Unconditionally stable FETD method using Laguerre polynomials for eigenvalue problems

Abstract

This paper presents an unconditionally stable finite-element time-domain (FETD) scheme to solve time-dependent vector wave equations for eigenvalue problems. With the weighted Laguerre polynomials as basis functions and Galerkin's testing procedure, the temporal derivative in the vector wave equation can be handled analytically. Combined with the discrete Fourier transform (DFT), the Laguerre-FETD method is applied to the solution of eigenvalue problems. The numerical example of a circle dielectric-loaded waveguide shows its advantages of accuracy and efficiency.