.linspace(0, 1, nelements + 1), target_order)
coarse_density_discr = Discretization(
cl_ctx, mesh, InterpolatoryQuadratureSimplexGroupFactory(target_order))
from pytential.qbx import QBXLayerPotentialSource
target_association_tolerance = 0.05
qbx, _ = QBXLayerPotentialSource(
coarse_density_discr,
fine_order=ovsmp_target_order,
qbx_order=qbx_order,
fmm_order=fmm_order,
target_association_tolerance=target_association_tolerance,
_expansions_in_tree_have_extent=True,
).with_refinement()
density_discr = qbx.density_discr
normal = bind(density_discr, sym.normal(2).as_vector())(queue)
path_length = bind(density_discr, sym.integral(2, 1, 1))(queue)
# {{{ describe bvp
from pytential.symbolic.stokes import StressletWrapper, StokesletWrapper
dim = 2
cse = sym.cse
sigma_sym = sym.make_sym_vector("sigma", dim)
meanless_sigma_sym = cse(sigma_sym - sym.mean(2, 1, sigma_sym))
int_sigma = sym.Ones() * sym.integral(2, 1, sigma_sym)
nvec_sym = sym.make_sym_vector("normal", dim)
mu_sym = sym.var("mu")
# -1 for interior Dirichlet
# +1 for exterior Dirichlet
loc_sign = 1
stresslet_obj = StressletWrapper(dim=2)
stokeslet_obj = StokesletWrapper(dim=2)
bdry_op_sym = (-loc_sign * 0.5 * sigma_sym - stresslet_obj.apply(
sigma_sym, nvec_sym, mu_sym, qbx_forced_limit='avg') +
stokeslet_obj.apply(
meanless_sigma_sym, mu_sym, qbx_forced_limit='avg') -
(0.5 / np.pi) * int_sigma)
# }}}
bound_op = bind(qbx, bdry_op_sym)
# {{{ fix rhs and solve
def fund_soln(x, y, loc, strength):
#with direction (1,0) for point source
r = cl.clmath.sqrt((x - loc[0])**2 + (y - loc[1])**2)
scaling = strength / (4 * np.pi * mu)
xcomp = (-cl.clmath.log(r) + (x - loc[0])**2 / r**2) * scaling
ycomp = ((x - loc[0]) * (y - loc[1]) / r**2) * scaling
return [xcomp, ycomp]
def rotlet_soln(x, y, loc):
r = cl.clmath.sqrt((x - loc[0])**2 + (y - loc[1])**2)
xcomp = -(y - loc[1]) / r**2
ycomp = (x - loc[0]) / r**2
return [xcomp, ycomp]
def fund_and_rot_soln(x, y, loc, strength):
#with direction (1,0) for point source
r = cl.clmath.sqrt((x - loc[0])**2 + (y - loc[1])**2)
scaling = strength / (4 * np.pi * mu)
xcomp = ((-cl.clmath.log(r) + (x - loc[0])**2 / r**2) * scaling -
(y - loc[1]) * strength * 0.125 / r**2 + 3.3)
ycomp = (((x - loc[0]) * (y - loc[1]) / r**2) * scaling +
(x - loc[0]) * strength * 0.125 / r**2 + 1.5)
return [xcomp, ycomp]
nodes = density_discr.nodes().with_queue(queue)
fund_soln_loc = np.array([0.5, -0.2])
strength = 100.
bc = fund_and_rot_soln(nodes[0], nodes[1], fund_soln_loc, strength)
omega_sym = sym.make_sym_vector("omega", dim)
u_A_sym_bdry = stokeslet_obj.apply( # noqa: N806
omega_sym, mu_sym, qbx_forced_limit=1)
omega = [
cl.array.to_device(queue,
(strength / path_length) * np.ones(len(nodes[0]))),
cl.array.to_device(queue, np.zeros(len(nodes[0])))
]
bvp_rhs = bind(qbx,
sym.make_sym_vector("bc", dim) + u_A_sym_bdry)(queue,
bc=bc,
mu=mu,
omega=omega)
gmres_result = gmres(bound_op.scipy_op(queue,
"sigma",
np.float64,
mu=mu,
normal=normal),
bvp_rhs,
x0=bvp_rhs,
tol=1e-9,
progress=True,
stall_iterations=0,
hard_failure=True)
# }}}
# {{{ postprocess/visualize
sigma = gmres_result.solution
sigma_int_val_sym = sym.make_sym_vector("sigma_int_val", 2)
int_val = bind(qbx, sym.integral(2, 1, sigma_sym))(queue, sigma=sigma)
int_val = -int_val / (2 * np.pi)
print("int_val = ", int_val)
u_A_sym_vol = stokeslet_obj.apply( # noqa: N806
omega_sym, mu_sym, qbx_forced_limit=2)
representation_sym = (
-stresslet_obj.apply(sigma_sym, nvec_sym, mu_sym, qbx_forced_limit=2) +
stokeslet_obj.apply(meanless_sigma_sym, mu_sym, qbx_forced_limit=2) -
u_A_sym_vol + sigma_int_val_sym)
nsamp = 30
eval_points_1d = np.linspace(-3., 3., nsamp)
eval_points = np.zeros((2, len(eval_points_1d)**2))
eval_points[0, :] = np.tile(eval_points_1d, len(eval_points_1d))
eval_points[1, :] = np.repeat(eval_points_1d, len(eval_points_1d))
def circle_mask(test_points, radius):
return (test_points[0, :]**2 + test_points[1, :]**2 > radius**2)
def outside_circle(test_points, radius):
mask = circle_mask(test_points, radius)
return np.array([row[mask] for row in test_points])
eval_points = outside_circle(eval_points, radius=circle_rad)
from pytential.target import PointsTarget
vel = bind((qbx, PointsTarget(eval_points)),
representation_sym)(queue,
sigma=sigma,
mu=mu,
normal=normal,
sigma_int_val=int_val,
omega=omega)
print("@@@@@@@@")
fplot = FieldPlotter(np.zeros(2), extent=6, npoints=100)
plot_pts = outside_circle(fplot.points, radius=circle_rad)
plot_vel = bind((qbx, PointsTarget(plot_pts)),
representation_sym)(queue,
sigma=sigma,
mu=mu,
normal=normal,
sigma_int_val=int_val,
omega=omega)
def get_obj_array(obj_array):
return make_obj_array([ary.get() for ary in obj_array])
exact_soln = fund_and_rot_soln(cl.array.to_device(queue, eval_points[0]),
cl.array.to_device(queue, eval_points[1]),
fund_soln_loc, strength)
vel = get_obj_array(vel)
err = vel - get_obj_array(exact_soln)
