def test_surface_mass_operator_inverse(actx_factory, name):
actx = actx_factory()
# {{{ cases
if name == "2-1-ellipse":
from mesh_data import EllipseMeshBuilder
builder = EllipseMeshBuilder(radius=3.1, aspect_ratio=2.0)
elif name == "spheroid":
from mesh_data import SpheroidMeshBuilder
builder = SpheroidMeshBuilder()
else:
raise ValueError("unknown geometry name: %s" % name)
# }}}
# {{{ convergence
from pytools.convergence import EOCRecorder
eoc = EOCRecorder()
for resolution in builder.resolutions:
mesh = builder.get_mesh(resolution, builder.mesh_order)
discr = DiscretizationCollection(actx, mesh, order=builder.order)
volume_discr = discr.discr_from_dd(dof_desc.DD_VOLUME)
logger.info("ndofs: %d", volume_discr.ndofs)
logger.info("nelements: %d", volume_discr.mesh.nelements)
# {{{ compute inverse mass
dd = dof_desc.DD_VOLUME
sym_f = sym.cos(4.0 * sym.nodes(mesh.ambient_dim, dd)[0])
sym_op = sym.InverseMassOperator(dd, dd)(sym.MassOperator(dd, dd)(
sym.var("f")))
f = bind(discr, sym_f)(actx)
f_inv = bind(discr, sym_op)(actx, f=f)
inv_error = bind(
discr,
sym.norm(2,
sym.var("x") - sym.var("y")) / sym.norm(2, sym.var("y")))(
actx, x=f_inv, y=f)
# }}}
h_max = bind(
discr,
sym.h_max_from_volume(discr.ambient_dim, dim=discr.dim,
dd=dd))(actx)
eoc.add_data_point(h_max, inv_error)
# }}}
logger.info("inverse mass error\n%s", str(eoc))
# NOTE: both cases give 1.0e-16-ish at the moment, but just to be on the
# safe side, choose a slightly larger tolerance
assert eoc.max_error() < 1.0e-14
def sym_operator(self):
u = sym.var("u")
# boundary conditions -------------------------------------------------
bc_in = self.inflow_u
all_faces_dd = sym.DOFDesc(sym.FACE_RESTR_ALL, self.quad_tag)
boundary_dd = sym.DOFDesc(sym.BTAG_ALL, self.quad_tag)
def flux(pair):
return sym.interp(pair.dd, all_faces_dd)(
self.flux(pair))
quad_dd = sym.DOFDesc("vol", self.quad_tag)
to_quad = sym.interp("vol", quad_dd)
stiff_t = sym.stiffness_t(self.ambient_dim, quad_dd, "vol")
quad_v = to_quad(self.v)
quad_u = to_quad(u)
return sym.InverseMassOperator()(
(stiff_t[0](quad_u * quad_v[0]) + stiff_t[1](quad_u * quad_v[1]))
- sym.FaceMassOperator(all_faces_dd, "vol")(
flux(sym.int_tpair(u, self.quad_tag))
+ flux(sym.bv_tpair(boundary_dd, u, bc_in))
# FIXME: Add back support for inflow/outflow tags
#+ flux(sym.bv_tpair(self.inflow_tag, u, bc_in))
#+ flux(sym.bv_tpair(self.outflow_tag, u, bc_out))
))
def sym_operator(self):
u = sym.var("u")
def flux(pair):
return sym.project(pair.dd, face_dd)(self.flux(pair))
face_dd = sym.DOFDesc(sym.FACE_RESTR_ALL, self.quad_tag)
boundary_dd = sym.DOFDesc(sym.BTAG_ALL, self.quad_tag)
quad_dd = sym.DOFDesc(sym.DTAG_VOLUME_ALL, self.quad_tag)
to_quad = sym.project(sym.DD_VOLUME, quad_dd)
stiff_t_op = sym.stiffness_t(self.ambient_dim,
dd_in=quad_dd, dd_out=sym.DD_VOLUME)
quad_v = to_quad(self.v)
quad_u = to_quad(u)
return sym.InverseMassOperator()(
sum(stiff_t_op[n](quad_u * quad_v[n])
for n in range(self.ambient_dim))
- sym.FaceMassOperator(face_dd, sym.DD_VOLUME)(
flux(sym.int_tpair(u, self.quad_tag))
+ flux(sym.bv_tpair(boundary_dd, u, self.inflow_u))
# FIXME: Add back support for inflow/outflow tags
#+ flux(sym.bv_tpair(self.inflow_tag, u, bc_in))
#+ flux(sym.bv_tpair(self.outflow_tag, u, bc_out))
))
def sym_operator(self, w=None):
"""The full operator template - the high level description of
the Maxwell operator.
