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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  • Tsuburaya Tomonori
    Department of Electrical Engineering, Faculty of Engineering, Fukuoka University
  • Okamoto Yoshifumi
    Department of Electronics and Electrical Engineering, Faculty of Science and Engineering, Hosei University
  • Sato Shuji
    Department of Electrical and Electronic Systems Engineering, Graduate School of Engineering, Utsunomiya University

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Other Title
  • 辺有限要素法による電磁界解析におけるブロックマルチカラーオーダリングを援用した並列化前処理付きMRTR法に基づく線形方程式求解の高速化
  • ヘン ユウゲン ヨウソホウ ニ ヨル デンジカイ カイセキ ニ オケル ブロックマルチカラーオーダリング オ エンヨウ シタ ヘイレツカ マエショリ ツキ MRTRホウ ニ モトズク センケイ ホウテイシキキュウカイ ノ コウソクカ

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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.

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