# FIXME: Pointwise relative errors don't make sense!
rel_err = err / (get_obj_array(exact_soln))
if 0:
print("@@@@@@@@")
print("vel[0], err[0], rel_err[0] ***** vel[1], err[1], rel_err[1]: ")
for i in range(len(vel[0])):
print("%15.8e, %15.8e, %15.8e ***** %15.8e, %15.8e, %15.8e\n" %
(vel[0][i], err[0][i], rel_err[0][i], vel[1][i], err[1][i],
rel_err[1][i]))
print("@@@@@@@@")
l2_err = np.sqrt((6. / (nsamp - 1))**2 * np.sum(err[0] * err[0]) +
(6. / (nsamp - 1))**2 * np.sum(err[1] * err[1]))
l2_rel_err = np.sqrt((6. /
(nsamp - 1))**2 * np.sum(rel_err[0] * rel_err[0]) +
(6. /
(nsamp - 1))**2 * np.sum(rel_err[1] * rel_err[1]))
print("L2 error estimate: ", l2_err)
print("L2 rel error estimate: ", l2_rel_err)
print("max error at sampled points: ", max(abs(err[0])), max(abs(err[1])))
print("max rel error at sampled points: ", max(abs(rel_err[0])),
max(abs(rel_err[1])))
if do_plot:
import matplotlib
matplotlib.use("Agg")
import matplotlib.pyplot as plt
full_pot = np.zeros_like(fplot.points) * float("nan")
mask = circle_mask(fplot.points, radius=circle_rad)
for i, vel in enumerate(plot_vel):
full_pot[i, mask] = vel.get()
plt.quiver(fplot.points[0],
fplot.points[1],
full_pot[0],
full_pot[1],
linewidth=0.1)
plt.savefig("exterior-2d-field.pdf")
# }}}
h_max = bind(qbx, sym.h_max(qbx.ambient_dim))(queue)
return h_max, l2_err
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)
]
)
def test_off_surface_eval_vs_direct(ctx_factory, do_plot=False):
logging.basicConfig(level=logging.INFO)
cl_ctx = ctx_factory()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue)
# prevent cache 'splosion
from sympy.core.cache import clear_cache
clear_cache()
nelements = 300
target_order = 8
qbx_order = 3
mesh = make_curve_mesh(WobblyCircle.random(8, seed=30),
np.linspace(0, 1, nelements+1),
target_order)
from pytential.qbx import QBXLayerPotentialSource
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import \
InterpolatoryQuadratureSimplexGroupFactory
pre_density_discr = Discretization(
actx, mesh, InterpolatoryQuadratureSimplexGroupFactory(target_order))
direct_qbx = QBXLayerPotentialSource(
pre_density_discr, 4*target_order, qbx_order,
fmm_order=False,
target_association_tolerance=0.05,
)
fmm_qbx = QBXLayerPotentialSource(
pre_density_discr, 4*target_order, qbx_order,
fmm_order=qbx_order + 3,
_expansions_in_tree_have_extent=True,
target_association_tolerance=0.05,
)
fplot = FieldPlotter(np.zeros(2), extent=5, npoints=500)
from pytential.target import PointsTarget
ptarget = PointsTarget(fplot.points)
from sumpy.kernel import LaplaceKernel
places = GeometryCollection({
"direct_qbx": direct_qbx,
"fmm_qbx": fmm_qbx,
"target": ptarget})
direct_density_discr = places.get_discretization("direct_qbx")
fmm_density_discr = places.get_discretization("fmm_qbx")
from pytential.qbx import QBXTargetAssociationFailedException
op = sym.D(LaplaceKernel(2), sym.var("sigma"), qbx_forced_limit=None)
try:
direct_sigma = direct_density_discr.zeros(actx) + 1
direct_fld_in_vol = bind(places, op,
auto_where=("direct_qbx", "target"))(
actx, sigma=direct_sigma)
except QBXTargetAssociationFailedException as e:
fplot.show_scalar_in_matplotlib(
actx.to_numpy(actx.thaw(e.failed_target_flags)))
import matplotlib.pyplot as pt
pt.show()
raise
fmm_sigma = fmm_density_discr.zeros(actx) + 1
fmm_fld_in_vol = bind(places, op,
auto_where=("fmm_qbx", "target"))(
actx, sigma=fmm_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)
if do_plot:
#fplot.show_scalar_in_mayavi(0.1*.get(queue))
fplot.write_vtk_file("potential.vts", [
("fmm_fld_in_vol", actx.to_numpy(fmm_fld_in_vol)),
("direct_fld_in_vol", actx.to_numpy(direct_fld_in_vol))
])
assert linf_err < 1e-3
def test_p2e2p(ctx_getter, base_knl, expn_class, order, with_source_derivative):
#logging.basicConfig(level=logging.INFO)
from sympy.core.cache import clear_cache
clear_cache()
ctx = ctx_getter()
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 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, out_kernels)
e2p = E2PFromSingleBox(ctx, expn, 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], 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 with_source_derivative:
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]) + 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]) + center
fp = FieldPlotter(eval_center, extent=0.1, npoints=res)
centers = (
np.array([0.0, 0.0], 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, 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_off_surface_eval_vs_direct(ctx_getter, do_plot=False):
logging.basicConfig(level=logging.INFO)
cl_ctx = ctx_getter()
queue = cl.CommandQueue(cl_ctx)
# prevent cache 'splosion
from sympy.core.cache import clear_cache
clear_cache()
nelements = 300
target_order = 8
qbx_order = 3
mesh = make_curve_mesh(WobblyCircle.random(8, seed=30),
np.linspace(0, 1, nelements+1),
target_order)
from pytential.qbx import QBXLayerPotentialSource
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import \
InterpolatoryQuadratureSimplexGroupFactory
pre_density_discr = Discretization(
cl_ctx, mesh, InterpolatoryQuadratureSimplexGroupFactory(target_order))
direct_qbx, _ = QBXLayerPotentialSource(
pre_density_discr, 4*target_order, qbx_order,
fmm_order=False,
target_association_tolerance=0.05,
).with_refinement()
fmm_qbx, _ = QBXLayerPotentialSource(
pre_density_discr, 4*target_order, qbx_order,
fmm_order=qbx_order + 3,
_expansions_in_tree_have_extent=True,
target_association_tolerance=0.05,
).with_refinement()
fplot = FieldPlotter(np.zeros(2), extent=5, npoints=1000)
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)
from pytential.qbx import QBXTargetAssociationFailedException
try:
direct_density_discr = direct_qbx.density_discr
direct_sigma = direct_density_discr.zeros(queue) + 1
direct_fld_in_vol = bind((direct_qbx, ptarget), op)(
queue, sigma=direct_sigma)
except QBXTargetAssociationFailedException as e:
fplot.show_scalar_in_matplotlib(e.failed_target_flags.get(queue))
import matplotlib.pyplot as pt
pt.show()
raise
fmm_density_discr = fmm_qbx.density_discr
fmm_sigma = fmm_density_discr.zeros(queue) + 1
fmm_fld_in_vol = bind((fmm_qbx, ptarget), op)(queue, sigma=fmm_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)
if do_plot:
#fplot.show_scalar_in_mayavi(0.1*.get(queue))
fplot.write_vtk_file("potential.vts", [
("fmm_fld_in_vol", fmm_fld_in_vol.get(queue)),
("direct_fld_in_vol", direct_fld_in_vol.get(queue))
])
assert linf_err < 1e-3
representation = sym.S(0, sym.var("sigma"))
op = representation
bc = cl.clmath.cos(mode_nr * angle)
bound_op = bind(discr, op)
from pytential.gmres import gmres
gmres_result = gmres(bound_op.scipy_op(queue, "sigma"),
bc,
tol=1e-14,
progress=True,
hard_failure=True)
import sys
sys.exit()
sigma = gmres_result.solution
fplot = FieldPlotter(np.zeros(2), extent=5, npoints=500)
from pytential.discretization.target import PointsTarget
fld_in_vol = bind((discr, PointsTarget(fplot.points)),
representation)(queue, sigma=sigma).get()
fld_on_bdry = bound_op(queue, sigma=sigma).get()
from mayavi import mlab
fplot.show_scalar_in_mayavi(fld_in_vol.real, max_val=5)
mlab.colorbar()
mlab.show()
representation = sym.S(0, sym.var("sigma"))
op = representation
bc = cl.clmath.cos(mode_nr*angle)
bound_op = bind(discr, op)
from pytential.gmres import gmres
gmres_result = gmres(
bound_op.scipy_op(queue, "sigma"),
bc, tol=1e-14, progress=True,
hard_failure=True)
import sys
sys.exit()
sigma = gmres_result.solution
fplot = FieldPlotter(np.zeros(2), extent=5, npoints=500)
from pytential.discretization.target import PointsTarget
fld_in_vol = bind(
(discr, PointsTarget(fplot.points)),
representation)(queue, sigma=sigma).get()
fld_on_bdry = bound_op(queue, sigma=sigma).get()
from mayavi import mlab
fplot.show_scalar_in_mayavi(fld_in_vol.real, max_val=5)
mlab.colorbar()
mlab.show()
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)
def main():
# cl.array.to_device(queue, numpy_array)
from meshmode.mesh.io import generate_gmsh, FileSource
mesh = generate_gmsh(
FileSource("ellipsoid.step"), 2, order=2,
other_options=["-string", "Mesh.CharacteristicLengthMax = %g;" % h])
