FDTD Programming Steps and Implementation Methods with MATLAB

This document presents a systematic approach to implementing FDTD simulations using MATLAB, designed specifically for beginners entering computational electromagnetics. The guide covers fundamental programming steps including grid generation, field update equations, and boundary condition implementation. Key aspects include three-dimensional structure modeling using MATLAB's matrix operations and spatial indexing, where electric and magnetic field components (Ex, Ey, Ez, Hx, Hy, Hz) are updated iteratively using central difference approximations of Maxwell's equations. The implementation incorporates Mur's first-order absorbing boundary conditions to minimize unwanted reflections, achieved through specialized update equations at domain boundaries. Code organization typically involves main simulation loops with separate functions for field updates, source excitation (Gaussian pulses or sinusoidal waves), and boundary condition application. Performance optimization techniques include vectorized operations to handle 3D field arrays efficiently and time-stepping algorithms that maintain numerical stability through Courant condition verification. By following this guide, users will gain practical experience in creating custom FDTD simulations, understanding core concepts like Yee cell discretization, and implementing professional-grade boundary treatments for accurate wave propagation modeling in three-dimensional spaces.