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