def test_chained_full_resample_matrix(ctx_factory, ndim, visualize=False):
from meshmode.discretization.connection.chained import \
make_full_resample_matrix
ctx = ctx_factory()
queue = cl.CommandQueue(ctx)
actx = PyOpenCLArrayContext(queue)
discr = create_discretization(actx, ndim)
connections = []
conn = create_refined_connection(actx, discr)
connections.append(conn)
conn = create_refined_connection(actx, conn.to_discr)
connections.append(conn)
from meshmode.discretization.connection import \
ChainedDiscretizationConnection
chained = ChainedDiscretizationConnection(connections)
def f(x):
from six.moves import reduce
return 0.1 * reduce(lambda x, y: x * actx.np.sin(5 * y), x)
resample_mat = actx.to_numpy(make_full_resample_matrix(actx, chained))
x = thaw(actx, connections[0].from_discr.nodes())
fx = f(x)
f1 = resample_mat @ actx.to_numpy(flatten(fx))
f2 = actx.to_numpy(flatten(chained(fx)))
f3 = actx.to_numpy(flatten(connections[1](connections[0](fx))))
assert np.allclose(f1, f2)
assert np.allclose(f2, f3)
def test_vortex_init(ctx_factory):
"""
Simple test to check that Vortex2D initializer
creates the expected solution field.
"""
cl_ctx = ctx_factory()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue)
dim = 2
nel_1d = 4
from meshmode.mesh.generation import generate_regular_rect_mesh
mesh = generate_regular_rect_mesh(a=[(0.0, ), (-5.0, )],
b=[(10.0, ), (5.0, )],
nelements_per_axis=(nel_1d, ) * dim)
order = 3
logger.info(f"Number of elements: {mesh.nelements}")
discr = EagerDGDiscretization(actx, mesh, order=order)
nodes = thaw(actx, discr.nodes())
# Init soln with Vortex
vortex = Vortex2D()
cv = vortex(nodes)
gamma = 1.4
p = 0.4 * (cv.energy - 0.5 * np.dot(cv.momentum, cv.momentum) / cv.mass)
exp_p = cv.mass**gamma
errmax = actx.to_numpy(discr.norm(p - exp_p, np.inf))
logger.info(f"vortex_soln = {cv}")
logger.info(f"pressure = {p}")
assert errmax < 1e-15
def test_external_call(ctx_factory):
cl_ctx = ctx_factory()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue)
def double(queue, x):
return 2 * x
from meshmode.mesh.generation import generate_regular_rect_mesh
dims = 2
mesh = generate_regular_rect_mesh(a=(0, ) * dims,
b=(1, ) * dims,
n=(4, ) * dims)
discr = DGDiscretizationWithBoundaries(actx, mesh, order=1)
ones = sym.Ones(sym.DD_VOLUME)
op = (ones * 3 + sym.FunctionSymbol("double")(ones))
from grudge.function_registry import (base_function_registry,
register_external_function)
freg = register_external_function(base_function_registry,
"double",
implementation=double,
dd=sym.DD_VOLUME)
bound_op = bind(discr, op, function_registry=freg)
result = bound_op(actx, double=double)
assert actx.to_numpy(flatten(result) == 5).all()
def test_unregularized_off_surface_fmm_vs_direct(ctx_factory):
cl_ctx = ctx_factory()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue)
nelements = 300
target_order = 8
fmm_order = 4
# {{{ geometry
mesh = make_curve_mesh(WobblyCircle.random(8, seed=30),
np.linspace(0, 1, nelements+1),
target_order)
from pytential.unregularized import UnregularizedLayerPotentialSource
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import \
InterpolatoryQuadratureSimplexGroupFactory
density_discr = Discretization(
actx, mesh, InterpolatoryQuadratureSimplexGroupFactory(target_order))
direct = UnregularizedLayerPotentialSource(
density_discr,
fmm_order=False,
)
fmm = direct.copy(
fmm_level_to_order=lambda kernel, kernel_args, tree, level: fmm_order)
sigma = density_discr.zeros(actx) + 1
fplot = FieldPlotter(np.zeros(2), extent=5, npoints=100)
from pytential.target import PointsTarget
ptarget = PointsTarget(fplot.points)
from pytential import GeometryCollection
places = GeometryCollection({
"unregularized_direct": direct,
"unregularized_fmm": fmm,
"targets": ptarget})
# }}}
# {{{ check
from sumpy.kernel import LaplaceKernel
op = sym.D(LaplaceKernel(2), sym.var("sigma"), qbx_forced_limit=None)
direct_fld_in_vol = bind(places, op,
auto_where=("unregularized_direct", "targets"))(
actx, sigma=sigma)
fmm_fld_in_vol = bind(places, op,
auto_where=("unregularized_fmm", "targets"))(actx, sigma=sigma)
err = actx.np.fabs(fmm_fld_in_vol - direct_fld_in_vol)
linf_err = actx.to_numpy(err).max()
print("l_inf error:", linf_err)
assert linf_err < 5e-3
def test_unregularized_with_ones_kernel(ctx_factory):
cl_ctx = ctx_factory()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue)
nelements = 10
order = 8
mesh = make_curve_mesh(partial(ellipse, 1),
np.linspace(0, 1, nelements+1),
order)
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import \
InterpolatoryQuadratureSimplexGroupFactory
discr = Discretization(actx, mesh,
InterpolatoryQuadratureSimplexGroupFactory(order))
from pytential.unregularized import UnregularizedLayerPotentialSource
lpot_source = UnregularizedLayerPotentialSource(discr)
from pytential.target import PointsTarget
targets = PointsTarget(np.zeros((2, 1), dtype=float))
places = GeometryCollection({
sym.DEFAULT_SOURCE: lpot_source,
sym.DEFAULT_TARGET: lpot_source,
"target_non_self": targets})
from sumpy.kernel import one_kernel_2d
sigma_sym = sym.var("sigma")
op = sym.IntG(one_kernel_2d, sigma_sym, qbx_forced_limit=None)
sigma = discr.zeros(actx) + 1
result_self = bind(places, op,
auto_where=places.auto_where)(
actx, sigma=sigma)
result_nonself = bind(places, op,
auto_where=(places.auto_source, "target_non_self"))(
actx, sigma=sigma)
from meshmode.dof_array import flatten
assert np.allclose(actx.to_numpy(flatten(result_self)), 2 * np.pi)
assert np.allclose(actx.to_numpy(result_nonself), 2 * np.pi)