from meshmode.mesh.processing import perform_flips
# Flip elements--gmsh generates inside-out geometry.
mesh = perform_flips(mesh, np.ones(mesh.nelements))
print("%d elements" % mesh.nelements)
from meshmode.mesh.processing import find_bounding_box
bbox_min, bbox_max = find_bounding_box(mesh)
bbox_center = 0.5*(bbox_min+bbox_max)
bbox_size = max(bbox_max-bbox_min) / 2
logger.info("%d elements" % mesh.nelements)
from pytential.qbx import QBXLayerPotentialSource
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import \
InterpolatoryQuadratureSimplexGroupFactory
density_discr = Discretization(
cl_ctx, mesh, InterpolatoryQuadratureSimplexGroupFactory(target_order))
qbx = QBXLayerPotentialSource(density_discr, 4*target_order, qbx_order,
fmm_order=qbx_order + 10, fmm_backend="fmmlib")
from pytential.symbolic.pde.maxwell import MuellerAugmentedMFIEOperator
pde_op = MuellerAugmentedMFIEOperator(
omega=0.4,
epss=[1.4, 1.0],
mus=[1.2, 1.0],
)
from pytential import bind, sym
unk = pde_op.make_unknown("sigma")
sym_operator = pde_op.operator(unk)
sym_rhs = pde_op.rhs(
sym.make_sym_vector("Einc", 3),
sym.make_sym_vector("Hinc", 3))
sym_repr = pde_op.representation(0, unk)
if 1:
expr = sym_repr
print(sym.pretty(expr))
print("#"*80)
from pytential.target import PointsTarget
tgt_points=np.zeros((3,1))
tgt_points[0,0] = 100
tgt_points[1,0] = -200
tgt_points[2,0] = 300
bound_op = bind((qbx, PointsTarget(tgt_points)), expr)
print(bound_op.code)
if 1:
def green3e(x,y,z,source,strength,k):
# electric field corresponding to dyadic green's function
# due to monochromatic electric dipole located at "source".
# "strength" is the the intensity of the dipole.
# E = (I + Hess)(exp(ikr)/r) dot (strength)
#
dx = x - source[0]
dy = y - source[1]
dz = z - source[2]
rr = np.sqrt(dx**2 + dy**2 + dz**2)
fout = np.exp(1j*k*rr)/rr
evec = fout*strength
qmat = np.zeros((3,3),dtype=np.complex128)
qmat[0,0]=(2*dx**2-dy**2-dz**2)*(1-1j*k*rr)
qmat[1,1]=(2*dy**2-dz**2-dx**2)*(1-1j*k*rr)
qmat[2,2]=(2*dz**2-dx**2-dy**2)*(1-1j*k*rr)
qmat[0,0]=qmat[0,0]+(-k**2*dx**2*rr**2)
qmat[1,1]=qmat[1,1]+(-k**2*dy**2*rr**2)
qmat[2,2]=qmat[2,2]+(-k**2*dz**2*rr**2)
qmat[0,1]=(3-k**2*rr**2-3*1j*k*rr)*(dx*dy)
qmat[1,2]=(3-k**2*rr**2-3*1j*k*rr)*(dy*dz)
qmat[2,0]=(3-k**2*rr**2-3*1j*k*rr)*(dz*dx)
qmat[1,0]=qmat[0,1]
qmat[2,1]=qmat[1,2]
qmat[0,2]=qmat[2,0]
fout=np.exp(1j*k*rr)/rr**5/k**2
fvec = fout*np.dot(qmat,strength)
evec = evec + fvec
return evec
def green3m(x,y,z,source,strength,k):
# magnetic field corresponding to dyadic green's function
# due to monochromatic electric dipole located at "source".
# "strength" is the the intensity of the dipole.
# H = curl((I + Hess)(exp(ikr)/r) dot (strength)) =
# strength \cross \grad (exp(ikr)/r)
#
dx = x - source[0]
dy = y - source[1]
dz = z - source[2]
rr = np.sqrt(dx**2 + dy**2 + dz**2)
fout=(1-1j*k*rr)*np.exp(1j*k*rr)/rr**3
fvec = np.zeros(3,dtype=np.complex128)
fvec[0] = fout*dx
fvec[1] = fout*dy
fvec[2] = fout*dz
hvec = np.cross(strength,fvec)
return hvec
def dipole3e(x,y,z,source,strength,k):
#
# evalaute electric and magnetic field due
# to monochromatic electric dipole located at "source"
# with intensity "strength"
evec = green3e(x,y,z,source,strength,k)
evec = evec*1j*k
hvec = green3m(x,y,z,source,strength,k)
return evec,hvec
def dipole3m(x,y,z,source,strength,k):
#
# evalaute electric and magnetic field due
# to monochromatic magnetic dipole located at "source"
# with intensity "strength"
evec = green3m(x,y,z,source,strength,k)
hvec = green3e(x,y,z,source,strength,k)
hvec = -hvec*1j*k
return evec,hvec
def dipole3eall(x,y,z,sources,strengths,k):
ns = len(strengths)
evec = np.zeros(3,dtype=np.complex128)
hvec = np.zeros(3,dtype=np.complex128)
for i in range(ns):
evect,hvect = dipole3e(x,y,z,sources[i],strengths[i],k)
evec = evec + evect
hvec = hvec + hvect
nodes = density_discr.nodes().with_queue(queue).get()
source = [0.01,-0.03,0.02]
# source = cl.array.to_device(queue,np.zeros(3))
# source[0] = 0.01
# source[1] =-0.03
# source[2] = 0.02
strength = np.ones(3)
# evec = cl.array.to_device(queue,np.zeros((3,len(nodes[0])),dtype=np.complex128))
# hvec = cl.array.to_device(queue,np.zeros((3,len(nodes[0])),dtype=np.complex128))
evec = np.zeros((3,len(nodes[0])),dtype=np.complex128)
hvec = np.zeros((3,len(nodes[0])),dtype=np.complex128)
for i in range(len(nodes[0])):
evec[:,i],hvec[:,i] = dipole3e(nodes[0][i],nodes[1][i],nodes[2][i],source,strength,k)
print(np.shape(hvec))
print(type(evec))
print(type(hvec))
evec = cl.array.to_device(queue,evec)
hvec = cl.array.to_device(queue,hvec)
bvp_rhs = bind(qbx, sym_rhs)(queue,Einc=evec,Hinc=hvec)
print(np.shape(bvp_rhs))
print(type(bvp_rhs))
# print(bvp_rhs)
1/-1
bound_op = bind(qbx, sym_operator)
from pytential.solve import gmres
if 0:
gmres_result = gmres(
bound_op.scipy_op(queue, "sigma", dtype=np.complex128, k=k),
bvp_rhs, tol=1e-8, progress=True,
stall_iterations=0,
hard_failure=True)
sigma = gmres_result.solution
fld_at_tgt = bind((qbx, PointsTarget(tgt_points)), sym_repr)(queue,
sigma=bvp_rhs,k=k)
fld_at_tgt = np.array([
fi.get() for fi in fld_at_tgt
])
print(fld_at_tgt)
1/0
# }}}
#mlab.figure(bgcolor=(1, 1, 1))
if 1:
from meshmode.discretization.visualization import make_visualizer
bdry_vis = make_visualizer(queue, density_discr, target_order)
bdry_normals = bind(density_discr, sym.normal(3))(queue)\
.as_vector(dtype=object)
bdry_vis.write_vtk_file("source.vtu", [
("sigma", sigma),
("bdry_normals", bdry_normals),
])
fplot = FieldPlotter(bbox_center, extent=2*bbox_size, npoints=(150, 150, 1))
qbx_tgt_tol = qbx.copy(target_association_tolerance=0.1)
from pytential.target import PointsTarget
from pytential.qbx import QBXTargetAssociationFailedException
rho_sym = sym.var("rho")
try:
fld_in_vol = bind(
(qbx_tgt_tol, PointsTarget(fplot.points)),
sym.make_obj_array([
sym.S(pde_op.kernel, rho_sym, k=sym.var("k"),
qbx_forced_limit=None),
sym.d_dx(3, sym.S(pde_op.kernel, rho_sym, k=sym.var("k"),
qbx_forced_limit=None)),
sym.d_dy(3, sym.S(pde_op.kernel, rho_sym, k=sym.var("k"),
qbx_forced_limit=None)),
sym.d_dz(3, sym.S(pde_op.kernel, rho_sym, k=sym.var("k"),
qbx_forced_limit=None)),
])
