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PEC and PMC for all wave operators

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fdtd
jan 8 years ago
parent a512a88930
commit e288e59021
2 changed files with 51 additions and 15 deletions
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12
examples/test.py
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@ -177,12 +177,18 @@ def test1():
J = waveguide_mode.compute_source(**wg_args, **wg_results)
H_overlap = waveguide_mode.compute_overlap_e(**wg_args, **wg_results)
pecg = gridlock.Grid(edge_coords, initial=0, num_grids=3)
pecg = gridlock.Grid(edge_coords, initial=0.0, num_grids=3)
# pecg.draw_cuboid(center=[700, 0, 0], dimensions=[80, 1e8, 1e8], eps=1)
pecg.grids = [numpy.sign(r) for r in pecg.grids]
# pecg.visualize_isosurface()
A = fdfd_tools.operators.e_full(omega, dxes, vec(grid.grids), pec=vec(pecg.grids)).tocsr()
pmcg = gridlock.Grid(edge_coords, initial=0.0, num_grids=3)
# pmcg.draw_cuboid(center=[700, 0, 0], dimensions=[80, 1e8, 1e8], eps=1)
# pmcg.visualize_isosurface()
A = fdfd_tools.operators.e_full(omega, dxes,
epsilon=vec(grid.grids),
pec=vec(pecg.grids),
pmc=vec(pmcg.grids)).tocsr()
b = -1j * omega * vec(J)
x = solve_A(A, b)
E = unvec(x, grid.shape)

54
fdfd_tools/operators.py
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@ -47,6 +47,7 @@ def e_full(omega: complex,
epsilon: vfield_t,
mu: vfield_t = None,
pec: vfield_t = None,
pmc: vfield_t = None,
) -> sparse.spmatrix:
"""
Wave operator del x (1/mu * del x) - omega**2 * epsilon, for use with E-field,
@ -61,6 +62,8 @@ def e_full(omega: complex,
: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).
: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
"""
ce = curl_e(dxes)
@ -68,10 +71,15 @@ def e_full(omega: complex,
ev = epsilon
if numpy.any(numpy.equal(pec, None)):
pe = sparse.eye(epsilon.size)
else:
pe = sparse.diags(numpy.where(pec, 0, 1)) # Set pe to (not PEC)
ev = numpy.where(pec, 1.0, ev) # Set epsilon to 1 at PEC
if numpy.any(numpy.equal(pmc, 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
pm = sparse.diags(numpy.where(pmc, 0, 1)) # set pm to (not PMC)
e = sparse.diags(ev)
if numpy.any(numpy.equal(mu, None)):
@ -79,7 +87,7 @@ def e_full(omega: complex,
else:
m_div = sparse.diags(1 / mu)
op = pm @ ch @ m_div @ ce @ pm - omega**2 * e
op = pe @ ch @ pm @ m_div @ ce @ pe - omega**2 * e
return op
@ -110,6 +118,7 @@ def h_full(omega: complex,
dxes: dx_lists_t,
epsilon: vfield_t,
mu: vfield_t = None,
pec: vfield_t = None,
pmc: vfield_t = None,
) -> sparse.spmatrix:
"""
@ -121,6 +130,8 @@ def h_full(omega: complex,
:param dxes: Grid parameters [dx_e, dx_h] as described in fdfd_tools.operators header
:param epsilon: Vectorized dielectric constant
: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).
: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
@ -134,19 +145,24 @@ def h_full(omega: complex,
mv = mu
if numpy.any(numpy.equal(pmc, None)):
pm = sparse.eye(epsilon.size)
else:
pm = 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
if numpy.any(numpy.equal(pec, 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
pe = sparse.diags(numpy.where(pec, 0, 1)) # set pe to (not PEC)
e_div = sparse.diags(1 / epsilon)
m = sparse.diags(mv)
A = pe @ ec @ e_div @ hc @ pe - omega**2 * m
A = pm @ ec @ pe @ e_div @ hc @ pm - omega**2 * m
return A
def eh_full(omega, dxes, epsilon, mu=None):
def eh_full(omega, dxes, epsilon, mu=None, pec=None, pmc=None):
"""
Wave operator for [E, H] field representation. This operator implements Maxwell's
equations without cancelling out either E or H. The operator is
@ -159,18 +175,32 @@ def eh_full(omega, dxes, epsilon, mu=None):
:param dxes: Grid parameters [dx_e, dx_h] as described in fdfd_tools.operators header
:param epsilon: Vectorized dielectric constant
: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).
: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
"""
A2 = curl_e(dxes)
A1 = curl_h(dxes)
if numpy.any(numpy.equal(pec, None)):
pe = sparse.eye(epsilon.size)
else:
pe = sparse.diags(numpy.where(pec, 0, 1)) # set pe to (not PEC)
iwe = 1j * omega * sparse.diags(epsilon)
iwm = 1j * omega
if numpy.any(numpy.equal(pmc, None)):
pm = sparse.eye(epsilon.size)
else:
pm = sparse.diags(numpy.where(pmc, 0, 1)) # set pm to (not PMC)
iwe = pe @ (1j * omega * sparse.diags(epsilon))
iwm = pm * 1j * omega
if not numpy.any(numpy.equal(mu, None)):
iwm *= sparse.diags(mu)
A1 = pe @ curl_h(dxes) @ pm
A2 = pm @ curl_e(dxes) @ pe
A = sparse.bmat([[-iwe, A1],
[A2, +iwm]])
[A2, iwm]])
return A

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