def test_to_fd_idempotency(ctx_factory, mm_mesh, fspace_degree):
"""
Make sure mm->fd->mm and (mm->)->fd->mm->fd are identity
"""
cl_ctx = ctx_factory()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue)
# make sure degree is higher order than mesh
fspace_degree += mm_mesh.groups[0].order
# Make a function space and a function with unique values at each node
factory = InterpolatoryQuadratureSimplexGroupFactory(fspace_degree)
discr = Discretization(actx, mm_mesh, factory)
fdrake_connection = build_connection_to_firedrake(discr)
fdrake_mesh = fdrake_connection.firedrake_fspace().mesh()
dtype = fdrake_mesh.coordinates.dat.data.dtype
mm_unique = discr.zeros(actx, dtype=dtype)
unique_vals = np.arange(np.size(mm_unique[0]), dtype=dtype)
mm_unique[0].set(unique_vals.reshape(mm_unique[0].shape))
mm_unique_copy = DOFArray(actx, (mm_unique[0].copy(), ))
# Test for idempotency mm->fd->mm
fdrake_unique = fdrake_connection.from_meshmode(mm_unique)
fdrake_connection.from_firedrake(fdrake_unique, out=mm_unique_copy)
np.testing.assert_allclose(actx.to_numpy(mm_unique_copy[0]),
actx.to_numpy(mm_unique[0]),
atol=CLOSE_ATOL)
# Test for idempotency (mm->)fd->mm->fd
fdrake_unique_copy = fdrake_connection.from_meshmode(mm_unique_copy)
np.testing.assert_allclose(fdrake_unique_copy.dat.data,
fdrake_unique.dat.data,
atol=CLOSE_ATOL)
def main():
cl_ctx = cl.create_some_context()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue)
nel_1d = 16
from meshmode.mesh.generation import generate_regular_rect_mesh
mesh = generate_regular_rect_mesh(a=(-0.5, -0.5),
b=(0.5, 0.5),
n=(nel_1d, nel_1d))
order = 3
# no deep meaning here, just a fudge factor
dt = 0.75 / (nel_1d * order**2)
print("%d elements" % mesh.nelements)
discr = DGDiscretization(actx, mesh, order=order)
fields = flat_obj_array(bump(actx, discr),
[discr.zeros(actx) for i in range(discr.dim)])
from meshmode.discretization.visualization import make_visualizer
vis = make_visualizer(actx, discr.volume_discr, discr.order + 3)
def rhs(t, w):
return wave_operator(actx, discr, c=1, w=w)
t = 0
t_final = 3
istep = 0
while t < t_final:
fields = rk4_step(fields, t, dt, rhs)
if istep % 10 == 0:
# FIXME: Maybe an integral function to go with the
# DOFArray would be nice?
assert len(fields[0]) == 1
print(istep, t, la.norm(actx.to_numpy(fields[0][0])))
vis.write_vtk_file("fld-wave-min-%04d.vtu" % istep, [
("u", fields[0]),
("v", fields[1:]),
])
t += dt
istep += 1
def _visualize_refinement(actx: PyOpenCLArrayContext,
discr,
niter,
stage_nr,
stage_name,
flags,
visualize=False):
if not visualize:
return
if stage_nr not in (1, 2):
raise ValueError("unexpected stage number")
flags = flags.get()
logger.info("for stage %s: splitting %d/%d stage-%d elements", stage_name,
np.sum(flags), discr.mesh.nelements, stage_nr)
from meshmode.discretization.visualization import make_visualizer
vis = make_visualizer(actx, discr, 3)
assert len(flags) == discr.mesh.nelements
flags = flags.astype(bool)
nodes_flags_template = discr.zeros(actx)
nodes_flags = []
for grp in discr.groups:
meg = grp.mesh_el_group
nodes_flags_grp = actx.to_numpy(nodes_flags_template[grp.index])
nodes_flags_grp[flags[meg.element_nr_base:meg.nelements +
meg.element_nr_base]] = 1
nodes_flags.append(actx.from_numpy(nodes_flags_grp))
nodes_flags = DOFArray(actx, tuple(nodes_flags))
vis_data = [
("refine_flags", nodes_flags),
]
if 0:
from pytential import sym, bind
bdry_normals = bind(discr, sym.normal(
discr.ambient_dim))(actx).as_vector(dtype=object)
vis_data.append(("bdry_normals", bdry_normals), )
vis.write_vtk_file(f"refinement-{stage_name}-{niter:03d}.vtu", vis_data)
def test_lump_init(ctx_factory):
"""
Simple test to check that Lump initializer
creates the expected solution field.
"""
cl_ctx = ctx_factory()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue)
dim = 2
nel_1d = 4
from meshmode.mesh.generation import generate_regular_rect_mesh
mesh = generate_regular_rect_mesh(a=[(0.0, ), (-5.0, )],
b=[(10.0, ), (5.0, )],
nelements_per_axis=(nel_1d, ) * dim)
order = 3
logger.info(f"Number of elements: {mesh.nelements}")
discr = EagerDGDiscretization(actx, mesh, order=order)
nodes = thaw(actx, discr.nodes())
# Init soln with Vortex
center = np.zeros(shape=(dim, ))
velocity = np.zeros(shape=(dim, ))
center[0] = 5
velocity[0] = 1
lump = Lump(dim=dim, center=center, velocity=velocity)
cv = lump(nodes)
p = 0.4 * (cv.energy - 0.5 * np.dot(cv.momentum, cv.momentum) / cv.mass)
exp_p = 1.0
errmax = actx.to_numpy(discr.norm(p - exp_p, np.inf))
logger.info(f"lump_soln = {cv}")
logger.info(f"pressure = {p}")
assert errmax < 1e-15
def test_shock_init(ctx_factory):
"""
Simple test to check that Shock1D initializer
creates the expected solution field.
"""
cl_ctx = ctx_factory()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue)
nel_1d = 10
dim = 2
from meshmode.mesh.generation import generate_regular_rect_mesh
mesh = generate_regular_rect_mesh(a=[(0.0, ), (1.0, )],
b=[(-0.5, ), (0.5, )],
nelements_per_axis=(nel_1d, ) * dim)
order = 3
print(f"Number of elements: {mesh.nelements}")
discr = EagerDGDiscretization(actx, mesh, order=order)
nodes = thaw(actx, discr.nodes())
initr = SodShock1D()
initsoln = initr(time=0.0, x_vec=nodes)
print("Sod Soln:", initsoln)
xpl = 1.0
xpr = 0.1
tol = 1e-15
nodes_x = nodes[0]
eos = IdealSingleGas()
p = eos.pressure(initsoln)
assert actx.to_numpy(
discr.norm(actx.np.where(nodes_x < 0.5, p - xpl, p - xpr),
np.inf)) < tol
def test_mass_mat_trig(ctx_factory, ambient_dim, quad_tag):
"""Check the integral of some trig functions on an interval using the mass
matrix.
