Vector Parallel Preconditioning Methods for the Conjugate Gradient Algorithm and Its Variants

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  • 共役勾配法系アルゴリズムにおけるベクトル、並列処理向き前処理手法
  • キョウヤク コウバイホウケイ アルゴリズム ニ オケル ベクトル ヘイレツ シ

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Conjugate Gradient Algorithm and its variants have been widely used as an excellent solution method for linear equations on vector and/or parallel supercomputers. But the effectiveness depends on the ability to parallelize the preconditioning procedure. Here, we first deal with Neumann expansion preconditioning method and extend it to polynomial preconditioning method. Both are very simple and available for a wide class of matrices. The numerical studies are made on vector/parallel supercomputer S-3800 and parallel processors KSR-1 and AP1000 to validate the vactor/parallel effect. The methods are applied to a matrix discretized by Fourier series expansion of a plasma fluid flow equation, as well as usual finite difference and finite element methods.

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