Finite-Difference Time-Domain Code for Maxwell's Equations in Conductors and Media of Arbitrary Geometries

This article presents a comprehensive implementation of the Finite-Difference Time-Domain (FDTD) method for simulating electromagnetic phenomena in conductors and dielectric media with arbitrary geometric configurations. The FDTD method, a powerful numerical technique for computational electromagnetics, discretizes Maxwell's equations directly in the time domain using central difference approximations. The core algorithm employs the Yee grid spatial arrangement where electric and magnetic field components are interleaved at half-cell intervals, ensuring second-order accuracy and natural satisfaction of divergence conditions. Key implementation aspects include: - Structured grid discretization of Maxwell's curl equations using leapfrog time-stepping - Material parameter assignment through epsilon and mu arrays mapping to geometric boundaries - Perfectly Matched Layer (PML) absorbing boundary conditions for open region simulations - Field update equations: E-field updates incorporating magnetic field curls and material conductivity, H-field updates using E-field curls and magnetic permeability The FDTD methodology enables full-wave simulation of electromagnetic wave propagation, scattering, and interaction with complex structures, making it particularly valuable for applications in photonics, antenna design, and electromagnetic compatibility analysis. This implementation demonstrates handling of arbitrary material distributions through pixel-based material masks and supports both conductive losses and dielectric dispersion models.