"""
cl_ctx = ctx_factory()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue)
nelements = 17
order = 4
a = -4.0 * np.pi
b = +9.0 * np.pi
true_integral = 13 * np.pi / 2 * (b - a)**(ambient_dim - 1)
from meshmode.discretization.poly_element import QuadratureSimplexGroupFactory
dd_quad = sym.DOFDesc(sym.DTAG_VOLUME_ALL, quad_tag)
if quad_tag is sym.QTAG_NONE:
quad_tag_to_group_factory = {}
else:
quad_tag_to_group_factory = {
quad_tag: QuadratureSimplexGroupFactory(order=2 * order)
}
from meshmode.mesh.generation import generate_regular_rect_mesh
mesh = generate_regular_rect_mesh(a=(a, ) * ambient_dim,
b=(b, ) * ambient_dim,
n=(nelements, ) * ambient_dim,
order=1)
discr = DGDiscretizationWithBoundaries(
actx,
mesh,
order=order,
quad_tag_to_group_factory=quad_tag_to_group_factory)
def _get_variables_on(dd):
sym_f = sym.var("f", dd=dd)
sym_x = sym.nodes(ambient_dim, dd=dd)
sym_ones = sym.Ones(dd)
return sym_f, sym_x, sym_ones
sym_f, sym_x, sym_ones = _get_variables_on(sym.DD_VOLUME)
f_volm = actx.to_numpy(flatten(bind(discr, sym.cos(sym_x[0])**2)(actx)))
ones_volm = actx.to_numpy(flatten(bind(discr, sym_ones)(actx)))
sym_f, sym_x, sym_ones = _get_variables_on(dd_quad)
f_quad = bind(discr, sym.cos(sym_x[0])**2)(actx)
ones_quad = bind(discr, sym_ones)(actx)
mass_op = bind(discr, sym.MassOperator(dd_quad, sym.DD_VOLUME)(sym_f))
num_integral_1 = np.dot(ones_volm,
actx.to_numpy(flatten(mass_op(f=f_quad))))
err_1 = abs(num_integral_1 - true_integral)
assert err_1 < 1e-9, err_1
num_integral_2 = np.dot(f_volm,
actx.to_numpy(flatten(mass_op(f=ones_quad))))
err_2 = abs(num_integral_2 - true_integral)
assert err_2 < 1.0e-9, err_2
if quad_tag is sym.QTAG_NONE:
# NOTE: `integral` always makes a square mass matrix and
# `QuadratureSimplexGroupFactory` does not have a `mass_matrix` method.
num_integral_3 = bind(discr, sym.integral(sym_f, dd=dd_quad))(f=f_quad)
err_3 = abs(num_integral_3 - true_integral)
assert err_3 < 5.0e-10, err_3
def test_ellipse_eigenvalues(ctx_factory,
ellipse_aspect,
mode_nr,
qbx_order,
force_direct,
visualize=False):
logging.basicConfig(level=logging.INFO)
print("ellipse_aspect: %s, mode_nr: %d, qbx_order: %d" %
(ellipse_aspect, mode_nr, qbx_order))
cl_ctx = ctx_factory()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue)
target_order = 8
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import \
InterpolatoryQuadratureSimplexGroupFactory
from pytential.qbx import QBXLayerPotentialSource
from pytools.convergence import EOCRecorder
s_eoc_rec = EOCRecorder()
d_eoc_rec = EOCRecorder()
sp_eoc_rec = EOCRecorder()
if ellipse_aspect != 1:
nelements_values = [60, 100, 150, 200]
else:
nelements_values = [30, 70]
# See
#
# [1] G. J. Rodin and O. Steinbach, "Boundary Element Preconditioners
# for Problems Defined on Slender Domains", SIAM Journal on Scientific
# Computing, Vol. 24, No. 4, pg. 1450, 2003.
# https://dx.doi.org/10.1137/S1064827500372067
for nelements in nelements_values:
mesh = make_curve_mesh(partial(ellipse, ellipse_aspect),
np.linspace(0, 1, nelements + 1), target_order)
fmm_order = 12
if force_direct:
fmm_order = False
pre_density_discr = Discretization(
actx, mesh,
InterpolatoryQuadratureSimplexGroupFactory(target_order))
qbx = QBXLayerPotentialSource(
pre_density_discr,
4 * target_order,
qbx_order,
fmm_order=fmm_order,
_expansions_in_tree_have_extent=True,
)
places = GeometryCollection(qbx)
density_discr = places.get_discretization(places.auto_source.geometry)
from meshmode.dof_array import thaw, flatten
nodes = thaw(actx, density_discr.nodes())
if visualize:
# plot geometry, centers, normals
centers = bind(places, sym.expansion_centers(qbx.ambient_dim,
+1))(actx)
normals = bind(places,
sym.normal(qbx.ambient_dim))(actx).as_vector(object)
nodes_h = np.array(
[actx.to_numpy(axis) for axis in flatten(nodes)])
centers_h = np.array(
[actx.to_numpy(axis) for axis in flatten(centers)])
normals_h = np.array(
[actx.to_numpy(axis) for axis in flatten(normals)])
pt.plot(nodes_h[0], nodes_h[1], "x-")
pt.plot(centers_h[0], centers_h[1], "o")
pt.quiver(nodes_h[0], nodes_h[1], normals_h[0], normals_h[1])
pt.gca().set_aspect("equal")
pt.show()
angle = actx.np.arctan2(nodes[1] * ellipse_aspect, nodes[0])
ellipse_fraction = ((1 - ellipse_aspect) /
(1 + ellipse_aspect))**mode_nr
# (2.6) in [1]
J = actx.np.sqrt( # noqa
actx.np.sin(angle)**2 +
(1 / ellipse_aspect)**2 * actx.np.cos(angle)**2)
from sumpy.kernel import LaplaceKernel
lap_knl = LaplaceKernel(2)
# {{{ single layer
sigma_sym = sym.var("sigma")
s_sigma_op = sym.S(lap_knl, sigma_sym, qbx_forced_limit=+1)
sigma = actx.np.cos(mode_nr * angle) / J
s_sigma = bind(places, s_sigma_op)(actx, sigma=sigma)
# SIGN BINGO! :)
s_eigval = 1 / (2 * mode_nr) * (1 + (-1)**mode_nr * ellipse_fraction)
# (2.12) in [1]
s_sigma_ref = s_eigval * J * sigma
if 0:
#pt.plot(s_sigma.get(), label="result")
#pt.plot(s_sigma_ref.get(), label="ref")
pt.plot(actx.to_numpy(flatten(s_sigma_ref - s_sigma)), label="err")
pt.legend()
pt.show()
h_max = bind(places, sym.h_max(qbx.ambient_dim))(actx)
s_err = (norm(density_discr, s_sigma - s_sigma_ref) /
norm(density_discr, s_sigma_ref))
s_eoc_rec.add_data_point(h_max, s_err)
# }}}
# {{{ double layer
d_sigma_op = sym.D(lap_knl, sigma_sym, qbx_forced_limit="avg")
sigma = actx.np.cos(mode_nr * angle)
