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150 lines
4.5 KiB
Python
150 lines
4.5 KiB
Python
"""
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Functional versions of many FDFD operators. These can be useful for performing
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FDFD calculations without needing to construct large matrices in memory.
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The functions generated here expect inputs in the form E = [E_x, E_y, E_z], where each
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component E_* is an ndarray of equal shape.
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"""
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from typing import List, Callable
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import numpy
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from . import dx_lists_t, field_t
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__author__ = 'Jan Petykiewicz'
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functional_matrix = Callable[[field_t], field_t]
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def curl_h(dxes: dx_lists_t) -> functional_matrix:
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"""
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Curl operator for use with the H field.
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:param dxes: Grid parameters [dx_e, dx_h] as described in fdfd_tools.operators header
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:return: Function for taking the discretized curl of the H-field, F(H) -> curlH
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"""
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dxyz_b = numpy.meshgrid(*dxes[1], indexing='ij')
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def dh(f, ax):
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return (f - numpy.roll(f, 1, axis=ax)) / dxyz_b[ax]
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def ch_fun(h: field_t) -> field_t:
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e = [dh(h[2], 1) - dh(h[1], 2),
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dh(h[0], 2) - dh(h[2], 0),
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dh(h[1], 0) - dh(h[0], 1)]
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return e
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return ch_fun
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def curl_e(dxes: dx_lists_t) -> functional_matrix:
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"""
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Curl operator for use with the E field.
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:param dxes: Grid parameters [dx_e, dx_h] as described in fdfd_tools.operators header
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:return: Function for taking the discretized curl of the E-field, F(E) -> curlE
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"""
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dxyz_a = numpy.meshgrid(*dxes[0], indexing='ij')
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def de(f, ax):
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return (numpy.roll(f, -1, axis=ax) - f) / dxyz_a[ax]
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def ce_fun(e: field_t) -> field_t:
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h = [de(e[2], 1) - de(e[1], 2),
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de(e[0], 2) - de(e[2], 0),
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de(e[1], 0) - de(e[0], 1)]
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return h
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return ce_fun
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def e_full(omega: complex,
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dxes: dx_lists_t,
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epsilon: field_t,
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mu: field_t = None
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) -> functional_matrix:
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"""
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Wave operator del x (1/mu * del x) - omega**2 * epsilon, for use with E-field,
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with wave equation
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(del x (1/mu * del x) - omega**2 * epsilon) E = -i * omega * J
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:param omega: Angular frequency of the simulation
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:param dxes: Grid parameters [dx_e, dx_h] as described in fdfd_tools.operators header
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:param epsilon: Dielectric constant
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:param mu: Magnetic permeability (default 1 everywhere)
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:return: Function implementing the wave operator A(E) -> E
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"""
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ch = curl_h(dxes)
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ce = curl_e(dxes)
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def op_1(e):
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curls = ch(ce(e))
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return [c - omega ** 2 * e * x for c, e, x in zip(curls, epsilon, e)]
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def op_mu(e):
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curls = ch([m * y for m, y in zip(mu, ce(e))])
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return [c - omega ** 2 * p * x for c, p, x in zip(curls, epsilon, e)]
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if numpy.any(numpy.equal(mu, None)):
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return op_1
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else:
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return op_mu
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def eh_full(omega: complex,
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dxes: dx_lists_t,
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epsilon: field_t,
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mu: field_t = None
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) -> functional_matrix:
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"""
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Wave operator for full (both E and H) field representation.
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:param omega: Angular frequency of the simulation
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:param dxes: Grid parameters [dx_e, dx_h] as described in fdfd_tools.operators header
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:param epsilon: Dielectric constant
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:param mu: Magnetic permeability (default 1 everywhere)
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:return: Function implementing the wave operator A(E, H) -> (E, H)
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"""
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ch = curl_h(dxes)
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ce = curl_e(dxes)
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def op_1(e, h):
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return ([c - 1j * omega * p * x for c, p, x in zip(ch(h), epsilon, e)],
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[c + 1j * omega * y for c, y in zip(ce(e), h)])
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def op_mu(e, h):
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return ([c - 1j * omega * p * x for c, p, x in zip(ch(h), epsilon, e)],
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[c + 1j * omega * m * y for c, m, y in zip(ce(e), mu, h)])
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if numpy.any(numpy.equal(mu, None)):
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return op_1
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else:
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return op_mu
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def e2h(omega: complex,
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dxes: dx_lists_t,
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mu: field_t = None,
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) -> functional_matrix:
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"""
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Utility operator for converting the E field into the H field.
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For use with e_full -- assumes that there is no magnetic current M.
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:param omega: Angular frequency of the simulation
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:param dxes: Grid parameters [dx_e, dx_h] as described in fdfd_tools.operators header
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:param mu: Magnetic permeability (default 1 everywhere)
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:return: Function for converting E to H
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"""
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A2 = curl_e(dxes)
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def e2h_1_1(e):
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return [y / (-1j * omega) for y in A2(e)]
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def e2h_mu(e):
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return [y / (-1j * omega * m) for y, m in zip(A2(e), mu)]
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if numpy.any(numpy.equal(mu, None)):
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return e2h_1_1
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else:
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return e2h_mu
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