88 lines
2.2 KiB
Python
88 lines
2.2 KiB
Python
"""
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Basic FDTD field updates
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"""
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from typing import List, Callable, Tuple, Dict
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import numpy
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from .. import dx_lists_t, field_t, field_updater
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__author__ = 'Jan Petykiewicz'
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def curl_h(dxes: dx_lists_t = None) -> field_updater:
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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 meanas.types
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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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if dxes:
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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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else:
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def dh(f, ax):
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return f - numpy.roll(f, 1, axis=ax)
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def ch_fun(h: field_t) -> field_t:
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output = numpy.empty_like(h)
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output[0] = dh(h[2], 1)
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output[1] = dh(h[0], 2)
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output[2] = dh(h[1], 0)
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output[0] -= dh(h[1], 2)
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output[1] -= dh(h[2], 0)
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output[2] -= dh(h[0], 1)
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return output
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return ch_fun
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def curl_e(dxes: dx_lists_t = None) -> field_updater:
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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 meanas.types
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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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if dxes is not None:
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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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else:
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def de(f, ax):
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return numpy.roll(f, -1, axis=ax) - f
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def ce_fun(e: field_t) -> field_t:
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output = numpy.empty_like(e)
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output[0] = de(e[2], 1)
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output[1] = de(e[0], 2)
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output[2] = de(e[1], 0)
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output[0] -= de(e[1], 2)
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output[1] -= de(e[2], 0)
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output[2] -= de(e[0], 1)
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return output
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return ce_fun
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def maxwell_e(dt: float, dxes: dx_lists_t = None) -> field_updater:
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curl_h_fun = curl_h(dxes)
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def me_fun(e: field_t, h: field_t, epsilon: field_t):
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e += dt * curl_h_fun(h) / epsilon
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return e
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return me_fun
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def maxwell_h(dt: float, dxes: dx_lists_t = None) -> field_updater:
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curl_e_fun = curl_e(dxes)
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def mh_fun(e: field_t, h: field_t):
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h -= dt * curl_e_fun(e)
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return h
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return mh_fun
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