A Parallel Finite-Element Time-Domain Method for Nonlinear Dispersive Media

In this article, a novel use of graphics processing units (GPUs) is presented for the acceleration of finite-element time-domain (FETD) methods containing electrically complex media. By leveraging the massively parallel architecture of the GPU via NVIDIA's Compute Unified Device Architecture (CUDA) language, the immense computational burden imposed by these materials can be largely alleviated, facilitating their modeling and incorporation into electromagnetic devices and systems. To that end, an analysis of both mixed and vector wave equation-based nonlinear dispersive FETD algorithms is presented in order to both identify computational bottlenecks and determine their amenability to parallelization. Based on this analysis, a parallel elemental matrix-evaluation procedure is proposed, which when coupled to the recently derived Gaussian belief propagation method for matrix assembly and solution, demonstrates a performance increase of up to 200 times as compared with a traditionally serial implementation.