2019-08-04 13:48:41 -07:00
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"""
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2019-11-24 23:47:31 -08:00
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Utilities for running finite-difference time-domain (FDTD) simulations
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2020-01-08 00:51:56 -08:00
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Timestep
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========
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From the discussion of "Plane waves and the Dispersion relation" in `meanas.fdmath`,
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we have
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$$ c^2 \\Delta_t^2 = \\frac{\\Delta_t^2}{\\mu \\epsilon} < 1/(\\frac{1}{\\Delta_x^2} + \\frac{1}{\\Delta_y^2} + \\frac{1}{\\Delta_z^2}) $$
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or, if \\( \\Delta_x = \\Delta_y = \\Delta_z \\), then \\( c \\Delta_t < \\frac{\\Delta_x}{\\sqrt{3}} \\).
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Based on this, we can set
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dt = sqrt(mu.min() * epsilon.min()) / sqrt(1/dx_min**2 + 1/dy_min**2 + 1/dz_min**2)
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The `dx_min`, `dy_min`, `dz_min` should be the minimum value across both the base and derived grids.
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Poynting Vector
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===============
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# TODO
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Energy conservation
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===================
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# TODO
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Boundary conditions
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===================
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# TODO notes about boundaries / PMLs
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2019-08-04 13:48:41 -07:00
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"""
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from .base import maxwell_e, maxwell_h
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from .pml import cpml
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from .energy import (poynting, poynting_divergence, energy_hstep, energy_estep,
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delta_energy_h2e, delta_energy_h2e, delta_energy_j)
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from .boundaries import conducting_boundary
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