)(queue, jt=jt, rho=rho, k=k)
except QBXTargetAssociationFailedException as e:
fplot.write_vtk_file(
"failed-targets.vts",
[
("failed_targets", e.failed_target_flags.get(queue))
])
raise
fld_in_vol = sym.make_obj_array(
[fiv.get() for fiv in fld_in_vol])
#fplot.show_scalar_in_mayavi(fld_in_vol.real, max_val=5)
fplot.write_vtk_file(
"potential.vts",
[
("potential", fld_in_vol[0]),
("grad", fld_in_vol[1:]),
]
)
def 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 test_sumpy_fmm(ctx_getter, knl, local_expn_class, mpole_expn_class):
logging.basicConfig(level=logging.INFO)
ctx = ctx_getter()
queue = cl.CommandQueue(ctx)
nsources = 1000
ntargets = 300
dtype = np.float64
from boxtree.tools import (make_normal_particle_array as p_normal)
sources = p_normal(queue, nsources, knl.dim, dtype, seed=15)
if 1:
offset = np.zeros(knl.dim)
offset[0] = 0.1
targets = (p_normal(queue, ntargets, knl.dim, dtype, seed=18) + offset)
del offset
else:
from sumpy.visualization import FieldPlotter
fp = FieldPlotter(np.array([0.5, 0]), extent=3, npoints=200)
from pytools.obj_array import make_obj_array
targets = make_obj_array([fp.points[i] for i in range(knl.dim)])
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)
# {{{ plot tree
if 0:
host_tree = tree.get()
host_trav = trav.get()
if 1:
print("src_box", host_tree.find_box_nr_for_source(403))
print("tgt_box", host_tree.find_box_nr_for_target(28))
print(list(host_trav.target_or_target_parent_boxes).index(37))
print(host_trav.get_box_list("sep_bigger", 22))
from boxtree.visualization import TreePlotter
plotter = TreePlotter(host_tree)
plotter.draw_tree(fill=False, edgecolor="black", zorder=10)
plotter.set_bounding_box()
plotter.draw_box_numbers()
import matplotlib.pyplot as pt
pt.show()
# }}}
from pyopencl.clrandom import PhiloxGenerator
rng = PhiloxGenerator(ctx, seed=44)
weights = rng.uniform(queue, nsources, dtype=np.float64)
logger.info("computing direct (reference) result")
from pytools.convergence import PConvergenceVerifier
pconv_verifier = PConvergenceVerifier()
extra_kwargs = {}
dtype = np.float64
order_values = [1, 2, 3]
if isinstance(knl, HelmholtzKernel):
extra_kwargs["k"] = 0.05
dtype = np.complex128
if knl.dim == 3:
order_values = [1, 2]
elif knl.dim == 2 and issubclass(local_expn_class, H2DLocalExpansion):
order_values = [10, 12]
elif isinstance(knl, YukawaKernel):
extra_kwargs["lam"] = 2
dtype = np.complex128
if knl.dim == 3:
order_values = [1, 2]
elif knl.dim == 2 and issubclass(local_expn_class, Y2DLocalExpansion):
order_values = [10, 12]
from functools import partial
for order in order_values:
out_kernels = [knl]
from sumpy.fmm import SumpyExpansionWranglerCodeContainer
wcc = SumpyExpansionWranglerCodeContainer(
ctx, partial(mpole_expn_class, knl),
partial(local_expn_class, knl), out_kernels)
wrangler = wcc.get_wrangler(
queue,
tree,
dtype,
fmm_level_to_order=lambda kernel, kernel_args, tree, lev: order,
kernel_extra_kwargs=extra_kwargs)
from boxtree.fmm import drive_fmm
pot, = drive_fmm(trav, wrangler, weights)
from sumpy import P2P
p2p = P2P(ctx, out_kernels, exclude_self=False)
evt, (ref_pot, ) = p2p(queue, targets, sources, (weights, ),
**extra_kwargs)
pot = pot.get()
ref_pot = ref_pot.get()
rel_err = la.norm(pot - ref_pot, np.inf) / la.norm(ref_pot, np.inf)
logger.info("order %d -> relative l2 error: %g" % (order, rel_err))
pconv_verifier.add_data_point(order, rel_err)
print(pconv_verifier)
pconv_verifier()
def run_int_eq_test(
cl_ctx, queue, curve_f, nelements, qbx_order, bc_type, loc_sign, k,
target_order, source_order):
mesh = make_curve_mesh(curve_f,
np.linspace(0, 1, nelements+1),
target_order)
if 0:
from pytential.visualization import show_mesh
show_mesh(mesh)
pt.gca().set_aspect("equal")
pt.show()
from pytential.qbx import QBXLayerPotentialSource
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import \
InterpolatoryQuadratureSimplexGroupFactory
density_discr = Discretization(
cl_ctx, mesh, InterpolatoryQuadratureSimplexGroupFactory(target_order))
if source_order is None:
source_order = 4*target_order
qbx = QBXLayerPotentialSource(
density_discr, fine_order=source_order, qbx_order=qbx_order,
# Don't use FMM for now
fmm_order=False)
# {{{ set up operator
from pytential.symbolic.pde.scalar import (
DirichletOperator,
NeumannOperator)
from sumpy.kernel import LaplaceKernel, HelmholtzKernel, AxisTargetDerivative
if k:
knl = HelmholtzKernel(2)
knl_kwargs = {"k": k}
else:
knl = LaplaceKernel(2)
knl_kwargs = {}
if knl.is_complex_valued:
dtype = np.complex128
else:
dtype = np.float64
if bc_type == "dirichlet":
op = DirichletOperator((knl, knl_kwargs), loc_sign, use_l2_weighting=True)
elif bc_type == "neumann":
op = NeumannOperator((knl, knl_kwargs), loc_sign, use_l2_weighting=True,
use_improved_operator=False)
else:
assert False
op_u = op.operator(sym.var("u"))
# }}}
# {{{ set up test data
inner_radius = 0.1
outer_radius = 2
if loc_sign < 0:
test_src_geo_radius = outer_radius
test_tgt_geo_radius = inner_radius
else:
test_src_geo_radius = inner_radius
test_tgt_geo_radius = outer_radius
point_sources = make_circular_point_group(10, test_src_geo_radius,
func=lambda x: x**1.5)
test_targets = make_circular_point_group(20, test_tgt_geo_radius)
np.random.seed(22)
source_charges = np.random.randn(point_sources.shape[1])
source_charges[-1] = -np.sum(source_charges[:-1])
source_charges = source_charges.astype(dtype)
assert np.sum(source_charges) < 1e-15
# }}}
if 0:
# show geometry, centers, normals
nodes_h = density_discr.nodes().get(queue=queue)
pt.plot(nodes_h[0], nodes_h[1], "x-")
normal = bind(density_discr, sym.normal())(queue).as_vector(np.object)
pt.quiver(nodes_h[0], nodes_h[1], normal[0].get(queue), normal[1].get(queue))
pt.gca().set_aspect("equal")
pt.show()
# {{{ establish BCs
from sumpy.p2p import P2P
pot_p2p = P2P(cl_ctx,
[knl], exclude_self=False, value_dtypes=dtype)
evt, (test_direct,) = pot_p2p(
queue, test_targets, point_sources, [source_charges],
out_host=False, **knl_kwargs)
nodes = density_discr.nodes()
evt, (src_pot,) = pot_p2p(
queue, nodes, point_sources, [source_charges],
**knl_kwargs)
grad_p2p = P2P(cl_ctx,
