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122 lines
3.3 KiB
Python
122 lines
3.3 KiB
Python
"""
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Basic FDTD field updates
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"""
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from typing import Union
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from ..fdmath import dx_lists_t, fdfield_t, fdfield_updater_t
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from ..fdmath.functional import curl_forward, curl_back
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__author__ = 'Jan Petykiewicz'
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def maxwell_e(dt: float, dxes: dx_lists_t = None) -> fdfield_updater_t:
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"""
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Build a function which performs a portion the time-domain E-field update,
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E += curl_back(H[t]) / epsilon
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The full update should be
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E += (curl_back(H[t]) + J) / epsilon
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which requires an additional step of `E += J / epsilon` which is not performed
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by the generated function.
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See `meanas.fdmath` for descriptions of
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- This update step: "Maxwell's equations" section
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- `dxes`: "Datastructure: dx_lists_t" section
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- `epsilon`: "Permittivity and Permeability" section
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Also see the "Timestep" section of `meanas.fdtd` for a discussion of
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the `dt` parameter.
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Args:
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dt: Timestep. See `meanas.fdtd` for details.
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dxes: Grid description; see `meanas.fdmath`.
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Returns:
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Function `f(E_old, H_old, epsilon) -> E_new`.
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"""
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if dxes is not None:
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curl_h_fun = curl_back(dxes[1])
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else:
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curl_h_fun = curl_back()
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def me_fun(e: fdfield_t, h: fdfield_t, epsilon: Union[fdfield_t, float]) -> fdfield_t:
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"""
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Update the E-field.
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Args:
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e: E-field at time t=0
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h: H-field at time t=0.5
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epsilon: Dielectric constant distribution.
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Returns:
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E-field at time t=1
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"""
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e += dt * curl_h_fun(h) / epsilon # type: ignore # mypy gets confused around ndarray ops
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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) -> fdfield_updater_t:
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"""
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Build a function which performs part of the time-domain H-field update,
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H -= curl_forward(E[t]) / mu
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The full update should be
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H -= (curl_forward(E[t]) + M) / mu
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which requires an additional step of `H -= M / mu` which is not performed
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by the generated function; this step can be omitted if there is no magnetic
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current `M`.
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See `meanas.fdmath` for descriptions of
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- This update step: "Maxwell's equations" section
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- `dxes`: "Datastructure: dx_lists_t" section
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- `mu`: "Permittivity and Permeability" section
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Also see the "Timestep" section of `meanas.fdtd` for a discussion of
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the `dt` parameter.
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Args:
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dt: Timestep. See `meanas.fdtd` for details.
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dxes: Grid description; see `meanas.fdmath`.
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Returns:
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Function `f(E_old, H_old, epsilon) -> E_new`.
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"""
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if dxes is not None:
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curl_e_fun = curl_forward(dxes[0])
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else:
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curl_e_fun = curl_forward()
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def mh_fun(e: fdfield_t, h: fdfield_t, mu: Union[fdfield_t, float, None] = None) -> fdfield_t:
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"""
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Update the H-field.
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Args:
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e: E-field at time t=1
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h: H-field at time t=0.5
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mu: Magnetic permeability. Default is 1 everywhere.
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Returns:
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H-field at time t=1.5
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"""
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if mu is not None:
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h -= dt * curl_e_fun(e) / mu # type: ignore # mypy gets confused around ndarray ops
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else:
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h -= dt * curl_e_fun(e) # type: ignore # mypy gets confused around ndarray ops
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return h
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return mh_fun
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