Piecewise linear recursive convolution (PLRC) implementation of convolution perfectly matched layer (CPML) in finite-difference time-domain (FDTD)

Convolutional perfectly matched layer (CPML) is an important absorbing boundary condition (ABC) in finite-difference time-domain (FDTD). The formulation of CPML needs no modification for any kind of media theoretically. This paper presents a novel implementation of CPML using piecewise linear recursive convolution (PLRC) to improve the absorbing performance. Compared to the classical CPML that the field in the convolution integral is approximated by a piecewise constant function, the PLRC implementation approximates the field in the convolution integral as a piecewise linear function. Numerical experiments of one-dimensional planar wave's absorbance were performed and the reflected field is recorded at every time step. The frequency response of the reflection is achieved via Fourier transform The results show that the PLRC implementation of CPML has good absorbing effect at a broad frequency band and can achieve better absorbing performance than classical implementation of CPML at higher frequency. The CPML's constitutive parameters’ influence on the absorbing performance is studied via sweeping the parameters and the results are illustrated by contour plots which are very helpful in appropriate parameters choice. At last, the proper parameters in truncating one-dimensional planar waves in free space are advised.