[AxisTargetDerivative(0, knl), AxisTargetDerivative(1, knl)],
exclude_self=False, value_dtypes=dtype)
evt, (src_grad0, src_grad1) = grad_p2p(
queue, nodes, point_sources, [source_charges],
**knl_kwargs)
if bc_type == "dirichlet":
bc = src_pot
elif bc_type == "neumann":
normal = bind(density_discr, sym.normal())(queue).as_vector(np.object)
bc = (src_grad0*normal[0] + src_grad1*normal[1])
# }}}
# {{{ solve
bound_op = bind(qbx, op_u)
rhs = bind(density_discr, op.prepare_rhs(sym.var("bc")))(queue, bc=bc)
from pytential.solve import gmres
gmres_result = gmres(
bound_op.scipy_op(queue, "u", k=k),
rhs, tol=1e-14, progress=True,
hard_failure=False)
u = gmres_result.solution
print("gmres state:", gmres_result.state)
if 0:
# {{{ build matrix for spectrum check
from sumpy.tools import build_matrix
mat = build_matrix(bound_op.scipy_op("u"))
w, v = la.eig(mat)
if 0:
pt.imshow(np.log10(1e-20+np.abs(mat)))
pt.colorbar()
pt.show()
#assert abs(s[-1]) < 1e-13, "h
#assert abs(s[-2]) > 1e-7
#from pudb import set_trace; set_trace()
# }}}
# }}}
# {{{ error check
from pytential.target import PointsTarget
bound_tgt_op = bind((qbx, PointsTarget(test_targets)),
op.representation(sym.var("u")))
test_via_bdry = bound_tgt_op(queue, u=u, k=k)
err = test_direct-test_via_bdry
err = err.get()
test_direct = test_direct.get()
test_via_bdry = test_via_bdry.get()
# {{{ remove effect of net source charge
if k == 0 and bc_type == "neumann" and loc_sign == -1:
# remove constant offset in interior Laplace Neumann error
tgt_ones = np.ones_like(test_direct)
tgt_ones = tgt_ones/la.norm(tgt_ones)
err = err - np.vdot(tgt_ones, err)*tgt_ones
# }}}
rel_err_2 = la.norm(err)/la.norm(test_direct)
rel_err_inf = la.norm(err, np.inf)/la.norm(test_direct, np.inf)
# }}}
print("rel_err_2: %g rel_err_inf: %g" % (rel_err_2, rel_err_inf))
# {{{ test tangential derivative
bound_t_deriv_op = bind(qbx,
op.representation(
sym.var("u"), map_potentials=sym.tangential_derivative,
qbx_forced_limit=loc_sign))
#print(bound_t_deriv_op.code)
tang_deriv_from_src = bound_t_deriv_op(queue, u=u).as_scalar().get()
tangent = bind(
density_discr,
sym.pseudoscalar()/sym.area_element())(queue).as_vector(np.object)
tang_deriv_ref = (src_grad0 * tangent[0] + src_grad1 * tangent[1]).get()
if 0:
pt.plot(tang_deriv_ref.real)
pt.plot(tang_deriv_from_src.real)
pt.show()
td_err = tang_deriv_from_src - tang_deriv_ref
rel_td_err_inf = la.norm(td_err, np.inf)/la.norm(tang_deriv_ref, np.inf)
print("rel_td_err_inf: %g" % rel_td_err_inf)
# }}}
# {{{ plotting
if 0:
fplot = FieldPlotter(np.zeros(2),
extent=1.25*2*max(test_src_geo_radius, test_tgt_geo_radius),
npoints=200)
#pt.plot(u)
#pt.show()
evt, (fld_from_src,) = pot_p2p(
queue, fplot.points, point_sources, [source_charges],
**knl_kwargs)
fld_from_bdry = bind(
(qbx, PointsTarget(fplot.points)),
op.representation(sym.var("u"))
)(queue, u=u, k=k)
fld_from_src = fld_from_src.get()
fld_from_bdry = fld_from_bdry.get()
nodes = density_discr.nodes().get(queue=queue)
def prep():
pt.plot(point_sources[0], point_sources[1], "o",
label="Monopole 'Point Charges'")
pt.plot(test_targets[0], test_targets[1], "v",
label="Observation Points")
pt.plot(nodes[0], nodes[1], "k-",
label=r"$\Gamma$")
from matplotlib.cm import get_cmap
cmap = get_cmap()
cmap._init()
if 0:
cmap._lut[(cmap.N*99)//100:, -1] = 0 # make last percent transparent?
prep()
if 1:
pt.subplot(131)
pt.title("Field error (loc_sign=%s)" % loc_sign)
log_err = np.log10(1e-20+np.abs(fld_from_src-fld_from_bdry))
log_err = np.minimum(-3, log_err)
fplot.show_scalar_in_matplotlib(log_err, cmap=cmap)
#from matplotlib.colors import Normalize
#im.set_norm(Normalize(vmin=-6, vmax=1))
cb = pt.colorbar(shrink=0.9)
cb.set_label(r"$\log_{10}(\mathdefault{Error})$")
if 1:
pt.subplot(132)
prep()
pt.title("Source Field")
fplot.show_scalar_in_matplotlib(
fld_from_src.real, max_val=3)
pt.colorbar(shrink=0.9)
if 1:
pt.subplot(133)
prep()
pt.title("Solved Field")
fplot.show_scalar_in_matplotlib(
fld_from_bdry.real, max_val=3)
pt.colorbar(shrink=0.9)
# total field
#fplot.show_scalar_in_matplotlib(
#fld_from_src.real+fld_from_bdry.real, max_val=0.1)
#pt.colorbar()
pt.legend(loc="best", prop=dict(size=15))
from matplotlib.ticker import NullFormatter
pt.gca().xaxis.set_major_formatter(NullFormatter())
pt.gca().yaxis.set_major_formatter(NullFormatter())
pt.gca().set_aspect("equal")
if 0:
border_factor_top = 0.9
border_factor = 0.3
xl, xh = pt.xlim()
xhsize = 0.5*(xh-xl)
pt.xlim(xl-border_factor*xhsize, xh+border_factor*xhsize)
yl, yh = pt.ylim()
yhsize = 0.5*(yh-yl)
pt.ylim(yl-border_factor_top*yhsize, yh+border_factor*yhsize)
#pt.savefig("helmholtz.pdf", dpi=600)
pt.show()
# }}}
class Result(Record):
pass
return Result(
rel_err_2=rel_err_2,
rel_err_inf=rel_err_inf,
rel_td_err_inf=rel_td_err_inf,
gmres_result=gmres_result)
def test_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 run_dielectric_test(cl_ctx,
queue,
nelements,
qbx_order,
op_class,
mode,
k0=3,
k1=2.9,
mesh_order=10,
bdry_quad_order=None,
bdry_ovsmp_quad_order=None,
use_l2_weighting=False,
fmm_order=None,
visualize=False):
if fmm_order is None:
fmm_order = qbx_order * 2
if bdry_quad_order is None:
bdry_quad_order = mesh_order
if bdry_ovsmp_quad_order is None:
bdry_ovsmp_quad_order = 4 * bdry_quad_order
from meshmode.mesh.generation import ellipse, make_curve_mesh
from functools import partial
mesh = make_curve_mesh(partial(ellipse, 3),
np.linspace(0, 1, nelements + 1), mesh_order)
density_discr = Discretization(
cl_ctx, mesh,
InterpolatoryQuadratureSimplexGroupFactory(bdry_quad_order))
logger.info("%d elements" % mesh.nelements)
# from meshmode.discretization.visualization import make_visualizer
# bdry_vis = make_visualizer(queue, density_discr, 20)
# {{{ solve bvp
from sumpy.kernel import HelmholtzKernel, AxisTargetDerivative
kernel = HelmholtzKernel(2)
beta = 2.5
K0 = np.sqrt(k0**2 - beta**2) # noqa
K1 = np.sqrt(k1**2 - beta**2) # noqa
pde_op = op_class(mode,
k_vacuum=1,
interfaces=((0, 1, sym.DEFAULT_SOURCE), ),
domain_k_exprs=(k0, k1),
beta=beta,
use_l2_weighting=use_l2_weighting)
op_unknown_sym = pde_op.make_unknown("unknown")
representation0_sym = pde_op.representation(op_unknown_sym, 0)
