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首页> 外文期刊>Electronics and communications in Japan >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
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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

机译：基于边基有限元方法的电磁场分析中基于块多色排序的并行预处理MRTR方法的线性系统快速计算

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摘要

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 owning 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 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.
机译：为了实现快速的电磁场分析，通常将并行化技术引入预处理的Krylov子空间方法中。当多色排序应用于正向和反向替换的并行化时，由于带宽的增加，矩阵计算的经过时间可能会增加。因此，已经开发了基于在反向Cuthill-McKee排序中出现的级别结构的块多色排序。平行不完全Cholesky预处理共轭梯度法证明了该方法的有效性。本文研究了基于已开发的有序排序的CG型（MRTR）方法的三项递归公式的预处理最小残留方法的并行化性能。此外，在Eisenstat技术中，特别检查了已开发的排序或缓存-缓存元素技术对并行正向和反向替换的亲和力。

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