def impedance_single_parts(self, Z, s, part_o, part_s=None):
"""Calculate a self or mutual impedance matrix at a given complex
frequency
Parameters
----------
s : complex
Complex frequency at which to calculate impedance
part_o : SinglePart
The observing part, which must be a single part, not a composite
part_s : SinglePart, optional
The source part, if not specified will default to observing part
"""
# if source part is not given, default to observer part
part_s = part_s or part_o
basis_o = self.basis_container[part_o]
basis_s = self.basis_container[part_s]
eps = self.background_material.epsilon_r(s)
mu = self.background_material.epsilon_r(s)
normals = basis_o.mesh.surface_normals
if not (basis_o.mesh.closed_surface and basis_s.mesh.closed_surface):
raise ValueError("CFIE can only be solved for closed objects")
if isinstance(basis_o, LinearTriangleBasis):
L, S = rwg.impedance_G(s, self.integration_rule, basis_o,
part_o.nodes, basis_s, part_s.nodes,
normals, part_o == part_s, eps, mu,
self.num_singular_terms,
self.singularity_accuracy)
M, _ = rwg.impedance_curl_G(s,
self.integration_rule,
basis_o,
part_o.nodes,
basis_s,
part_s.nodes,
normals,
part_o == part_s,
eps,
mu,
self.num_singular_terms,
self.singularity_accuracy,
tangential_form=False)
else:
raise NotImplementedError
Z.matrices['L'][part_o, part_s] = L * (mu * mu_0)
Z.matrices['S'][part_o, part_s] = S / (eps * epsilon_0)
Z.matrices['M'][part_o, part_s] = M
def impedance_single_parts(self, Z, s, part_o, part_s=None):
"""Calculate a self or mutual impedance matrix at a given complex
frequency
Parameters
----------
s : complex
Complex frequency at which to calculate impedance
part_o : SinglePart
The observing part, which must be a single part, not a composite
part_s : SinglePart, optional
The source part, if not specified will default to observing part
"""
# if source part is not given, default to observer part
part_s = part_s or part_o
basis_o = self.basis_container[part_o]
basis_s = self.basis_container[part_s]
eps = self.background_material.epsilon_r(s)
mu = self.background_material.epsilon_r(s)
normals = basis_o.mesh.surface_normals
if not (basis_o.mesh.closed_surface and basis_s.mesh.closed_surface):
raise ValueError("CFIE can only be solved for closed objects")
if isinstance(basis_o, LinearTriangleBasis):
L, S = rwg.impedance_G(s, self.integration_rule, basis_o,
part_o.nodes, basis_s, part_s.nodes,
normals, part_o == part_s, eps, mu,
self.num_singular_terms,
self.singularity_accuracy)
M, _ = rwg.impedance_curl_G(s, self.integration_rule, basis_o,
part_o.nodes, basis_s, part_s.nodes,
normals, part_o == part_s, eps, mu,
self.num_singular_terms,
self.singularity_accuracy,
tangential_form=False)
else:
raise NotImplementedError
Z.matrices['L'][part_o, part_s] = L*(mu*mu_0)
Z.matrices['S'][part_o, part_s] = S/(eps*epsilon_0)
Z.matrices['M'][part_o, part_s] = M
def impedance_single_parts(self, Z, s, part_o, part_s):
"""Calculate a self or mutual impedance matrix at a given complex
frequency
Parameters
----------
s : complex
Complex frequency at which to calculate impedance
part_o : SinglePart
The observing part, which must be a single part, not a composite
part_s : SinglePart, optional
The source part, if not specified will default to observing part
"""
basis_o = self.basis_container[part_o]
basis_s = self.basis_container[part_s]
eps = self.background_material.epsilon_r(s)
mu = self.background_material.epsilon_r(s)
normals = basis_o.mesh.surface_normals
if isinstance(basis_o, LinearTriangleBasis):
res = rwg.impedance_G(s, self.integration_rule, basis_o,
part_o.nodes, basis_s, part_s.nodes, normals,
part_o == part_s, eps, mu,
self.num_singular_terms,
self.singularity_accuracy, True)
else:
raise NotImplementedError
L, S, dL_ds, dS_ds = res
Z.matrices['L'][part_o, part_s] = L * (mu * mu_0)
Z.matrices['S'][part_o, part_s] = S / (eps * epsilon_0)