representation1_sym = pde_op.representation(op_unknown_sym, 1)
from pytential.qbx import QBXLayerPotentialSource
qbx = QBXLayerPotentialSource(density_discr,
fine_order=bdry_ovsmp_quad_order,
qbx_order=qbx_order,
fmm_order=fmm_order).with_refinement()
#print(sym.pretty(pde_op.operator(op_unknown_sym)))
#1/0
bound_pde_op = bind(qbx, pde_op.operator(op_unknown_sym))
e_factor = float(pde_op.ez_enabled)
h_factor = float(pde_op.hz_enabled)
e_sources_0 = make_obj_array(list(np.array([[0.1, 0.2]]).T.copy()))
e_strengths_0 = np.array([1 * e_factor])
e_sources_1 = make_obj_array(list(np.array([[4, 4]]).T.copy()))
e_strengths_1 = np.array([1 * e_factor])
h_sources_0 = make_obj_array(list(np.array([[0.2, 0.1]]).T.copy()))
h_strengths_0 = np.array([1 * h_factor])
h_sources_1 = make_obj_array(list(np.array([[4, 5]]).T.copy()))
h_strengths_1 = np.array([1 * h_factor])
kernel_grad = [
AxisTargetDerivative(i, kernel)
for i in range(density_discr.ambient_dim)
]
from sumpy.p2p import P2P
pot_p2p = P2P(cl_ctx, [kernel], exclude_self=False)
pot_p2p_grad = P2P(cl_ctx, kernel_grad, exclude_self=False)
normal = bind(density_discr, sym.normal())(queue).as_vector(np.object)
tangent = bind(density_discr,
sym.pseudoscalar() / sym.area_element())(queue).as_vector(
np.object)
_, (E0, ) = pot_p2p(queue,
density_discr.nodes(),
e_sources_0, [e_strengths_0],
out_host=False,
k=K0)
_, (E1, ) = pot_p2p(queue,
density_discr.nodes(),
e_sources_1, [e_strengths_1],
out_host=False,
k=K1)
_, (grad0_E0, grad1_E0) = pot_p2p_grad(queue,
density_discr.nodes(),
e_sources_0, [e_strengths_0],
out_host=False,
k=K0)
_, (grad0_E1, grad1_E1) = pot_p2p_grad(queue,
density_discr.nodes(),
e_sources_1, [e_strengths_1],
out_host=False,
k=K1)
_, (H0, ) = pot_p2p(queue,
density_discr.nodes(),
h_sources_0, [h_strengths_0],
out_host=False,
k=K0)
_, (H1, ) = pot_p2p(queue,
density_discr.nodes(),
h_sources_1, [h_strengths_1],
out_host=False,
k=K1)
_, (grad0_H0, grad1_H0) = pot_p2p_grad(queue,
density_discr.nodes(),
h_sources_0, [h_strengths_0],
out_host=False,
k=K0)
_, (grad0_H1, grad1_H1) = pot_p2p_grad(queue,
density_discr.nodes(),
h_sources_1, [h_strengths_1],
out_host=False,
k=K1)
E0_dntarget = (grad0_E0 * normal[0] + grad1_E0 * normal[1]) # noqa
E1_dntarget = (grad0_E1 * normal[0] + grad1_E1 * normal[1]) # noqa
H0_dntarget = (grad0_H0 * normal[0] + grad1_H0 * normal[1]) # noqa
H1_dntarget = (grad0_H1 * normal[0] + grad1_H1 * normal[1]) # noqa
E0_dttarget = (grad0_E0 * tangent[0] + grad1_E0 * tangent[1]) # noqa
E1_dttarget = (grad0_E1 * tangent[0] + grad1_E1 * tangent[1]) # noqa
H0_dttarget = (grad0_H0 * tangent[0] + grad1_H0 * tangent[1]) # noqa
H1_dttarget = (grad0_H1 * tangent[0] + grad1_H1 * tangent[1]) # noqa
sqrt_w = bind(density_discr, sym.sqrt_jac_q_weight())(queue)
bvp_rhs = np.zeros(len(pde_op.bcs), dtype=np.object)
for i_bc, terms in enumerate(pde_op.bcs):
for term in terms:
assert term.i_interface == 0
if term.field_kind == pde_op.field_kind_e:
if term.direction == pde_op.dir_none:
bvp_rhs[i_bc] += (term.coeff_outer * E0 +
term.coeff_inner * E1)
elif term.direction == pde_op.dir_normal:
bvp_rhs[i_bc] += (term.coeff_outer * E0_dntarget +
term.coeff_inner * E1_dntarget)
elif term.direction == pde_op.dir_tangential:
bvp_rhs[i_bc] += (term.coeff_outer * E0_dttarget +
term.coeff_inner * E1_dttarget)
else:
raise NotImplementedError("direction spec in RHS")
elif term.field_kind == pde_op.field_kind_h:
if term.direction == pde_op.dir_none:
bvp_rhs[i_bc] += (term.coeff_outer * H0 +
term.coeff_inner * H1)
elif term.direction == pde_op.dir_normal:
bvp_rhs[i_bc] += (term.coeff_outer * H0_dntarget +
term.coeff_inner * H1_dntarget)
elif term.direction == pde_op.dir_tangential:
bvp_rhs[i_bc] += (term.coeff_outer * H0_dttarget +
term.coeff_inner * H1_dttarget)
else:
raise NotImplementedError("direction spec in RHS")
if use_l2_weighting:
bvp_rhs[i_bc] *= sqrt_w
scipy_op = bound_pde_op.scipy_op(queue,
"unknown",
domains=[sym.DEFAULT_TARGET] *
len(pde_op.bcs),
K0=K0,
K1=K1,
dtype=np.complex128)
if mode == "tem" or op_class is SRep:
from sumpy.tools import vector_from_device, vector_to_device
from pytential.solve import lu
unknown = lu(scipy_op, vector_from_device(queue, bvp_rhs))
unknown = vector_to_device(queue, unknown)
else:
from pytential.solve import gmres
gmres_result = gmres(scipy_op,
bvp_rhs,
tol=1e-14,
progress=True,
hard_failure=True,
stall_iterations=0)
unknown = gmres_result.solution
# }}}
targets_0 = make_obj_array(
list(np.array([[3.2 + t, -4] for t in [0, 0.5, 1]]).T.copy()))
targets_1 = make_obj_array(
list(np.array([[t * -0.3, t * -0.2] for t in [0, 0.5, 1]]).T.copy()))
from pytential.target import PointsTarget
from sumpy.tools import vector_from_device
F0_tgt = vector_from_device(
queue,
bind( # noqa
(qbx, PointsTarget(targets_0)),
representation0_sym)(queue, unknown=unknown, K0=K0, K1=K1))
F1_tgt = vector_from_device(
queue,
bind( # noqa
(qbx, PointsTarget(targets_1)),
representation1_sym)(queue, unknown=unknown, K0=K0, K1=K1))
_, (E0_tgt_true, ) = pot_p2p(queue,
targets_0,
e_sources_0, [e_strengths_0],
out_host=True,
k=K0)
_, (E1_tgt_true, ) = pot_p2p(queue,
targets_1,
e_sources_1, [e_strengths_1],
out_host=True,
k=K1)
_, (H0_tgt_true, ) = pot_p2p(queue,
targets_0,
h_sources_0, [h_strengths_0],
out_host=True,
k=K0)
_, (H1_tgt_true, ) = pot_p2p(queue,
targets_1,
h_sources_1, [h_strengths_1],
out_host=True,
k=K1)
err_F0_total = 0 # noqa
err_F1_total = 0 # noqa
i_field = 0
def vec_norm(ary):
return la.norm(ary.reshape(-1))
def field_kind_to_string(field_kind):
return {pde_op.field_kind_e: "E", pde_op.field_kind_h: "H"}[field_kind]
for field_kind in pde_op.field_kinds:
if not pde_op.is_field_present(field_kind):
continue
if field_kind == pde_op.field_kind_e:
F0_tgt_true = E0_tgt_true # noqa
F1_tgt_true = E1_tgt_true # noqa
elif field_kind == pde_op.field_kind_h:
F0_tgt_true = H0_tgt_true # noqa
F1_tgt_true = H1_tgt_true # noqa
else:
assert False
abs_err_F0 = vec_norm(F0_tgt[i_field] - F0_tgt_true) # noqa
abs_err_F1 = vec_norm(F1_tgt[i_field] - F1_tgt_true) # noqa
rel_err_F0 = abs_err_F0 / vec_norm(F0_tgt_true) # noqa
rel_err_F1 = abs_err_F1 / vec_norm(F1_tgt_true) # noqa