d_sigma = bind(places, d_sigma_op)(actx, sigma=sigma)
# SIGN BINGO! :)
d_eigval = -(-1)**mode_nr * 1 / 2 * ellipse_fraction
d_sigma_ref = d_eigval * sigma
if 0:
pt.plot(actx.to_numpy(flatten(d_sigma)), label="result")
pt.plot(actx.to_numpy(flatten(d_sigma_ref)), label="ref")
pt.legend()
pt.show()
if ellipse_aspect == 1:
d_ref_norm = norm(density_discr, sigma)
else:
d_ref_norm = norm(density_discr, d_sigma_ref)
d_err = (norm(density_discr, d_sigma - d_sigma_ref) / d_ref_norm)
d_eoc_rec.add_data_point(h_max, d_err)
# }}}
if ellipse_aspect == 1:
# {{{ S'
sp_sigma_op = sym.Sp(lap_knl,
sym.var("sigma"),
qbx_forced_limit="avg")
sigma = actx.np.cos(mode_nr * angle)
sp_sigma = bind(places, sp_sigma_op)(actx, sigma=sigma)
sp_eigval = 0
sp_sigma_ref = sp_eigval * sigma
sp_err = (norm(density_discr, sp_sigma - sp_sigma_ref) /
norm(density_discr, sigma))
sp_eoc_rec.add_data_point(h_max, sp_err)
# }}}
print("Errors for S:")
print(s_eoc_rec)
required_order = qbx_order + 1
assert s_eoc_rec.order_estimate() > required_order - 1.5
print("Errors for D:")
print(d_eoc_rec)
required_order = qbx_order
assert d_eoc_rec.order_estimate() > required_order - 1.5
if ellipse_aspect == 1:
print("Errors for S':")
print(sp_eoc_rec)
required_order = qbx_order
assert sp_eoc_rec.order_estimate() > required_order - 1.5
def test_target_specific_qbx(ctx_factory, op, helmholtz_k, qbx_order):
logging.basicConfig(level=logging.INFO)
cl_ctx = ctx_factory()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue)
target_order = 4
fmm_tol = 1e-3
from meshmode.mesh.generation import generate_icosphere
mesh = generate_icosphere(1, target_order)
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import \
InterpolatoryQuadratureSimplexGroupFactory
from pytential.qbx import QBXLayerPotentialSource
pre_density_discr = Discretization(
actx, mesh,
InterpolatoryQuadratureSimplexGroupFactory(target_order))
from sumpy.expansion.level_to_order import SimpleExpansionOrderFinder
qbx = QBXLayerPotentialSource(
pre_density_discr, 4*target_order,
qbx_order=qbx_order,
fmm_level_to_order=SimpleExpansionOrderFinder(fmm_tol),
fmm_backend="fmmlib",
_expansions_in_tree_have_extent=True,
_expansion_stick_out_factor=0.9,
_use_target_specific_qbx=False,
)
kernel_length_scale = 5 / abs(helmholtz_k) if helmholtz_k else None
places = {
"qbx": qbx,
"qbx_target_specific": qbx.copy(_use_target_specific_qbx=True)
}
from pytential.qbx.refinement import refine_geometry_collection
places = GeometryCollection(places, auto_where="qbx")
places = refine_geometry_collection(places,
kernel_length_scale=kernel_length_scale)
density_discr = places.get_discretization("qbx")
from meshmode.dof_array import thaw
nodes = thaw(actx, density_discr.nodes())
u_dev = actx.np.sin(nodes[0])
if helmholtz_k == 0:
kernel = LaplaceKernel(3)
kernel_kwargs = {}
else:
kernel = HelmholtzKernel(3, allow_evanescent=True)
kernel_kwargs = {"k": sym.var("k")}
u_sym = sym.var("u")
if op == "S":
op = sym.S
elif op == "D":
op = sym.D
elif op == "Sp":
op = sym.Sp
else:
raise ValueError("unknown operator: '%s'" % op)
expr = op(kernel, u_sym, qbx_forced_limit=-1, **kernel_kwargs)
from meshmode.dof_array import flatten
bound_op = bind(places, expr)
pot_ref = actx.to_numpy(flatten(bound_op(actx, u=u_dev, k=helmholtz_k)))
bound_op = bind(places, expr, auto_where="qbx_target_specific")
pot_tsqbx = actx.to_numpy(flatten(bound_op(actx, u=u_dev, k=helmholtz_k)))
assert np.allclose(pot_tsqbx, pot_ref, atol=1e-13, rtol=1e-13)
def test_target_association(ctx_factory,
curve_name,
curve_f,
nelements,
visualize=False):
cl_ctx = ctx_factory()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue)
# {{{ generate lpot source
order = 16
# Make the curve mesh.
mesh = make_curve_mesh(curve_f, np.linspace(0, 1, nelements + 1), order)
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import \
InterpolatoryQuadratureSimplexGroupFactory
factory = InterpolatoryQuadratureSimplexGroupFactory(order)
discr = Discretization(actx, mesh, factory)
lpot_source = QBXLayerPotentialSource(
discr,
qbx_order=order, # not used in target association
fine_order=order)
places = GeometryCollection(lpot_source)
# }}}
# {{{ generate targets
from pyopencl.clrandom import PhiloxGenerator
rng = PhiloxGenerator(cl_ctx, seed=RNG_SEED)
dd = places.auto_source.to_stage1()
centers = dof_array_to_numpy(
actx,
bind(
places,
sym.interleaved_expansion_centers(lpot_source.ambient_dim,
dofdesc=dd))(actx))
density_discr = places.get_discretization(dd.geometry)
noise = actx.to_numpy(
rng.uniform(queue, density_discr.ndofs, dtype=np.float, a=0.01, b=1.0))
tunnel_radius = dof_array_to_numpy(
actx,
bind(
places,
sym._close_target_tunnel_radii(lpot_source.ambient_dim,
dofdesc=dd))(actx))
def targets_from_sources(sign, dist, dim=2):
nodes = dof_array_to_numpy(
actx,
bind(places, sym.nodes(dim,
dofdesc=dd))(actx).as_vector(np.object))
normals = dof_array_to_numpy(
actx,
bind(places, sym.normal(dim,
dofdesc=dd))(actx).as_vector(np.object))
return actx.from_numpy(nodes + normals * sign * dist)
from pytential.target import PointsTarget
int_targets = PointsTarget(targets_from_sources(-1, noise * tunnel_radius))
ext_targets = PointsTarget(targets_from_sources(+1, noise * tunnel_radius))
far_targets = PointsTarget(
targets_from_sources(+1, FAR_TARGET_DIST_FROM_SOURCE))
