Abstract
This paper describes a wavelet-based preconditioning technique for conjugate gradient method for linear systems derived from the Poisson equation. The linear systems solved with a conventional iterative matrix solver resulted in a marked increase in computing time with respect to an increase in grid points. Use of our wavelet-based technique leads to a matrix with a bounded condition number so that computing time is reduced significantly. In this study, one of the simplest wavelets, the Haar wavelet, is used for the purpose of developing a simple but efficient preconditioning algorithm. Simple wavelets having low data communication property such as the Haar wavelet are expected to be suitable for the purpose of improving computing performance. In this study, we also pay attention to the basic characteristics of the Haar-wavelet-based preconditioning method for a Poisson equation solver.
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