A Parallel-in-Space-and-Time Method for Transient Electromagnetic Problems

This paper aims to address a growing need for space-time parallel simulation capability in solving transient electromagnetic (EM) problems. Currently, time-domain (TD) EM solvers are typically parallel in space. The sequential-in-time nature of these solvers can achieve good parallel scaling when the number of spatial mesh points per core is large. However, the parallel efficiency quickly deteriorates and even saturates if spatial parallelism has been fully exploited. We propose a new TD method to harvest parallelism in both spatial and temporal dimensions. The objective is obtained through the investigation of space-time domain decomposition formulation and rational Krylov approximation of TD Green's function. The improved parallel performance over space-only parallel TD solvers is illustrated by numerical examples.