Finite-Difference Time-Domain

The Yee grid staggers E and H fields by half a cell, so E components are evaluated at cell edges and H at cell centers. This arrangement naturally satisfies the divergence-free conditions of Maxwell's equations and ensures second-order accuracy in both space and time, avoiding spurious modes and maintaining energy conservation.

The Courant criterion states Δt ≤ Δx / (c √3) for 3D (or Δx / (c √2) for 2D, Δx / c for 1D) where Δx is the smallest grid spacing and c is the light speed in the medium. A safe choice is Δt = 0.99 × Δx / (c √3). Smaller time steps increase accuracy but slow the simulation; larger steps risk instability.

Use PML to model open or semi-infinite domains where you want outgoing waves to exit without reflection. Use metal walls (perfect electric conductor) to model closed cavities or shielding. PML adds computational cost but is essential for modeling antennas, free-space radiation, and scattering from isolated objects.

Dispersive materials require frequency-dependent permittivity ε(ω). In FDTD, use auxiliary differential equations (ADE) to track polarization or magnetization currents, or use frequency-dependent conductivity (Drude models). These approaches add complexity but enable accurate simulation of chromatic dispersion and plasmonic resonances.