小規模ＰＣクラスタによる高周波電磁界解析のための並列マルチグリッドソルバ

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  • A Parallel Multigrid Solver for High Frequency Electromagnetic Field Analyses with Small-scale PC Cluster
  • 小規模PCクラスタによる高周波電磁界解析のための並列マルチグリツドソルバ
  • ショウキボ PC クラスタ ニ ヨル コウシュウハ デンジカイ カイセキ ノ タメノ ヘイレツ マルチグリツド ソルバ

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Finite element analyses of electromagnetic field are commonly used for designing of various electronic devices. The scale of the analyses becomes larger and larger, therefore, a fast linear solver is needed to solve linear equations arising from the finite element method. Since a multigrid solver is the fastest linear solver for these problems, parallelization of a multigrid solver is a quite useful approach. From the viewpoint of industrial applications, an effective usage of a small-scale PC cluster is important due to initial cost for introducing parallel computers.<br>In this paper, a distributed parallel multigrid solver for a small-scale PC cluster is developed. In high frequency electromagnetic field analyses, a special block Gauss-Seidel smoother is used for the multigrid solver instead of general smoothers such as Gauss-Seidel smoother or Jacobi smoother in order to improve a convergence rate. The block multicolor ordering technique is applied to parallelize the smoother. A numerical exsample shows that a 3.7-fold speed-up in computational time and a 3.0-fold increase in the scale of the analysis were attained when the number of CPU was increased from one to five.

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