def absorbing_bc(self, w=None):
"""Construct part of the flux operator template for 1st order
absorbing boundary conditions.
"""
from hedge.optemplate import normal
absorb_normal = normal(self.absorb_tag, self.dimensions)
from hedge.optemplate import BoundarizeOperator, Field
from hedge.tools import join_fields
e, h = self.split_eh(self.field_placeholder(w))
if self.fixed_material:
epsilon = self.epsilon
mu = self.mu
else:
epsilon = cse(
BoundarizeOperator(self.absorb_tag)(Field("epsilon")))
mu = cse(
BoundarizeOperator(self.absorb_tag)(Field("mu")))
absorb_Z = (mu/epsilon)**0.5
absorb_Y = 1/absorb_Z
absorb_e = BoundarizeOperator(self.absorb_tag)(e)
absorb_h = BoundarizeOperator(self.absorb_tag)(h)
bc = join_fields(
absorb_e + 1/2*(self.space_cross_h(absorb_normal, self.space_cross_e(
absorb_normal, absorb_e))
- absorb_Z*self.space_cross_h(absorb_normal, absorb_h)),
absorb_h + 1/2*(
self.space_cross_e(absorb_normal, self.space_cross_h(
absorb_normal, absorb_h))
+ absorb_Y*self.space_cross_e(absorb_normal, absorb_e)))
return bc
def absorbing_bc(self, w=None):
"""Construct part of the flux operator template for 1st order
absorbing boundary conditions.
"""
from hedge.optemplate import normal
absorb_normal = normal(self.absorb_tag, self.dimensions)
from hedge.optemplate import BoundarizeOperator, Field
from hedge.tools import join_fields
e, h = self.split_eh(self.field_placeholder(w))
if self.fixed_material:
epsilon = self.epsilon
mu = self.mu
else:
epsilon = cse(
BoundarizeOperator(self.absorb_tag)(Field("epsilon")))
mu = cse(BoundarizeOperator(self.absorb_tag)(Field("mu")))
absorb_Z = (mu / epsilon)**0.5
absorb_Y = 1 / absorb_Z
absorb_e = BoundarizeOperator(self.absorb_tag)(e)
absorb_h = BoundarizeOperator(self.absorb_tag)(h)
bc = join_fields(
absorb_e + 1 / 2 *
(self.space_cross_h(absorb_normal,
self.space_cross_e(absorb_normal, absorb_e)) -
absorb_Z * self.space_cross_h(absorb_normal, absorb_h)),
absorb_h + 1 / 2 *
(self.space_cross_e(absorb_normal,
self.space_cross_h(absorb_normal, absorb_h)) +
absorb_Y * self.space_cross_e(absorb_normal, absorb_e)))
return bc
def op_template(self):
from hedge.optemplate import \
make_sym_vector, \
BoundaryPair, \
get_flux_operator, \
make_nabla, \
InverseMassOperator, \
BoundarizeOperator
d = self.dimensions
w = make_sym_vector("w", d+1)
u = w[0]
v = w[1:]
# boundary conditions -------------------------------------------------
from hedge.tools import join_fields
# dirichlet BCs -------------------------------------------------------
from hedge.optemplate import normal, Field
dir_u = BoundarizeOperator(self.dirichlet_tag) * u
dir_v = BoundarizeOperator(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 = Field("dir_bc_u")
dir_bc = join_fields(2*dir_g - dir_u, dir_v)
else:
dir_bc = join_fields(-dir_u, dir_v)
# neumann BCs ---------------------------------------------------------
neu_u = BoundarizeOperator(self.neumann_tag) * u
neu_v = BoundarizeOperator(self.neumann_tag) * v
neu_bc = join_fields(neu_u, -neu_v)
# radiation BCs -------------------------------------------------------
rad_normal = normal(self.radiation_tag, d)
rad_u = BoundarizeOperator(self.radiation_tag) * u
rad_v = BoundarizeOperator(self.radiation_tag) * v
rad_bc = 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)
)
# entire operator -----------------------------------------------------
nabla = make_nabla(d)
flux_op = get_flux_operator(self.flux())
from hedge.tools import join_fields
result = (
- join_fields(
-self.c*np.dot(nabla, v),
-self.c*(nabla*u)
)
+
InverseMassOperator() * (
flux_op(w)
+ flux_op(BoundaryPair(w, dir_bc, self.dirichlet_tag))
+ flux_op(BoundaryPair(w, neu_bc, self.neumann_tag))
+ flux_op(BoundaryPair(w, rad_bc, self.radiation_tag))
))
result[0] += self.source_f
return result