Combines the relevant operator templates for spatial
derivatives, flux, boundary conditions etc.
"""
from grudge.tools import count_subset
w = sym.make_sym_array("w", count_subset(self.get_eh_subset()))
elec_components = count_subset(self.get_eh_subset()[0:3])
mag_components = count_subset(self.get_eh_subset()[3:6])
if self.fixed_material:
# need to check this
material_divisor = ([self.epsilon] * elec_components +
[self.mu] * mag_components)
tags_and_bcs = [
(self.pec_tag, self.pec_bc(w)),
(self.pmc_tag, self.pmc_bc(w)),
(self.absorb_tag, self.absorbing_bc(w)),
(self.incident_tag, self.incident_bc(w)),
]
def flux(pair):
return sym.project(pair.dd, "all_faces")(self.flux(pair))
return (-self.local_derivatives(w) - sym.InverseMassOperator()
(sym.FaceMassOperator()(flux(sym.int_tpair(w)) + sum(
flux(sym.bv_tpair(tag, w, bc))
for tag, bc in tags_and_bcs)))) / material_divisor
def sym_operator(self):
from grudge.dof_desc import DOFDesc, DD_VOLUME, DTAG_VOLUME_ALL
from meshmode.discretization.connection import FACE_RESTR_ALL
u = sym.var("u")
def flux(pair):
return sym.project(pair.dd, face_dd)(self.flux(pair))
face_dd = DOFDesc(FACE_RESTR_ALL, self.quad_tag)
quad_dd = DOFDesc(DTAG_VOLUME_ALL, self.quad_tag)
to_quad = sym.project(DD_VOLUME, quad_dd)
stiff_t_op = sym.stiffness_t(self.ambient_dim,
dd_in=quad_dd,
dd_out=DD_VOLUME)
quad_v = to_quad(self.v)
quad_u = to_quad(u)
return sym.InverseMassOperator()(
sum(stiff_t_op[n](quad_u * quad_v[n])
for n in range(self.ambient_dim)) -
sym.FaceMassOperator(face_dd, DD_VOLUME)
(flux(sym.int_tpair(u, self.quad_tag))))
def sym_operator(self):
from grudge.dof_desc import DOFDesc, DD_VOLUME, DTAG_VOLUME_ALL
from meshmode.mesh import BTAG_ALL
from meshmode.discretization.connection import FACE_RESTR_ALL
u = sym.var("u")
def flux(pair):
return sym.project(pair.dd, face_dd)(self.flux(pair))
face_dd = DOFDesc(FACE_RESTR_ALL, self.quad_tag)
boundary_dd = DOFDesc(BTAG_ALL, self.quad_tag)
quad_dd = DOFDesc(DTAG_VOLUME_ALL, self.quad_tag)
to_quad = sym.project(DD_VOLUME, quad_dd)
stiff_t_op = sym.stiffness_t(self.ambient_dim,
dd_in=quad_dd,
dd_out=DD_VOLUME)
quad_v = to_quad(self.v)
quad_u = to_quad(u)
return sym.InverseMassOperator()(
sum(stiff_t_op[n](quad_u * quad_v[n])
for n in range(self.ambient_dim)) -
sym.FaceMassOperator(face_dd, DD_VOLUME)(
flux(sym.int_tpair(u, self.quad_tag)) +
flux(sym.bv_tpair(boundary_dd, u, self.inflow_u))
# FIXME: Add back support for inflow/outflow tags
#+ flux(sym.bv_tpair(self.inflow_tag, u, bc_in))
#+ flux(sym.bv_tpair(self.outflow_tag, u, bc_out))
))
def sym_operator(self):
d = self.ambient_dim
w = sym.make_sym_array("w", d + 1)
u = w[0]
v = w[1:]
# boundary conditions -------------------------------------------------
# dirichlet BCs -------------------------------------------------------
dir_u = sym.cse(sym.interp("vol", self.dirichlet_tag)(u))
dir_v = sym.cse(sym.interp("vol", self.dirichlet_tag)(v))
if self.dirichlet_bc_f:
# FIXME
from warnings import warn
warn("Inhomogeneous Dirichlet conditions on the wave equation "
"are still having issues.")
