不完全離散ウェ-ブレット変換のポアソン方程式解法への応用と並列処理

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  • Application of Incomplete Discrete Wavelet Transform to a Poisson Equation Solver and Its Parallel Processing
  • フカンゼン リサン ウェーブレット ヘンカン ノ ポアソン ホウテイシキ カイ

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This paper describes a powerful and simple new wavelet-based preconditioning method for the CG solvers of Poisson equation. The equation can be solved with an iterative matrix solver, however, in the absence of our method, the computing time will increase exponentially with respect to an increase in grid points. Use of our technique leads to a matrix with a bounded condition number so that computing time is reduced significantly. Results from our numerical experiments confirm the power and accuracy of our wavelet-based preconditioning method. Unlike many preconditioning methods which are not suitable for vector and parallel processing, our algorithm can take advantage of the extreme processing capabilities and enhance computing performance. For example, a speed up of over 100 fold can be achieved when solving Poisson equations on a Cray T3D using 128 processors in parallel.

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