FDTD Algorithm Implementation from 1D to 3D with MATLAB Examples

This documentation presents the FDTD (Finite-Difference Time-Domain) algorithm, a comprehensive numerical simulation method covering one-dimensional to three-dimensional implementations. The algorithm employs Yee's grid formulation for solving Maxwell's equations in the time domain, making it particularly effective for analyzing electromagnetic wave scattering characteristics across various object geometries. The MATLAB implementation features structured code organization with separate functions for field updating, boundary condition handling (including PML absorption), and scatterer definition. Key computational components include: - Central-difference approximations for spatial and temporal derivatives - Material parameter matrices (epsilon, mu) supporting heterogeneous media - Time-stepping loops with stability-controlled Courant conditions - Visualization routines for electromagnetic field propagation animation Beyond scattering analysis for different object shapes, the algorithm's modular architecture allows adaptations for optical and acoustic wave simulations. The codebase utilizes MATLAB's vectorization capabilities for efficient computation, with configurable parameters for grid resolution, time steps, and source excitations. Researchers in electromagnetics, photonics, and wave physics can leverage this implementation for customized numerical experiments and result validation through integrated plotting functions.