err_F0_total = max(rel_err_F0, err_F0_total) # noqa
err_F1_total = max(rel_err_F1, err_F1_total) # noqa
print("Abs Err %s0" % field_kind_to_string(field_kind), abs_err_F0)
print("Abs Err %s1" % field_kind_to_string(field_kind), abs_err_F1)
print("Rel Err %s0" % field_kind_to_string(field_kind), rel_err_F0)
print("Rel Err %s1" % field_kind_to_string(field_kind), rel_err_F1)
i_field += 1
if visualize:
from sumpy.visualization import FieldPlotter
fplot = FieldPlotter(np.zeros(2), extent=5, npoints=300)
from pytential.target import PointsTarget
fld0 = bind((qbx, PointsTarget(fplot.points)),
representation0_sym)(queue, unknown=unknown, K0=K0)
fld1 = bind((qbx, PointsTarget(fplot.points)),
representation1_sym)(queue, unknown=unknown, K1=K1)
comp_fields = []
i_field = 0
for field_kind in pde_op.field_kinds:
if not pde_op.is_field_present(field_kind):
continue
fld_str = field_kind_to_string(field_kind)
comp_fields.extend([
("%s_fld0" % fld_str, fld0[i_field].get()),
("%s_fld1" % fld_str, fld1[i_field].get()),
])
i_field += 0
low_order_qbx = QBXLayerPotentialSource(
density_discr,
fine_order=bdry_ovsmp_quad_order,
qbx_order=2,
fmm_order=3).with_refinement()
from sumpy.kernel import LaplaceKernel
from pytential.target import PointsTarget
ones = (cl.array.empty(queue, (density_discr.nnodes, ),
dtype=np.float64).fill(1))
ind_func = -bind(
(low_order_qbx, PointsTarget(fplot.points)),
sym.D(LaplaceKernel(2), sym.var("u")))(queue, u=ones).get()
_, (e_fld0_true, ) = pot_p2p(queue,
fplot.points,
e_sources_0, [e_strengths_0],
out_host=True,
k=K0)
_, (e_fld1_true, ) = pot_p2p(queue,
fplot.points,
e_sources_1, [e_strengths_1],
out_host=True,
k=K1)
_, (h_fld0_true, ) = pot_p2p(queue,
fplot.points,
h_sources_0, [h_strengths_0],
out_host=True,
k=K0)
_, (h_fld1_true, ) = pot_p2p(queue,
fplot.points,
h_sources_1, [h_strengths_1],
out_host=True,
k=K1)
#fplot.show_scalar_in_mayavi(fld_in_vol.real, max_val=5)
fplot.write_vtk_file("potential-n%d.vts" % nelements, [
("e_fld0_true", e_fld0_true),
("e_fld1_true", e_fld1_true),
("h_fld0_true", h_fld0_true),
("h_fld1_true", h_fld1_true),
("ind", ind_func),
] + comp_fields)
return err_F0_total, err_F1_total
def main(mesh_name="ellipse", visualize=False):
import logging
logging.basicConfig(level=logging.INFO) # INFO for more progress info
cl_ctx = cl.create_some_context()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue)
from meshmode.mesh.generation import ellipse, make_curve_mesh
from functools import partial
if mesh_name == "ellipse":
mesh = make_curve_mesh(partial(ellipse, 1),
np.linspace(0, 1, nelements + 1), mesh_order)
elif mesh_name == "ellipse_array":
base_mesh = make_curve_mesh(partial(ellipse, 1),
np.linspace(0, 1, nelements + 1),
mesh_order)
from meshmode.mesh.processing import affine_map, merge_disjoint_meshes
nx = 2
ny = 2
dx = 2 / nx
meshes = [
affine_map(base_mesh,
A=np.diag([dx * 0.25, dx * 0.25]),
b=np.array([dx * (ix - nx / 2), dx * (iy - ny / 2)]))
for ix in range(nx) for iy in range(ny)
]
mesh = merge_disjoint_meshes(meshes, single_group=True)
if visualize:
from meshmode.mesh.visualization import draw_curve
draw_curve(mesh)
import matplotlib.pyplot as plt
plt.show()
else:
raise ValueError(f"unknown mesh name: {mesh_name}")
pre_density_discr = Discretization(
actx, mesh,
InterpolatoryQuadratureSimplexGroupFactory(bdry_quad_order))
from pytential.qbx import (QBXLayerPotentialSource,
QBXTargetAssociationFailedException)
qbx = QBXLayerPotentialSource(pre_density_discr,
fine_order=bdry_ovsmp_quad_order,
qbx_order=qbx_order,
fmm_order=fmm_order)
from sumpy.visualization import FieldPlotter
fplot = FieldPlotter(np.zeros(2), extent=5, npoints=500)
targets = actx.from_numpy(fplot.points)
from pytential import GeometryCollection
places = GeometryCollection(
{
"qbx":
qbx,
"qbx_high_target_assoc_tol":
qbx.copy(target_association_tolerance=0.05),
"targets":
PointsTarget(targets)
},
auto_where="qbx")
density_discr = places.get_discretization("qbx")
# {{{ describe bvp
from sumpy.kernel import LaplaceKernel, 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")
bdry_op_sym = (
-loc_sign * 0.5 * sigma_sym + sqrt_w *
(alpha * sym.S(kernel, inv_sqrt_w_sigma, k=k_sym, qbx_forced_limit=+1)
- sym.D(kernel, inv_sqrt_w_sigma, k=k_sym, qbx_forced_limit="avg")))
# }}}
bound_op = bind(places, bdry_op_sym)
# {{{ fix rhs and solve
from meshmode.dof_array import thaw
nodes = thaw(actx, density_discr.nodes())
k_vec = np.array([2, 1])
k_vec = k * k_vec / la.norm(k_vec, 2)
def u_incoming_func(x):
return actx.np.exp(1j * (x[0] * k_vec[0] + x[1] * k_vec[1]))
bc = -u_incoming_func(nodes)
bvp_rhs = bind(places, sqrt_w * sym.var("bc"))(actx, bc=bc)
from pytential.solve import gmres
gmres_result = gmres(bound_op.scipy_op(actx,
sigma_sym.name,
dtype=np.complex128,
k=k),
bvp_rhs,
tol=1e-8,
progress=True,
stall_iterations=0,
hard_failure=True)
# }}}
# {{{ postprocess/visualize
repr_kwargs = dict(source="qbx_high_target_assoc_tol",
target="targets",
qbx_forced_limit=None)
representation_sym = (
alpha * sym.S(kernel, inv_sqrt_w_sigma, k=k_sym, **repr_kwargs) -
sym.D(kernel, inv_sqrt_w_sigma, k=k_sym, **repr_kwargs))
u_incoming = u_incoming_func(targets)
ones_density = density_discr.zeros(actx)
for elem in ones_density:
elem.fill(1)
indicator = actx.to_numpy(
bind(places, sym.D(LaplaceKernel(2), sigma_sym,
**repr_kwargs))(actx, sigma=ones_density))
try:
fld_in_vol = actx.to_numpy(
bind(places, representation_sym)(actx,
sigma=gmres_result.solution,
k=k))
except QBXTargetAssociationFailedException as e:
fplot.write_vtk_file("helmholtz-dirichlet-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("helmholtz-dirichlet-potential.vts", [
("potential", fld_in_vol),
("indicator", indicator),
("u_incoming", actx.to_numpy(u_incoming)),
])
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 main():
import logging
logger = logging.getLogger(__name__)
logging.basicConfig(level=logging.WARNING) # INFO for more progress info
from meshmode.mesh.io import generate_gmsh, FileSource
mesh = generate_gmsh(
FileSource(cad_file_name), 2, order=2,
other_options=["-string", "Mesh.CharacteristicLengthMax = %g;" % h])