# Create target discretizations.
target_discrs = (
# On-surface targets, interior
(density_discr, -1),
# On-surface targets, exterior
(density_discr, +1),
# Interior close targets
(int_targets, -2),
# Exterior close targets
(ext_targets, +2),
# Far targets, should not need centers
(far_targets, 0),
)
sizes = np.cumsum([discr.ndofs for discr, _ in target_discrs])
(
surf_int_slice,
surf_ext_slice,
vol_int_slice,
vol_ext_slice,
far_slice,
) = [slice(start, end) for start, end in zip(np.r_[0, sizes], sizes)]
# }}}
# {{{ run target associator and check
from pytential.qbx.target_assoc import (TargetAssociationCodeContainer,
associate_targets_to_qbx_centers)
from pytential.qbx.utils import TreeCodeContainer
code_container = TargetAssociationCodeContainer(actx,
TreeCodeContainer(actx))
target_assoc = (associate_targets_to_qbx_centers(
places,
places.auto_source,
code_container.get_wrangler(actx),
target_discrs,
target_association_tolerance=1e-10).get(queue=queue))
expansion_radii = dof_array_to_numpy(
actx,
bind(
places,
sym.expansion_radii(lpot_source.ambient_dim,
granularity=sym.GRANULARITY_CENTER))(actx))
from meshmode.dof_array import thaw
surf_targets = dof_array_to_numpy(actx, thaw(actx, density_discr.nodes()))
int_targets = actx.to_numpy(int_targets.nodes())
ext_targets = actx.to_numpy(ext_targets.nodes())
def visualize_curve_and_assoc():
import matplotlib.pyplot as plt
from meshmode.mesh.visualization import draw_curve
draw_curve(density_discr.mesh)
targets = int_targets
tgt_slice = surf_int_slice
plt.plot(centers[0], centers[1], "+", color="orange")
ax = plt.gca()
for tx, ty, tcenter in zip(targets[0, tgt_slice], targets[1,
tgt_slice],
target_assoc.target_to_center[tgt_slice]):
if tcenter >= 0:
ax.add_artist(
plt.Line2D(
(tx, centers[0, tcenter]),
(ty, centers[1, tcenter]),
))
ax.set_aspect("equal")
plt.show()
if visualize:
visualize_curve_and_assoc()
# Checks that the targets match with centers on the appropriate side and
# within the allowable distance.
def check_close_targets(centers, targets, true_side, target_to_center,
target_to_side_result, tgt_slice):
targets_have_centers = (target_to_center >= 0).all()
assert targets_have_centers
assert (target_to_side_result == true_side).all()
TOL = 1e-3
dists = la.norm((targets.T - centers.T[target_to_center]), axis=1)
assert (dists <= (1 + TOL) * expansion_radii[target_to_center]).all()
# Center side order = -1, 1, -1, 1, ...
target_to_center_side = 2 * (target_assoc.target_to_center % 2) - 1
# interior surface
check_close_targets(centers, surf_targets, -1,
target_assoc.target_to_center[surf_int_slice],
target_to_center_side[surf_int_slice], surf_int_slice)
# exterior surface
check_close_targets(centers, surf_targets, +1,
target_assoc.target_to_center[surf_ext_slice],
target_to_center_side[surf_ext_slice], surf_ext_slice)
# interior volume
check_close_targets(centers, int_targets, -1,
target_assoc.target_to_center[vol_int_slice],
target_to_center_side[vol_int_slice], vol_int_slice)
# exterior volume
check_close_targets(centers, ext_targets, +1,
target_assoc.target_to_center[vol_ext_slice],
target_to_center_side[vol_ext_slice], vol_ext_slice)
# Checks that far targets are not assigned a center.
assert (target_assoc.target_to_center[far_slice] == -1).all()
def test_sphere_eigenvalues(ctx_factory, mode_m, mode_n, qbx_order,
fmm_backend):
logging.basicConfig(level=logging.INFO)
special = pytest.importorskip("scipy.special")
cl_ctx = ctx_factory()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue)
target_order = 8
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import \
InterpolatoryQuadratureSimplexGroupFactory
from pytential.qbx import QBXLayerPotentialSource
from pytools.convergence import EOCRecorder
s_eoc_rec = EOCRecorder()
d_eoc_rec = EOCRecorder()
sp_eoc_rec = EOCRecorder()
dp_eoc_rec = EOCRecorder()
def rel_err(comp, ref):
return (norm(density_discr, comp - ref) / norm(density_discr, ref))
for nrefinements in [0, 1]:
from meshmode.mesh.generation import generate_icosphere
mesh = generate_icosphere(1, target_order)
from meshmode.mesh.refinement import Refiner
refiner = Refiner(mesh)
for i in range(nrefinements):
flags = np.ones(mesh.nelements, dtype=bool)
refiner.refine(flags)
mesh = refiner.get_current_mesh()
pre_density_discr = Discretization(
actx, mesh,
InterpolatoryQuadratureSimplexGroupFactory(target_order))
qbx = QBXLayerPotentialSource(
pre_density_discr,
4 * target_order,
qbx_order,
fmm_order=6,
fmm_backend=fmm_backend,
)
places = GeometryCollection(qbx)
from meshmode.dof_array import flatten, unflatten, thaw
density_discr = places.get_discretization(places.auto_source.geometry)
nodes = thaw(actx, density_discr.nodes())
r = actx.np.sqrt(nodes[0] * nodes[0] + nodes[1] * nodes[1] +
nodes[2] * nodes[2])
phi = actx.np.arccos(nodes[2] / r)
theta = actx.np.arctan2(nodes[0], nodes[1])
ymn = unflatten(
actx, density_discr,
actx.from_numpy(
special.sph_harm(mode_m, mode_n, actx.to_numpy(flatten(theta)),
actx.to_numpy(flatten(phi)))))
from sumpy.kernel import LaplaceKernel
lap_knl = LaplaceKernel(3)
# {{{ single layer
s_sigma_op = bind(
places, sym.S(lap_knl, sym.var("sigma"), qbx_forced_limit=+1))
s_sigma = s_sigma_op(actx, sigma=ymn)
s_eigval = 1 / (2 * mode_n + 1)
h_max = bind(places, sym.h_max(qbx.ambient_dim))(actx)
s_eoc_rec.add_data_point(h_max, rel_err(s_sigma, s_eigval * ymn))
# }}}
# {{{ double layer
d_sigma_op = bind(
places, sym.D(lap_knl, sym.var("sigma"), qbx_forced_limit="avg"))
d_sigma = d_sigma_op(actx, sigma=ymn)
d_eigval = -1 / (2 * (2 * mode_n + 1))
