Large-scale time-harmonic electromagnetic field analysis using a multigrid solver on a distributed memory parallel computer

This paper reports on an investigation into large-scale parallel time-harmonic electromagnetic field analysis based on the finite element method. The parallel geometric multigrid preconditioned iterative solver for the resulting linear system was developed on a cluster of shared memory parallel computers. We propose a hybrid parallel ordering method for the parallelization of a multiplicative Schwarz smoother, which is a key component of the multigrid solver for electromagnetic field analysis. The method, using domain decomposition ordering for multi-process parallelism and introducing block multi-color ordering for multi-thread parallel processing, attains a high convergence rate with a small number of message passing interface communications and thread synchronizations. The numerical test confirms that the proposed method attains a solver performance more than twice as good as the conventional method based on multi-color ordering. Furthermore, an approximately 800 million degrees of freedom problem is successfully solved on 256 quad-core processors.

► Fast finite element electromagnetic field solver is developed on a SMP cluster.
► An approximately 800 million DOF electromagnetic filed problem is solved in 250 s.
► Hybrid parallel ordering method is proposed for parallelization of the AFW smoother.
► The proposed method attains 2.7-fold speedup compared with multi-color ordering.
► The proposed method effectively utilizes multi process and thread parallel processing.