Z.der['L'][part_o, part_s] = dL_ds * (mu * mu_0)
Z.der['S'][part_o, part_s] = dS_ds / (eps * epsilon_0)
def impedance_single_parts(self, Z, s, part_o, part_s):
"""Calculate a self or mutual impedance matrix at a given complex
frequency
Parameters
----------
s : complex
Complex frequency at which to calculate impedance
part_o : SinglePart
The observing part, which must be a single part, not a composite
part_s : SinglePart, optional
The source part, if not specified will default to observing part
"""
basis_o = self.basis_container[part_o]
basis_s = self.basis_container[part_s]
eps = self.background_material.epsilon_r(s)
mu = self.background_material.epsilon_r(s)
normals = basis_o.mesh.surface_normals
if isinstance(basis_o, LinearTriangleBasis):
res = rwg.impedance_G(s, self.integration_rule, basis_o,
part_o.nodes, basis_s, part_s.nodes,
normals, part_o == part_s, eps, mu,
self.num_singular_terms,
self.singularity_accuracy, True)
else:
raise NotImplementedError
L, S, dL_ds, dS_ds = res
Z.matrices['L'][part_o, part_s] = L*(mu*mu_0)
Z.matrices['S'][part_o, part_s] = S/(eps*epsilon_0)
Z.der['L'][part_o, part_s] = dL_ds*(mu*mu_0)
Z.der['S'][part_o, part_s] = dS_ds/(eps*epsilon_0)
def impedance_single_parts(self, Z, s, part_o, part_s=None):
"""Calculate a self or mutual impedance matrix at a given complex
frequency. Note that this abstract function should be called by
sub-classes, not by the user.
Parameters
----------
s : complex
Complex frequency at which to calculate impedance
part_o : SinglePart
The observing part, which must be a single part, not a composite
part_s : SinglePart, optional
The source part, if not specified will default to observing part
"""
# TODO: Handle the mutual impedance case
# if source part is not given, default to observer part
part_s = part_s or part_o
basis_o = self.basis_container[part_o]
basis_s = self.basis_container[part_s]
normals = basis_o.mesh.surface_normals
if not (basis_o.mesh.closed_surface and basis_s.mesh.closed_surface):
raise ValueError("Penetrable objects must be closed")
# TODO: fix this for mutual impedance terms
eps_i = part_s.material.epsilon_r(s)
eps_o = self.background_material.epsilon_r(s)
mu_i = part_s.material.mu_r(s)
mu_o = self.background_material.mu_r(s)
c_i = c/np.sqrt(eps_i*mu_i)
c_o = c/np.sqrt(eps_o*mu_o)
is_self_term = part_o == part_s
matrix_names = ('L_o', 'S_o', 'K_o')
if isinstance(basis_o, LinearTriangleBasis):
if is_self_term:
res = rwg.impedance_G(s, self.integration_rule, basis_o,
part_o.nodes, basis_s, part_s.nodes,
-normals, is_self_term, eps_i, mu_i,
self.num_singular_terms,
self.singularity_accuracy)
L_i = res[0]/c_i*eta_0
S_i = res[1]*c_i*eta_0
# note opposite sign of normals for interior problem
res = rwg.impedance_curl_G(s, self.integration_rule, basis_o,
part_o.nodes, basis_s, part_s.nodes,
-normals, is_self_term, eps_i, mu_i,
self.num_singular_terms,
self.singularity_accuracy,
tangential_form=True)
K_i = res[0]*eta_0
matrix_names += ('L_i', 'S_i', 'K_i')
res = rwg.impedance_G(s, self.integration_rule, basis_o,
part_o.nodes, basis_s, part_s.nodes,
normals, is_self_term, eps_o, mu_o,
self.num_singular_terms,
self.singularity_accuracy)
# This scaling ensures that this operator has the same definition
# as cursive D defined by Yla-Oijala, Radio Science 2005.
L_o = res[0]/c_o*eta_0
S_o = res[1]*c_o*eta_0
res = rwg.impedance_curl_G(s, self.integration_rule, basis_o,
part_o.nodes, basis_s, part_s.nodes,
normals, is_self_term, eps_o, mu_o,
self.num_singular_terms,
self.singularity_accuracy,
tangential_form=True)
K_o = res[0]*eta_0
else:
raise NotImplementedError
# Build the matrices and metadata for creating the impedance matrix
# object from the locally defined variables. This relies on them having
# the correct name in this function.
loc = locals()
for name in matrix_names:
Z.matrices[name][part_o, part_s] = loc[name]