def bind(self, discr, **extra_context):
"Convert the abstract operator template into compiled code."
from hedge.mesh import check_bc_coverage
check_bc_coverage(discr.mesh, [
self.pec_tag, self.absorb_tag, self.incident_tag])
compiled_op_template = discr.compile(self.op_template())
from hedge.tools import full_to_subset_indices
e_indices = full_to_subset_indices(self.get_eh_subset()[0:3])
all_indices = full_to_subset_indices(self.get_eh_subset())
def rhs(t, w):
if self.current is not None:
j = self.current.volume_interpolant(t, discr)[e_indices]
else:
j = 0
if self.incident_bc_data is not None:
incident_bc_data = self.incident_bc_data.boundary_interpolant(
t, discr, self.incident_tag)[all_indices]
else:
incident_bc_data = 0
kwargs = {}
kwargs.update(extra_context)
if not self.fixed_material:
kwargs["epsilon"] = self.epsilon.volume_interpolant(t, discr)
kwargs["mu"] = self.mu.volume_interpolant(t, discr)
return compiled_op_template(
w=w, j=j, incident_bc=incident_bc_data,
**kwargs)
return rhs
def pml_local_op(self, w):
sub_e, sub_h, sub_p, sub_q = self.split_ehpq(w)
e_subset = self.get_eh_subset()[0:3]
h_subset = self.get_eh_subset()[3:6]
dim_subset = (True,) * self.dimensions + (False,) * (3-self.dimensions)
def pad_vec(v, subset):
result = numpy.zeros((3,), dtype=object)
result[numpy.array(subset, dtype=bool)] = v
return result
from hedge.optemplate import make_vector_field
sig = pad_vec(
make_vector_field("sigma", self.dimensions),
dim_subset)
sig_prime = pad_vec(
make_vector_field("sigma_prime", self.dimensions),
dim_subset)
if self.add_decay:
tau = pad_vec(
make_vector_field("tau", self.dimensions),
dim_subset)
else:
tau = numpy.zeros((3,))
e = pad_vec(sub_e, e_subset)
h = pad_vec(sub_h, h_subset)
p = pad_vec(sub_p, dim_subset)
q = pad_vec(sub_q, dim_subset)
rhs = numpy.zeros(12, dtype=object)
for mx in range(3):
my = (mx+1) % 3
mz = (mx+2) % 3
from hedge.tools.mathematics import levi_civita
assert levi_civita((mx,my,mz)) == 1
rhs[mx] += -sig[my]/self.epsilon*(2*e[mx]+p[mx]) - 2*tau[my]/self.epsilon*e[mx]
rhs[my] += -sig[mx]/self.epsilon*(2*e[my]+p[my]) - 2*tau[mx]/self.epsilon*e[my]
rhs[3+mz] += 1/(self.epsilon*self.mu) * (
sig_prime[mx] * q[mx] - sig_prime[my] * q[my])
rhs[6+mx] += sig[my]/self.epsilon*e[mx]
rhs[6+my] += sig[mx]/self.epsilon*e[my]
rhs[9+mx] += -sig[mx]/self.epsilon*q[mx] - (e[my] + e[mz])
from hedge.tools import full_to_subset_indices
sub_idx = full_to_subset_indices(e_subset+h_subset+dim_subset+dim_subset)
return rhs[sub_idx]
def pml_local_op(self, w):
sub_e, sub_h, sub_p, sub_q = self.split_ehpq(w)
e_subset = self.get_eh_subset()[0:3]
h_subset = self.get_eh_subset()[3:6]
dim_subset = (True, ) * self.dimensions + (False, ) * (3 -
self.dimensions)
def pad_vec(v, subset):
result = numpy.zeros((3, ), dtype=object)
result[numpy.array(subset, dtype=bool)] = v
return result
from hedge.optemplate import make_sym_vector
sig = pad_vec(make_sym_vector("sigma", self.dimensions), dim_subset)
sig_prime = pad_vec(make_sym_vector("sigma_prime", self.dimensions),
dim_subset)
if self.add_decay:
tau = pad_vec(make_sym_vector("tau", self.dimensions), dim_subset)
else:
tau = numpy.zeros((3, ))
e = pad_vec(sub_e, e_subset)
h = pad_vec(sub_h, h_subset)
p = pad_vec(sub_p, dim_subset)
q = pad_vec(sub_q, dim_subset)
rhs = numpy.zeros(12, dtype=object)
for mx in range(3):
my = (mx + 1) % 3
mz = (mx + 2) % 3
from hedge.tools.mathematics import levi_civita
assert levi_civita((mx, my, mz)) == 1
rhs[mx] += -sig[my] / self.epsilon * (
2 * e[mx] + p[mx]) - 2 * tau[my] / self.epsilon * e[mx]
rhs[my] += -sig[mx] / self.epsilon * (
2 * e[my] + p[my]) - 2 * tau[mx] / self.epsilon * e[my]
rhs[3 +
mz] += 1 / (self.epsilon * self.mu) * (sig_prime[mx] * q[mx] -
sig_prime[my] * q[my])
rhs[6 + mx] += sig[my] / self.epsilon * e[mx]
rhs[6 + my] += sig[mx] / self.epsilon * e[my]
rhs[9 + mx] += -sig[mx] / self.epsilon * q[mx] - (e[my] + e[mz])
from hedge.tools import full_to_subset_indices
sub_idx = full_to_subset_indices(e_subset + h_subset + dim_subset +
dim_subset)
return rhs[sub_idx]
