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Add PEC, PMC options for E, H wave operators

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jan 2016-07-03 02:57:04 -07:00
parent 05d2557f6f
commit 2cac441717
1 changed files with 31 additions and 10 deletions
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41
fdfd_tools/operators.py
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@ -45,7 +45,8 @@ __author__ = 'Jan Petykiewicz'
def e_full(omega: complex, def e_full(omega: complex,
dxes: dx_lists_t, dxes: dx_lists_t,
epsilon: vfield_t, epsilon: vfield_t,
mu: vfield_t = None mu: vfield_t = None,
pec: vfield_t = None,
) -> sparse.spmatrix: ) -> sparse.spmatrix:
""" """
Wave operator del x (1/mu * del x) - omega**2 * epsilon, for use with E-field, Wave operator del x (1/mu * del x) - omega**2 * epsilon, for use with E-field,
@ -57,19 +58,28 @@ def e_full(omega: complex,
:param omega: Angular frequency of the simulation :param omega: Angular frequency of the simulation
:param dxes: Grid parameters [dx_e, dx_h] as described in fdfd_tools.operators header :param dxes: Grid parameters [dx_e, dx_h] as described in fdfd_tools.operators header
:param epsilon: Vectorized dielectric constant :param epsilon: Vectorized dielectric constant
:param mu: Vectorized magnetic permeability (default 1 everywhere).. :param mu: Vectorized magnetic permeability (default 1 everywhere).
:param pec: Vectorized mask specifying PEC cells. Any cells where pec != 0 are interpreted
as containing a perfect electrical conductor (PEC).
:return: Sparse matrix containing the wave operator :return: Sparse matrix containing the wave operator
""" """
ce = curl_e(dxes) ce = curl_e(dxes)
ch = curl_h(dxes) ch = curl_h(dxes)
e = sparse.diags(epsilon) ev = epsilon
if numpy.any(numpy.equal(pec, None)):
pm = sparse.eye(epsilon.size)
else:
pm = sparse.diags(numpy.where(pec, 0, 1)) # Set pm to (not PEC)
ev = numpy.where(pec, 1.0, ev) # Set epsilon to 1 at PEC
e = sparse.diags(ev)
if numpy.any(numpy.equal(mu, None)): if numpy.any(numpy.equal(mu, None)):
m_div = sparse.eye(epsilon.size) m_div = sparse.eye(epsilon.size)
else: else:
m_div = sparse.diags(1 / mu) m_div = sparse.diags(1 / mu)
op = ch @ m_div @ ce - omega**2 * e op = pm @ ch @ m_div @ ce @ pm - omega**2 * e
return op return op
@ -99,7 +109,8 @@ def e_full_preconditioners(dxes: dx_lists_t
def h_full(omega: complex, def h_full(omega: complex,
dxes: dx_lists_t, dxes: dx_lists_t,
epsilon: vfield_t, epsilon: vfield_t,
mu: vfield_t = None mu: vfield_t = None,
pmc: vfield_t = None,
) -> sparse.spmatrix: ) -> sparse.spmatrix:
""" """
Wave operator del x (1/epsilon * del x) - omega**2 * mu, for use with H-field, Wave operator del x (1/epsilon * del x) - omega**2 * mu, for use with H-field,
@ -110,18 +121,28 @@ def h_full(omega: complex,
:param dxes: Grid parameters [dx_e, dx_h] as described in fdfd_tools.operators header :param dxes: Grid parameters [dx_e, dx_h] as described in fdfd_tools.operators header
:param epsilon: Vectorized dielectric constant :param epsilon: Vectorized dielectric constant
:param mu: Vectorized magnetic permeability (default 1 everywhere) :param mu: Vectorized magnetic permeability (default 1 everywhere)
:param pmc: Vectorized mask specifying PMC cells. Any cells where pmc != 0 are interpreted
as containing a perfect magnetic conductor (PMC).
:return: Sparse matrix containing the wave operator :return: Sparse matrix containing the wave operator
""" """
ec = curl_e(dxes) ec = curl_e(dxes)
hc = curl_h(dxes) hc = curl_h(dxes)
e_div = sparse.diags(1 / epsilon) if mu is None:
if numpy.any(numpy.equal(mu, None)): mv = numpy.ones_like(epsilon)
m = sparse.eye(epsilon.size)
else: else:
m = sparse.diags(mu) mv = mu
A = ec @ e_div @ hc - omega**2 * m if numpy.any(numpy.equal(pmc, None)):
pe = sparse.eye(epsilon.size)
else:
pe = sparse.diags(numpy.where(pmc, 0, 1)) # Set pe to (not PMC)
mv = numpy.where(pmc, 1.0, mv) # Set mu to 1 at PMC
e_div = sparse.diags(1 / epsilon)
m = sparse.diags(mv)
A = pe @ ec @ e_div @ hc @ pe - omega**2 * m
return A return A