MATLAB Implementation of 2D FDTD with PML Boundary Conditions and Magnetic Field Computation

This paper presents a two-dimensional Finite-Difference Time-Domain (FDTD) program designed to handle electromagnetic field boundary problems using Perfectly Matched Layer (PML) conditions. To better simulate realistic scenarios, the implementation incorporates both PML and Mur boundary methods specifically for calculating the magnetic field component Hz(i,1) at the j=1 boundary position. The code structure includes separate computational modules for each boundary treatment method, allowing direct comparison of their performance and accuracy. The computational domain has been expanded to a 400×400 grid size to accommodate larger simulation spaces. Notably, no additional boundary treatments are applied beyond the specified PML/Mur implementations at j=1, preserving calculation accuracy by minimizing artificial interference. The algorithm maintains identical time steps across all simulation runs, employing a standard Yee grid discretization scheme for field updates. This consistency in temporal sampling ensures the stability and reliability of results through multiple execution cycles, with field updates governed by Maxwell's curl equations discretized using central differences. Key implementation aspects include efficient matrix operations for field component updates, proper PML parameter tuning for optimal absorption, and validation checks for numerical stability. The code structure facilitates easy modification of boundary conditions and grid parameters while maintaining computational efficiency through vectorized MATLAB operations.