A novel TDFEM scheme based on high‐performance parallel solver PaStiX

Abstract

AbstractIn this paper, we focus on the theory and fulfillment of parallel time domain finite element method (TDFEM) with PaStiX (Parallel Sparse matriX package) for solving three‐dimensional electromagnetic (EM) radiation problems. The motivation behind the research is required to maintain numerical stability and achieve high speed for parallel sparse LU factorization on parallel platforms. Firstly, we overview the concept of an unconditional stable TDFEM scheme, and numerical optimization for ill‐conditioned equations obtained from the TDFEM with perfectly matched layer (PML) was presented to alleviate nonconvergent results. Secondly, we develop sparse linear system solvers that use DS factorization to solve the preconditioned system. Numerical results were obtained from the cases of the cavity resonance problem and a cone antenna. A noteworthy observation from the time‐consuming results in different solvers is that PaStiX is usually much faster compared with UMFPACK and SuperLU.