dir_g = sym.Field("dir_bc_u")
dir_bc = join_fields(2 * dir_g - dir_u, dir_v)
else:
dir_bc = join_fields(-dir_u, dir_v)
dir_bc = sym.cse(dir_bc, "dir_bc")
# neumann BCs ---------------------------------------------------------
neu_u = sym.cse(sym.interp("vol", self.neumann_tag)(u))
neu_v = sym.cse(sym.interp("vol", self.neumann_tag)(v))
neu_bc = sym.cse(join_fields(neu_u, -neu_v), "neu_bc")
# radiation BCs -------------------------------------------------------
rad_normal = sym.normal(self.radiation_tag, d)
rad_u = sym.cse(sym.interp("vol", self.radiation_tag)(u))
rad_v = sym.cse(sym.interp("vol", self.radiation_tag)(v))
rad_bc = sym.cse(
join_fields(
0.5 * (rad_u - self.sign * np.dot(rad_normal, rad_v)), 0.5 *
rad_normal * (np.dot(rad_normal, rad_v) - self.sign * rad_u)),
"rad_bc")
# entire operator -----------------------------------------------------
def flux(pair):
return sym.interp(pair.dd, "all_faces")(self.flux(pair))
result = sym.InverseMassOperator()(
join_fields(-self.c *
np.dot(sym.stiffness_t(self.ambient_dim), v), -self.c *
(sym.stiffness_t(self.ambient_dim) * u)) -
sym.FaceMassOperator()
(flux(sym.int_tpair(w)) +
flux(sym.bv_tpair(self.dirichlet_tag, w, dir_bc)) +
flux(sym.bv_tpair(self.neumann_tag, w, neu_bc)) +
flux(sym.bv_tpair(self.radiation_tag, w, rad_bc))))
result[0] += self.source_f
return result
def get_strong_wave_op_with_discr_direct(cl_ctx, dims=2, order=4):
from meshmode.mesh.generation import generate_regular_rect_mesh
mesh = generate_regular_rect_mesh(a=(-0.5, ) * dims,
b=(0.5, ) * dims,
n=(16, ) * dims)
logger.debug("%d elements", mesh.nelements)
discr = DGDiscretizationWithBoundaries(cl_ctx, mesh, order=order)
source_center = np.array([0.1, 0.22, 0.33])[:dims]
source_width = 0.05
source_omega = 3
sym_x = sym.nodes(mesh.dim)
sym_source_center_dist = sym_x - source_center
sym_t = sym.ScalarVariable("t")
from meshmode.mesh import BTAG_ALL
c = -0.1
sign = -1
w = sym.make_sym_array("w", dims + 1)
u = w[0]
v = w[1:]
source_f = (
sym.sin(source_omega * sym_t) *
sym.exp(-np.dot(sym_source_center_dist, sym_source_center_dist) /
source_width**2))
rad_normal = sym.normal(BTAG_ALL, dims)
rad_u = sym.cse(sym.interp("vol", BTAG_ALL)(u))
rad_v = sym.cse(sym.interp("vol", BTAG_ALL)(v))
rad_bc = sym.cse(
sym.join_fields(
0.5 * (rad_u - sign * np.dot(rad_normal, rad_v)),
0.5 * rad_normal * (np.dot(rad_normal, rad_v) - sign * rad_u)),
"rad_bc")
sym_operator = (
-sym.join_fields(-c * np.dot(sym.nabla(dims), v) - source_f, -c *
(sym.nabla(dims) * u)) + sym.InverseMassOperator()(
sym.FaceMassOperator()
(dg_flux(c, sym.int_tpair(w)) +
dg_flux(c, sym.bv_tpair(BTAG_ALL, w, rad_bc)))))
return (sym_operator, discr)
def test_incorrect_assignment_aggregation(actx_factory, ambient_dim):
"""Tests that the greedy assignemnt aggregation code works on a non-trivial
expression (on which it didn't work at the time of writing).