d_eoc_rec.add_data_point(h_max, rel_err(d_sigma, d_eigval * ymn))
# }}}
# {{{ S'
sp_sigma_op = bind(
places, sym.Sp(lap_knl, sym.var("sigma"), qbx_forced_limit="avg"))
sp_sigma = sp_sigma_op(actx, sigma=ymn)
sp_eigval = -1 / (2 * (2 * mode_n + 1))
sp_eoc_rec.add_data_point(h_max, rel_err(sp_sigma, sp_eigval * ymn))
# }}}
# {{{ D'
dp_sigma_op = bind(
places, sym.Dp(lap_knl, sym.var("sigma"), qbx_forced_limit="avg"))
dp_sigma = dp_sigma_op(actx, sigma=ymn)
dp_eigval = -(mode_n * (mode_n + 1)) / (2 * mode_n + 1)
dp_eoc_rec.add_data_point(h_max, rel_err(dp_sigma, dp_eigval * ymn))
# }}}
print("Errors for S:")
print(s_eoc_rec)
required_order = qbx_order + 1
assert s_eoc_rec.order_estimate() > required_order - 1.5
print("Errors for D:")
print(d_eoc_rec)
required_order = qbx_order
assert d_eoc_rec.order_estimate() > required_order - 0.5
print("Errors for S':")
print(sp_eoc_rec)
required_order = qbx_order
assert sp_eoc_rec.order_estimate() > required_order - 1.5
print("Errors for D':")
print(dp_eoc_rec)
required_order = qbx_order
assert dp_eoc_rec.order_estimate() > required_order - 1.5
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 test_from_fd_transfer(ctx_factory, fspace_degree, fdrake_mesh_name,
fdrake_mesh_pars, dim, only_convert_bdy):
"""
Make sure creating a function which projects onto
one dimension then transports it is the same
(up to resampling error) as projecting to one
dimension on the transported mesh
"""
# build estimate-of-convergence recorder
from pytools.convergence import EOCRecorder
# (fd -> mm ? True : False, dimension projecting onto)
eoc_recorders = {(True, d): EOCRecorder() for d in range(dim)}
if not only_convert_bdy:
for d in range(dim):
eoc_recorders[(False, d)] = EOCRecorder()
# make a computing context
cl_ctx = ctx_factory()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue)
def get_fdrake_mesh_and_h_from_par(mesh_par):
if fdrake_mesh_name == "UnitInterval":
assert dim == 1
n = mesh_par
fdrake_mesh = UnitIntervalMesh(n)
h = 1 / n
elif fdrake_mesh_name == "UnitSquare":
assert dim == 2
n = mesh_par
fdrake_mesh = UnitSquareMesh(n, n)
h = 1 / n
elif fdrake_mesh_name == "UnitCube":
assert dim == 3
n = mesh_par
fdrake_mesh = UnitCubeMesh(n, n, n)
h = 1 / n
elif fdrake_mesh_name in ("blob2d-order1", "blob2d-order4"):
assert dim == 2
if fdrake_mesh_name == "blob2d-order1":
from firedrake import Mesh
fdrake_mesh = Mesh(f"{fdrake_mesh_name}-h{mesh_par}.msh",
dim=dim)
else:
from meshmode.mesh.io import read_gmsh
from meshmode.interop.firedrake import export_mesh_to_firedrake
mm_mesh = read_gmsh(f"{fdrake_mesh_name}-h{mesh_par}.msh",
force_ambient_dim=dim)
fdrake_mesh, _, _ = export_mesh_to_firedrake(mm_mesh)
h = float(mesh_par)
elif fdrake_mesh_name == "warp":
from meshmode.mesh.generation import generate_warped_rect_mesh
from meshmode.interop.firedrake import export_mesh_to_firedrake
mm_mesh = generate_warped_rect_mesh(dim, order=4, n=mesh_par)
fdrake_mesh, _, _ = export_mesh_to_firedrake(mm_mesh)
h = 1 / mesh_par
else:
raise ValueError("fdrake_mesh_name not recognized")
return (fdrake_mesh, h)
# Record error for each refinement of each mesh
for mesh_par in fdrake_mesh_pars:
fdrake_mesh, h = get_fdrake_mesh_and_h_from_par(mesh_par)
# make function space and build connection
fdrake_fspace = FunctionSpace(fdrake_mesh, "DG", fspace_degree)
if only_convert_bdy:
fdrake_connection = \
build_connection_from_firedrake(actx,
fdrake_fspace,
restrict_to_boundary="on_boundary")
else:
fdrake_connection = build_connection_from_firedrake(
actx, fdrake_fspace)
# get this for making functions in firedrake
spatial_coord = SpatialCoordinate(fdrake_mesh)
# get nodes in handier format for making meshmode functions
discr = fdrake_connection.discr
# nodes is np array (ambient_dim,) of DOFArray (ngroups,)
# of arrays (nelements, nunit_dofs), we want a single np array
# of shape (ambient_dim, nelements, nunit_dofs)
nodes = discr.nodes()
group_nodes = np.array(
[actx.to_numpy(dof_arr[0]) for dof_arr in nodes])
# Now, for each coordinate d, test transferring the function
# x -> sin(dth component of x)
for d in range(dim):
fdrake_f = Function(fdrake_fspace).interpolate(
sin(spatial_coord[d]))
# transport fdrake function and put in numpy
fd2mm_f = fdrake_connection.from_firedrake(fdrake_f, actx=actx)
fd2mm_f = actx.to_numpy(fd2mm_f[0])
meshmode_f = np.sin(group_nodes[d, :, :])
# record fd -> mm error
err = np.max(np.abs(fd2mm_f - meshmode_f))
eoc_recorders[(True, d)].add_data_point(h, err)
if not only_convert_bdy:
# now transport mm -> fd
meshmode_f_dofarr = discr.zeros(actx)
meshmode_f_dofarr[0][:] = meshmode_f
mm2fd_f = fdrake_connection.from_meshmode(meshmode_f_dofarr)
# record mm -> fd error
err = np.max(np.abs(fdrake_f.dat.data - mm2fd_f.dat.data))
eoc_recorders[(False, d)].add_data_point(h, err)
# assert that order is correct or error is "low enough"
for ((fd2mm, d), eoc_rec) in eoc_recorders.items():
print(
"\nfiredrake -> meshmode: %s\nvector *x* -> *sin(x[%s])*\n" %
(fd2mm, d), eoc_rec)
assert (eoc_rec.order_estimate() >= fspace_degree
or eoc_rec.max_error() < 2e-14)
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),
])
_expansion_stick_out_factor=getattr(
case, "_expansion_stick_out_factor", 0),
)
places = GeometryCollection(qbx)
from pytential.qbx.refinement import refine_geometry_collection
kernel_length_scale = 5 / case.k if case.k else None
places = refine_geometry_collection(places,
kernel_length_scale=kernel_length_scale)
# {{{ compute values of a solution to the PDE
density_discr = places.get_discretization(places.auto_source.geometry)
