Discontinuous Galerkin implementation of time‐domain finite‐element method using Crank–Nicolson scheme and complex frequency‐shifted perfectly matched layers for efficient analysis of dielectric loaded waveguide structures

Abstract

This article presents the development of discontinuous Galerkin time-domain finite-element method (DG-TDFEM) for modeling wideband electromagnetic response of dielectric loaded waveguide structures. The method can be considered as a kind of domain decomposition method. The hierarchical vector basis functions are used to expand the electric and magnetic fields in order to maintain high order accuracy and Crank-Nicolson difference scheme is utilized for the time-partial equation for each subdomain. Both the electric and magnetic fields are computed in each subdomain, and only the fields on the interfaces of adjacent subdomains are directly related to each other. Thus, there is no need to solve a global matrix equation related to all boundary values. The complex frequency-shifted perfectly matched layers are used for the truncation of unbounded solution region. Several three-dimensional cavity and waveguide structures with dielectric loading are simulated to demonstrate the accuracy and efficiency of the proposed method. Compared to the original single-domain problem, the size of each subdomain problem is reduced to result in a dramatic reduction of factorization time, as well as the overall computational time and peak memory usage.