from meshmode.mesh.processing import perform_flips
# Flip elements--gmsh generates inside-out geometry.
mesh = perform_flips(mesh, np.ones(mesh.nelements))
from meshmode.mesh.processing import find_bounding_box
bbox_min, bbox_max = find_bounding_box(mesh)
bbox_center = 0.5*(bbox_min+bbox_max)
bbox_size = max(bbox_max-bbox_min) / 2
logger.info("%d elements" % mesh.nelements)
from pytential.qbx import QBXLayerPotentialSource
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import \
InterpolatoryQuadratureSimplexGroupFactory
density_discr = Discretization(
cl_ctx, mesh, InterpolatoryQuadratureSimplexGroupFactory(target_order))
qbx, _ = QBXLayerPotentialSource(density_discr, 4*target_order, qbx_order,
fmm_order=qbx_order + 3,
target_association_tolerance=0.15).with_refinement()
nodes = density_discr.nodes().with_queue(queue)
angle = cl.clmath.atan2(nodes[1], nodes[0])
from pytential import bind, sym
#op = sym.d_dx(sym.S(kernel, sym.var("sigma"), qbx_forced_limit=None))
op = sym.D(kernel, sym.var("sigma"), qbx_forced_limit=None)
#op = sym.S(kernel, sym.var("sigma"), qbx_forced_limit=None)
sigma = cl.clmath.cos(mode_nr*angle)
if 0:
sigma = 0*angle
from random import randrange
for i in range(5):
sigma[randrange(len(sigma))] = 1
if isinstance(kernel, HelmholtzKernel):
sigma = sigma.astype(np.complex128)
fplot = FieldPlotter(bbox_center, extent=3.5*bbox_size, npoints=150)
from pytential.target import PointsTarget
fld_in_vol = bind(
(qbx, PointsTarget(fplot.points)),
op)(queue, sigma=sigma, k=k).get()
#fplot.show_scalar_in_mayavi(fld_in_vol.real, max_val=5)
fplot.write_vtk_file(
"potential-3d.vts",
[
("potential", fld_in_vol)
]
)
bdry_normals = bind(
density_discr,
sym.normal(density_discr.ambient_dim))(queue).as_vector(dtype=object)
from meshmode.discretization.visualization import make_visualizer
bdry_vis = make_visualizer(queue, density_discr, target_order)
bdry_vis.write_vtk_file("source-3d.vtu", [
("sigma", sigma),
("bdry_normals", bdry_normals),
])
def test_single_plus_double_with_single_fmm(actx_factory, do_plot=False):
logging.basicConfig(level=logging.INFO)
actx = actx_factory()
# prevent cache 'splosion
from sympy.core.cache import clear_cache
clear_cache()
nelements = 300
target_order = 8
qbx_order = 3
mesh = mgen.make_curve_mesh(mgen.WobblyCircle.random(8, seed=30),
np.linspace(0, 1, nelements + 1), target_order)
from pytential.qbx import QBXLayerPotentialSource
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import \
InterpolatoryQuadratureSimplexGroupFactory
pre_density_discr = Discretization(
actx, mesh, InterpolatoryQuadratureSimplexGroupFactory(target_order))
direct_qbx = QBXLayerPotentialSource(
pre_density_discr,
4 * target_order,
qbx_order,
fmm_order=False,
target_association_tolerance=0.05,
)
fmm_qbx = QBXLayerPotentialSource(
pre_density_discr,
4 * target_order,
qbx_order,
fmm_order=qbx_order + 3,
_expansions_in_tree_have_extent=True,
target_association_tolerance=0.05,
)
fplot = FieldPlotter(np.zeros(2), extent=5, npoints=500)
from pytential.target import PointsTarget
ptarget = PointsTarget(actx.freeze(actx.from_numpy(fplot.points)))
from sumpy.kernel import LaplaceKernel
places = GeometryCollection(
{
"direct_qbx": direct_qbx,
"fmm_qbx": fmm_qbx,
"target": ptarget,
},
auto_where=("fmm_qbx", "target"))
direct_density_discr = places.get_discretization("direct_qbx")
fmm_density_discr = places.get_discretization("fmm_qbx")
knl = LaplaceKernel(2)
from pytential.qbx import QBXTargetAssociationFailedException
op_d = sym.D(knl, sym.var("sigma"), qbx_forced_limit=None)
op_s = sym.S(knl, sym.var("sigma"), qbx_forced_limit=None)
op = op_d + op_s * 0.5
try:
direct_sigma = direct_density_discr.zeros(actx) + 1
direct_fld_in_vol = bind(places,
op,
auto_where=("direct_qbx",
"target"))(actx,
sigma=direct_sigma)
except QBXTargetAssociationFailedException as e:
fplot.show_scalar_in_matplotlib(
actx.to_numpy(actx.thaw(e.failed_target_flags)))
import matplotlib.pyplot as pt
pt.show()
raise
fmm_sigma = fmm_density_discr.zeros(actx) + 1
fmm_bound_op = bind(places, op, auto_where=("fmm_qbx", "target"))
print(fmm_bound_op.code)
fmm_fld_in_vol = fmm_bound_op(actx, sigma=fmm_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)
if do_plot:
fplot.write_vtk_file(
"potential.vts",
[("fmm_fld_in_vol", actx.to_numpy(fmm_fld_in_vol)),
("direct_fld_in_vol", actx.to_numpy(direct_fld_in_vol))])
assert linf_err < 1e-3
# check that using one FMM works
op = op_d.copy(source_kernels=op_d.source_kernels + (knl, ),
densities=op_d.densities + (sym.var("sigma") * 0.5, ))
single_fmm_bound_op = bind(places, op, auto_where=("fmm_qbx", "target"))
print(single_fmm_bound_op.code)
single_fmm_fld_in_vol = fmm_bound_op(actx, sigma=fmm_sigma)
err = actx.np.fabs(fmm_fld_in_vol - single_fmm_fld_in_vol)
linf_err = actx.to_numpy(err).max()
print("l_inf error:", linf_err)
assert linf_err < 1e-15