from meshmode.dof_array import thaw, flatten, unflatten
nodes_host = [actx.to_numpy(axis)
for axis in flatten(thaw(actx, density_discr.nodes()))]
normal = bind(places, sym.normal(d))(actx).as_vector(object)
normal_host = [actx.to_numpy(axis)for axis in flatten(normal)]
if k != 0:
if d == 2:
angle = 0.3
wave_vec = np.array([np.cos(angle), np.sin(angle)])
u = np.exp(1j*k*np.tensordot(wave_vec, nodes_host, axes=1))
grad_u = 1j*k*wave_vec[:, np.newaxis]*u
elif d == 3:
center = np.array([3, 1, 2])
diff = nodes_host - center[:, np.newaxis]
r = la.norm(diff, axis=0)
u = np.exp(1j*k*r) / r
def main():
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)
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(actx.freeze(actx.from_numpy(fplot.points)))
},
auto_where=("qbx", "targets"))
density_discr = places.get_discretization("unaccel_qbx")
nodes = thaw(density_discr.nodes(), actx)
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 = actx.to_numpy(
bind(places, op, auto_where=("unaccel_qbx", "targets"))(actx,
sigma=sigma,
k=k))
fmm_fld_in_vol = actx.to_numpy(
bind(places, op, auto_where=("qbx", "targets"))(actx, sigma=sigma,
k=k))
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)
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 timing_run(nx, ny, visualize=False):
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)
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 knl, knl_args, tree, 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
nodes = thaw(density_discr.nodes(), actx)
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 = 1 + density_discr.zeros(actx)
sym_op = sym_op.copy(qbx_forced_limit=None)
indicator = actx.to_numpy(
bind(places, sym_op,
auto_where=("qbx_indicator",
"plot_targets"))(actx, sigma=ones_density, k=k))
try:
fld_in_vol = actx.to_numpy(
bind(places,
sym_op,
auto_where=("qbx_target_assoc",
"plot_targets"))(actx, sigma=sigma, k=k))
except QBXTargetAssociationFailedException as e:
fplot.write_vtk_file("scaling-study-failed-targets.vts", [
("failed", actx.to_numpy(e.failed_target_flags)),
])
raise
fplot.write_vtk_file(f"scaling-study-potential-{nx}-{ny}.vts", [
("potential", fld_in_vol),
("indicator", indicator),
])
return (mesh.nelements, elapsed)
def test_from_fd_idempotency(ctx_factory, fdrake_mesh, fspace_degree,
fspace_type, only_convert_bdy):
"""
Make sure fd->mm->fd and (fd->)->mm->fd->mm are identity
"""
# Make a function space and a function with unique values at each node
if fspace_type == "scalar":
fdrake_fspace = FunctionSpace(fdrake_mesh, "DG", fspace_degree)
# Just use the node nr
fdrake_unique = Function(fdrake_fspace)
fdrake_unique.dat.data[:] = np.arange(fdrake_unique.dat.data.shape[0])
elif fspace_type == "vector":
fdrake_fspace = VectorFunctionSpace(fdrake_mesh, "DG", fspace_degree)
# use the coordinates
xx = SpatialCoordinate(fdrake_fspace.mesh())
fdrake_unique = Function(fdrake_fspace).interpolate(xx)
elif fspace_type == "tensor":
fdrake_fspace = TensorFunctionSpace(fdrake_mesh, "DG", fspace_degree)
# use the coordinates, duplicated into the right tensor shape
xx = SpatialCoordinate(fdrake_fspace.mesh())
dim = fdrake_fspace.mesh().geometric_dimension()
unique_expr = as_tensor([xx for _ in range(dim)])
fdrake_unique = Function(fdrake_fspace).interpolate(unique_expr)
# Make connection
cl_ctx = ctx_factory()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue)
# If only converting boundary, first go ahead and do one round of
# fd->mm->fd. This will zero out any degrees of freedom absent in
# the meshmode mesh (because they are not associated to cells
# with >= 1 node on the boundary)
#
# Otherwise, just continue as normal
if only_convert_bdy:
fdrake_connection = \
build_connection_from_firedrake(actx,
fdrake_fspace,
restrict_to_boundary="on_boundary")
temp = fdrake_connection.from_firedrake(fdrake_unique, actx=actx)
fdrake_unique = fdrake_connection.from_meshmode(temp)
else:
fdrake_connection = build_connection_from_firedrake(
actx, fdrake_fspace)
# Test for idempotency fd->mm->fd
mm_field = fdrake_connection.from_firedrake(fdrake_unique, actx=actx)
fdrake_unique_copy = Function(fdrake_fspace)
fdrake_connection.from_meshmode(mm_field, out=fdrake_unique_copy)
np.testing.assert_allclose(fdrake_unique_copy.dat.data,
fdrake_unique.dat.data,
atol=CLOSE_ATOL)
# Test for idempotency (fd->)mm->fd->mm
mm_field_copy = fdrake_connection.from_firedrake(fdrake_unique_copy,
actx=actx)
if fspace_type == "scalar":
np.testing.assert_allclose(actx.to_numpy(mm_field_copy[0]),
actx.to_numpy(mm_field[0]),
atol=CLOSE_ATOL)
else:
for dof_arr_cp, dof_arr in zip(mm_field_copy.flatten(),
mm_field.flatten()):
np.testing.assert_allclose(actx.to_numpy(dof_arr_cp[0]),
actx.to_numpy(dof_arr[0]),
atol=CLOSE_ATOL)
def test_to_fd_transfer(ctx_factory, fspace_degree, mesh_name, mesh_pars, dim):
"""
Make sure creating a function which projects onto
one dimension then transports it is the same
(up to resampling error) as projecting to one
dimension on the transported mesh
"""
# build estimate-of-convergence recorder
from pytools.convergence import EOCRecorder
# dimension projecting onto -> EOCRecorder
eoc_recorders = {d: EOCRecorder() for d in range(dim)}
# make a computing context
cl_ctx = ctx_factory()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue)
# Get each of the refinements of the meshmeshes and record
# conversions errors
for mesh_par in mesh_pars:
if mesh_name in ("blob2d-order1", "blob2d-order4"):
assert dim == 2
from meshmode.mesh.io import read_gmsh
mm_mesh = read_gmsh(f"{mesh_name}-h{mesh_par}.msh",
force_ambient_dim=dim)
h = float(mesh_par)
