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Acceleration of Computation for Electromagnetic Wave Scattering Problem with Many Dielectric Circular Cylinders by Means of a Fast Multipole Algorithm (2) : On Two-Step Block Jacobi Method for Block Partitioned Matrix

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Abstract 物体による電磁波散乱の境界要素法による数値計算では,計算に最も多くの時間を費やす部分は密な係数行列を持つ連立1次方程式の求解の部分である.そのため,解くべき問題が実際的になるほど連立1次方程式の求解の高速化はより重要となる.従来著者らは高速多重極アルゴリズムを利用して反復法中に現れる行列—ベクトル積計算の高速化を図ってきた.本論文では,連立1次方程式の求解に前処理つきのGMRES法を使用する.また...,係数行列がブロック構造をしていることを利用し,その構造上の特徴を利用した新しい前処理を考案する.そして数値実験を通して,提案する2段階BlockJacobi前処理が大規模問題に対して有用であることを明らかにする.
In the computation of electromagnetic wave scattering problem, the most time-comsuming part is that of solving a linear system of equations. This is largely caused by its dense coefficient matrix. This motivates the reduction of amount of operations. In the previous paper, we reduced drastically the amount of operations and necessary memory for matrix-vector product using a fast multipole algorithm. In this paper, we focus on variants of preconditioner. Moreover the GMRES method is adopted as an iterative method. The matrices with a natural block form often arise when the boundary element method is used. This situation is a key to improvement of efficiency of computation. Numerical results show that our proposed two-step block Jacobi method is effective for realizing a high-performance computation as well as standard block Jacobi preconditioner.
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Table of Contents 1. はじめに
2. N個の誘電体円柱による散乱数値計算
3. GMRES法
4. ブロック構造を利用した前処理
5. 数値計算例
6. おわりに

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Created Date 2022.05.19
Modified Date 2023.11.17

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