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):
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, 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 v_dot_n_tpair(velocity, dd=None):
if dd is None:
dd = sym.DOFDesc(sym.FACE_RESTR_INTERIOR)
ambient_dim = len(velocity)
normal = sym.normal(dd.with_qtag(None), ambient_dim, dim=ambient_dim - 2)
return sym.int_tpair(velocity.dot(normal),
qtag=dd.quadrature_tag,
from_dd=dd.with_qtag(None))
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 v_dot_n_tpair(velocity, dd=None):
from grudge.dof_desc import DOFDesc
from meshmode.discretization.connection import FACE_RESTR_INTERIOR
if dd is None:
dd = DOFDesc(FACE_RESTR_INTERIOR)
ambient_dim = len(velocity)
normal = sym.normal(dd.with_discr_tag(None),
ambient_dim,
dim=ambient_dim - 2)
return sym.int_tpair(velocity.dot(normal),
qtag=dd.discretization_tag,
from_dd=dd.with_discr_tag(None))
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))))