elif mesh_name == "warp":
from meshmode.mesh.generation import generate_warped_rect_mesh
mm_mesh = generate_warped_rect_mesh(dim, order=4, n=mesh_par)
h = 1 / mesh_par
else:
raise ValueError("mesh_name not recognized")
# Make discr and connect it to firedrake
factory = InterpolatoryQuadratureSimplexGroupFactory(fspace_degree)
discr = Discretization(actx, mm_mesh, factory)
fdrake_connection = build_connection_to_firedrake(discr)
fdrake_fspace = fdrake_connection.firedrake_fspace()
spatial_coord = SpatialCoordinate(fdrake_fspace.mesh())
# get the group's nodes in a numpy array
nodes = discr.nodes()
group_nodes = np.array(
[actx.to_numpy(dof_arr[0]) for dof_arr in nodes])
for d in range(dim):
meshmode_f = discr.zeros(actx)
meshmode_f[0][:] = group_nodes[d, :, :]
# connect to firedrake and evaluate expr in firedrake
fdrake_f = Function(fdrake_fspace).interpolate(spatial_coord[d])
# transport to firedrake and record error
mm2fd_f = fdrake_connection.from_meshmode(meshmode_f)
err = np.max(np.abs(fdrake_f.dat.data - mm2fd_f.dat.data))
eoc_recorders[d].add_data_point(h, err)
# assert that order is correct or error is "low enough"
for d, eoc_rec in eoc_recorders.items():
print("\nvector *x* -> *x[%s]*\n" % d, eoc_rec)
assert (eoc_rec.order_estimate() >= fspace_degree
or eoc_rec.max_error() < 2e-14)
def 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 test_off_surface_eval(ctx_factory, use_fmm, visualize=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 = 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(
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(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
err = actx.np.fabs(fld_in_vol - fld_in_vol_exact)
linf_err = actx.to_numpy(err).max()
print("l_inf error:", 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
("Einc", inc_field_scat.e),
("Hinc", inc_field_scat.h),
("bdry_normals", bdry_normals),
("e_bc_residual", eh_bc_values[:3]),
("h_bc_residual", eh_bc_values[3]),
])
from pytential.qbx import QBXTargetAssociationFailedException
try:
fplot_repr = eval_repr_at(places,
target="plot_targets",
source="qbx_target_tol")
except QBXTargetAssociationFailedException as e:
fplot.write_vtk_file("failed-targets.vts", [
("failed_targets",
actx.to_numpy(actx.thaw(e.failed_target_flags))),
])
raise
fplot_repr = EHField(vector_from_device(actx.queue, fplot_repr))
fplot_inc = EHField(
vector_from_device(
actx.queue, eval_inc_field_at(places,
target="plot_targets")))
fplot.write_vtk_file("potential-%s.vts" % resolution, [
("E", fplot_repr.e),
("H", fplot_repr.h),
("Einc", fplot_inc.e),
("Hinc", fplot_inc.h),
])
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),
])
qbx = case.get_layer_potential(actx, case.resolutions[-1],
case.target_order)
places = GeometryCollection(qbx, auto_where=case.name)
density_discr = places.get_discretization(case.name)
srcindices = case.get_block_indices(actx,
density_discr,
matrix_indices=False)
from pytential.linalg.proxy import ProxyGenerator
generator = ProxyGenerator(places)
proxies, pxyranges, pxycenters, pxyradii = \
generator(actx, places.auto_source, srcindices)
proxies = np.vstack([actx.to_numpy(p) for p in proxies])
pxyranges = actx.to_numpy(pxyranges)
pxycenters = np.vstack([actx.to_numpy(c) for c in pxycenters])
pxyradii = actx.to_numpy(pxyradii)
for i in range(srcindices.nblocks):
ipxy = np.s_[pxyranges[i]:pxyranges[i + 1]]
r = la.norm(proxies[:, ipxy] - pxycenters[:, i].reshape(-1, 1), axis=0)
assert np.allclose(r - pxyradii[i], 0.0, atol=1.0e-14)
# }}}
# {{{ visualization
srcindices = srcindices.get(queue)
def test_interpolation(ctx_factory, name, source_discr_stage,
target_granularity):
ctx = ctx_factory()
queue = cl.CommandQueue(ctx)
actx = PyOpenCLArrayContext(queue)
nelements = 32
target_order = 7
qbx_order = 4
where = sym.as_dofdesc("test_interpolation")
from_dd = sym.DOFDescriptor(geometry=where.geometry,
discr_stage=source_discr_stage,
granularity=sym.GRANULARITY_NODE)
to_dd = sym.DOFDescriptor(geometry=where.geometry,
discr_stage=sym.QBX_SOURCE_QUAD_STAGE2,
granularity=target_granularity)
mesh = make_curve_mesh(starfish, np.linspace(0.0, 1.0, nelements + 1),
target_order)
discr = Discretization(
actx, mesh, InterpolatoryQuadratureSimplexGroupFactory(target_order))
from pytential.qbx import QBXLayerPotentialSource
qbx = QBXLayerPotentialSource(discr,
fine_order=4 * target_order,
qbx_order=qbx_order,
fmm_order=False)
from pytential import GeometryCollection
places = GeometryCollection(qbx, auto_where=where)
sigma_sym = sym.var("sigma")
op_sym = sym.sin(sym.interp(from_dd, to_dd, sigma_sym))
bound_op = bind(places, op_sym, auto_where=where)
from meshmode.dof_array import thaw, flatten, unflatten
def discr_and_nodes(stage):
density_discr = places.get_discretization(where.geometry, stage)
return density_discr, np.array([
actx.to_numpy(flatten(axis))
for axis in thaw(actx, density_discr.nodes())
])
_, target_nodes = discr_and_nodes(sym.QBX_SOURCE_QUAD_STAGE2)
source_discr, source_nodes = discr_and_nodes(source_discr_stage)
sigma_target = np.sin(la.norm(target_nodes, axis=0))
sigma_dev = unflatten(actx, source_discr,
actx.from_numpy(la.norm(source_nodes, axis=0)))
sigma_target_interp = actx.to_numpy(
flatten(bound_op(actx, sigma=sigma_dev)))
if name in ("default", "default_explicit", "stage2", "quad"):
error = la.norm(sigma_target_interp -
sigma_target) / la.norm(sigma_target)
assert error < 1.0e-10
elif name in ("stage2_center", ):
assert len(sigma_target_interp) == 2 * len(sigma_target)
else:
raise ValueError(f"unknown test case name: {name}")
