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146 lines
4.5 KiB
Python
146 lines
4.5 KiB
Python
from typing import Optional, Union
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import numpy # type: ignore
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from ..fdmath import dx_lists_t, fdfield_t
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from ..fdmath.functional import deriv_back
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def poynting(e: fdfield_t,
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h: fdfield_t,
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dxes: Optional[dx_lists_t] = None,
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) -> fdfield_t:
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"""
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Calculate the poynting vector
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"""
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if dxes is None:
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dxes = tuple(tuple(numpy.ones(1) for _ in range(3)) for _ in range(2))
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ex = e[0] * dxes[0][0][:, None, None]
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ey = e[1] * dxes[0][1][None, :, None]
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ez = e[2] * dxes[0][2][None, None, :]
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hx = h[0] * dxes[1][0][:, None, None]
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hy = h[1] * dxes[1][1][None, :, None]
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hz = h[2] * dxes[1][2][None, None, :]
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s = numpy.empty_like(e)
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s[0] = numpy.roll(ey, -1, axis=0) * hz - numpy.roll(ez, -1, axis=0) * hy
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s[1] = numpy.roll(ez, -1, axis=1) * hx - numpy.roll(ex, -1, axis=1) * hz
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s[2] = numpy.roll(ex, -1, axis=2) * hy - numpy.roll(ey, -1, axis=2) * hx
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return s
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def poynting_divergence(s: Optional[fdfield_t] = None,
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*,
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e: Optional[fdfield_t] = None,
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h: Optional[fdfield_t] = None,
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dxes: Optional[dx_lists_t] = None,
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) -> fdfield_t:
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"""
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Calculate the divergence of the poynting vector
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"""
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if s is None:
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assert(e is not None)
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assert(h is not None)
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assert(dxes is not None)
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s = poynting(e, h, dxes=dxes)
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Dx, Dy, Dz = deriv_back()
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ds = Dx(s[0]) + Dy(s[1]) + Dz(s[2])
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return ds
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def energy_hstep(e0: fdfield_t,
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h1: fdfield_t,
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e2: fdfield_t,
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epsilon: Optional[fdfield_t] = None,
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mu: Optional[fdfield_t] = None,
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dxes: Optional[dx_lists_t] = None,
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) -> fdfield_t:
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u = dxmul(e0 * e2, h1 * h1, epsilon, mu, dxes)
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return u
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def energy_estep(h0: fdfield_t,
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e1: fdfield_t,
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h2: fdfield_t,
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epsilon: Optional[fdfield_t] = None,
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mu: Optional[fdfield_t] = None,
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dxes: Optional[dx_lists_t] = None,
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) -> fdfield_t:
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u = dxmul(e1 * e1, h0 * h2, epsilon, mu, dxes)
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return u
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def delta_energy_h2e(dt: float,
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e0: fdfield_t,
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h1: fdfield_t,
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e2: fdfield_t,
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h3: fdfield_t,
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epsilon: Optional[fdfield_t] = None,
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mu: Optional[fdfield_t] = None,
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dxes: Optional[dx_lists_t] = None,
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) -> fdfield_t:
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"""
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This is just from (e2 * e2 + h3 * h1) - (h1 * h1 + e0 * e2)
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"""
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de = e2 * (e2 - e0) / dt
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dh = h1 * (h3 - h1) / dt
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du = dxmul(de, dh, epsilon, mu, dxes)
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return du
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def delta_energy_e2h(dt: float,
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h0: fdfield_t,
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e1: fdfield_t,
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h2: fdfield_t,
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e3: fdfield_t,
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epsilon: Optional[fdfield_t] = None,
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mu: Optional[fdfield_t] = None,
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dxes: Optional[dx_lists_t] = None,
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) -> fdfield_t:
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"""
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This is just from (h2 * h2 + e3 * e1) - (e1 * e1 + h0 * h2)
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"""
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de = e1 * (e3 - e1) / dt
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dh = h2 * (h2 - h0) / dt
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du = dxmul(de, dh, epsilon, mu, dxes)
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return du
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def delta_energy_j(j0: fdfield_t,
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e1: fdfield_t,
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dxes: Optional[dx_lists_t] = None,
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) -> fdfield_t:
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if dxes is None:
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dxes = tuple(tuple(numpy.ones(1) for _ in range(3)) for _ in range(2))
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du = ((j0 * e1).sum(axis=0)
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* dxes[0][0][:, None, None]
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* dxes[0][1][None, :, None]
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* dxes[0][2][None, None, :])
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return du
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def dxmul(ee: fdfield_t,
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hh: fdfield_t,
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epsilon: Optional[Union[fdfield_t, float]] = None,
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mu: Optional[Union[fdfield_t, float]] = None,
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dxes: Optional[dx_lists_t] = None
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) -> fdfield_t:
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if epsilon is None:
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epsilon = 1
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if mu is None:
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mu = 1
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if dxes is None:
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dxes = tuple(tuple(numpy.ones(1) for _ in range(3)) for _ in range(2))
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result = ((ee * epsilon).sum(axis=0)
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* dxes[0][0][:, None, None]
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* dxes[0][1][None, :, None]
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* dxes[0][2][None, None, :]
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+ (hh * mu).sum(axis=0)
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* dxes[1][0][:, None, None]
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* dxes[1][1][None, :, None]
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* dxes[1][2][None, None, :])
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return result
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