Fast Computation of Linear Systems based on Parallelized Preconditioned MRTR Method Supported by Block-multicolor Ordering in Electromagnetic Field Analysis using Edge-based Finite Element Method

Abstract

To realize fast electromagnetic field analysis, the parallelization technique has been often introduced into the preconditioned Krylov subspace method. When the multicolor ordering is applied to parallelization of forward and backward substitution, the elapsed time of matrix calculation might increase owing to the increment of bandwidth. Therefore, the block-multicolor ordering based on the level structure arising in reverse Cuthill-McKee ordering has been developed. The validity of developed method was demonstrated on the parallelized incomplete-Cholesky-preconditioned conjugate gradient (ICCG) method. In this paper, the parallelization performance of preconditioned minimized residual method based on the three-term recurrence formula of the CG-type (MRTR) method supported by developed ordering is investigated. Furthermore, the affinity of developed ordering or cache-cache elements technique for parallelized forward and backward substitution in Eisenstat's technique is particularly examined.