Two-Dimensional FDTD Electromagnetic Simulation based on Sullivan's Method

This article presents a MATLAB-based implementation of a two-dimensional electromagnetic simulation using the Finite-Difference Time-Domain (FDTD) method, extensively covered in Sullivan's reference work. The FDTD method serves as an effective numerical approach for solving electromagnetic wave propagation problems, widely applied in antenna design, microwave circuits, optical devices, and related fields. The implementation employs the Yee grid discretization scheme, where electric and magnetic field components are staggered in both space and time to satisfy Maxwell's equations numerically. Key components include the update equations for E-field and H-field components using central difference approximations, along with Perfectly Matched Layer (PML) boundary conditions to minimize unwanted reflections. Through detailed code analysis, we demonstrate how to structure the main simulation loop, implement field updates using vectorized operations for efficiency, and visualize results through time-step animations and field distribution plots. Practical examples included illustrate applications in waveguide analysis and scattering problems, providing readers with comprehensive understanding of FDTD fundamentals and hands-on MATLAB implementation skills for electromagnetic simulations.