FDTD Method with CPML Absorbing Boundary Conditions

The Finite-Difference Time-Domain (FDTD) method is a numerical computation technique used for solving wave equations, widely applied in electromagnetics, optics, and acoustics. The method discretizes Maxwell's equations in both time and space domains using central-difference approximations, typically implemented through staggered grids (Yee grid) where electric and magnetic field components are sampled at alternating spatial positions and time steps. Meanwhile, the Convolutional Perfectly Matpled Layer (CPML) absorbing boundary condition serves as a sophisticated boundary treatment for simulating wave phenomena in open regions, effectively minimizing artificial reflections through complex frequency-shifted stretching coordinates and recursive convolution implementation. This article provides detailed explanations of FDTD fundamentals and CPML boundary implementation mechanics, including key algorithmic considerations such as field update equations, stability criteria (Courant condition), and PML parameter optimization. The content offers substantial reference value for FDTD beginners, with practical insights into code structure organization and boundary condition implementation strategies.