Weighted Laguerre polynomials-discrete singular convolution method for efficient solution of maxwell's equations

Abstract

This paper presents a three-dimensional weighted Laguerre polynomials-discrete singular convolution (WLP-DSC) method for efficient and unconditionally stable solution of time-domain Maxwell's equations in lossy media. In the proposed WLP-DSC method, temporal variations of fields are first expanded with the orthogonal and global WLP bases and a Galerkin's matching process is then invoked upon time-domain Maxwell's equations to eliminate the time variable, through which a marching on in degree scheme is obtained. Spatial derivatives are then approximated with a high-order DSC method. Adopting low spatial sampling density in the DSC method, computational burden is greatly reduced with the proposed method. Comparisons with conventional WLP-finite difference method are presented to demonstrate the validity and advantages of our proposed method.