A Large-Grained Parallel Solver for Linear Simultaneous Ordinary Differential Equations based on Matrix Exponential and its Evaluation(Application,Algorithms for Matrix/Eigenvalue Problems and their Applications,<Special Issue>Joint Symposium of JSIAM Activity Groups 2009)

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  • Noritake Sho
    Department of Computational Science & Engineering, Nagoya University
  • Imakura Akira
    Department of Computational Science & Engineering, Nagoya University
  • Yamamoto Yusaku
    Department of Computational Science & Engineering, Nagoya University
  • Zhang Shao-Liang
    Department of Computational Science & Engineering, Nagoya University

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Other Title
  • 行列の指数関数に基づく連立線形常微分方程式の大粒度並列解法とその評価(応用,行列・固有値問題の解法とその応用,<特集>平成21年研究部会連合発表会)
  • 行列の指数関数に基づく連立線形常微分方程式の大粒度並列解法とその評価
  • ギョウレツ ノ シスウ カンスウ ニ モトズク レンリツ センケイ ジョウ ビブン ホウテイシキ ノ オオツブド ヘイレツカイホウ ト ソノ ヒョウカ

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Abstract

We consider an application of the Krylov approximation method for the matrix exponential to the solution of linear simultaneous ordinary differential equations. Although this approach has large-grain parallelism, it has two potential problems, namely, the instability due to a large dimension of the Krylov subspace and the determination of an appropriate dimension of the Krylov subspace. In this paper, we show how to solve these problems. The resulting method is shown to be faster than the implicit finite difference method when the required accuracy is relatively high.

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