Implementation of 2D TM Wave FDTD Simulation Using PML Absorbing Boundary Conditions

This program implements Finite-Difference Time-Domain (FDTD) simulation for 2D Transverse Magnetic (TM) waves using Perfectly Matched Layer (PML) absorbing boundary conditions. The PML algorithm serves as a specialized computational technique that simulates electromagnetic wave absorption at the boundaries of the computational domain. By implementing appropriate absorbing boundary conditions through PML layers, the program significantly reduces numerical reflections and improves simulation accuracy. Key implementation aspects include: PML parameter optimization for gradual wave attenuation, convolutional PML implementation for broad frequency absorption, and proper field component splitting at boundary interfaces. The code structure typically involves separate update equations for field components within the PML regions using anisotropic material properties, while maintaining standard FDTD equations in the main computational domain. This approach enables effective simulation of wave propagation without artificial reflections from domain boundaries, making it suitable for open-region electromagnetic problems. The program achieves 2D TM wave FDTD simulation through careful PML implementation that ensures numerical stability while maintaining the divergence-free condition for electromagnetic fields. The TM wave formulation specifically handles Ez, Hx, and Hy field components with appropriate boundary condition treatments.