"""
actx = actx_factory()
target_order = 4
from meshmode.mesh.generation import generate_regular_rect_mesh
mesh = generate_regular_rect_mesh(a=(-0.5, ) * ambient_dim,
b=(0.5, ) * ambient_dim,
n=(8, ) * ambient_dim,
order=1)
discr = DiscretizationCollection(actx, mesh, order=target_order)
# {{{ test with a relative norm
from grudge.dof_desc import DD_VOLUME
dd = DD_VOLUME
sym_x = sym.make_sym_array("y", ambient_dim, dd=dd)
sym_y = sym.make_sym_array("y", ambient_dim, dd=dd)
sym_norm_y = sym.norm(2, sym_y, dd=dd)
sym_norm_d = sym.norm(2, sym_x - sym_y, dd=dd)
sym_op = sym_norm_d / sym_norm_y
logger.info("%s", sym.pretty(sym_op))
# FIXME: this shouldn't raise a RuntimeError
with pytest.raises(RuntimeError):
bind(discr, sym_op)(actx, x=1.0, y=discr.discr_from_dd(dd).nodes())
# }}}
# {{{ test with repeated mass inverses
sym_minv_y = sym.cse(sym.InverseMassOperator()(sym_y), "minv_y")
sym_u = make_obj_array([0.5 * sym.Ones(dd), 0.0, 0.0])[:ambient_dim]
sym_div_u = sum(d(u) for d, u in zip(sym.nabla(ambient_dim), sym_u))
sym_op = sym.MassOperator(dd)(sym_u) \
+ sym.MassOperator(dd)(sym_minv_y * sym_div_u)
logger.info("%s", sym.pretty(sym_op))
# FIXME: this shouldn't raise a RuntimeError either
bind(discr, sym_op)(actx, y=discr.discr_from_dd(dd).nodes())
def sym_operator(self):
u = sym.var("u")
def flux(pair):
return sym.project(pair.dd, "all_faces")(self.flux(pair))
return (-self.v.dot(
sym.nabla(self.ambient_dim) * u
) + sym.InverseMassOperator()(
sym.FaceMassOperator()(
flux(sym.int_tpair(u)) +
flux(sym.bv_tpair(sym.BTAG_ALL, u, self.inflow_u))
# FIXME: Add back support for inflow/outflow tags
#+ flux(sym.bv_tpair(self.inflow_tag, u, bc_in))
#+ flux(sym.bv_tpair(self.outflow_tag, u, bc_out))
)))
def sym_operator(self):
u = sym.var("u")
def flux(pair):
return sym.project(pair.dd, "all_faces")(self.flux(pair))
bc_in = self.inflow_u
# bc_out = sym.project(sym.DD_VOLUME, self.outflow_tag)(u)
return sym.InverseMassOperator()(
np.dot(self.v,
sym.stiffness_t(self.ambient_dim) * u) -
sym.FaceMassOperator()(
flux(sym.int_tpair(u)) +
flux(sym.bv_tpair(sym.BTAG_ALL, u, bc_in))
# FIXME: Add back support for inflow/outflow tags
#+ flux(sym.bv_tpair(self.inflow_tag, u, bc_in))
#+ flux(sym.bv_tpair(self.outflow_tag, u, bc_out))
))
def sym_operator(self):
u = sym.var("u")
# boundary conditions -------------------------------------------------
bc_in = self.inflow_u
# bc_out = sym.interp("vol", self.outflow_tag)(u)
def flux(pair):
return sym.interp(pair.dd, "all_faces")(
self.flux(pair))
return sym.InverseMassOperator()(
np.dot(
self.v, sym.stiffness_t(self.ambient_dim)*u)
- sym.FaceMassOperator()(
flux(sym.int_tpair(u))
+ flux(sym.bv_tpair(sym.BTAG_ALL, u, bc_in))
# FIXME: Add back support for inflow/outflow tags
#+ flux(sym.bv_tpair(self.inflow_tag, u, bc_in))
#+ flux(sym.bv_tpair(self.outflow_tag, u, bc_out))
))
def sym_operator(self):
u = sym.var("u")
def flux(pair):
return sym.project(pair.dd, face_dd)(self.flux(pair))
face_dd = sym.DOFDesc(sym.FACE_RESTR_ALL, self.quad_tag)
quad_dd = sym.DOFDesc(sym.DTAG_VOLUME_ALL, self.quad_tag)
to_quad = sym.project(sym.DD_VOLUME, quad_dd)
stiff_t_op = sym.stiffness_t(self.ambient_dim,
dd_in=quad_dd,
dd_out=sym.DD_VOLUME)
quad_v = to_quad(self.v)
quad_u = to_quad(u)
return sym.InverseMassOperator()(
sum(stiff_t_op[n](quad_u * quad_v[n])
for n in range(self.ambient_dim)) -
sym.FaceMassOperator(face_dd, sym.DD_VOLUME)
(flux(sym.int_tpair(u, self.quad_tag))))
def _bound_inverse_mass(dcoll):
return bind(dcoll,
sym.InverseMassOperator()(sym.Variable("u")),
local_only=True)
