Wavelet-based preconditioners for boundary integral equations

被引：0
作者：
Thanh Tran
Ernst P. Stephan
Stefan Zaprianov
机构：
[1] University of New South Wales,School of Mathematics
[2] University of Hannover,Institut für Angewandte Mathematik
来源：
Advances in Computational Mathematics | 1998年 / 9卷
关键词：
boundary integral equations; prewavelets; preconditioned conjugate gradient; additive Schwarz; hierarchical basis; 65N55; 65N38;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We study simple preconditioners for the conjugate gradient method when used to solve matrix systems arising from some hypersingular and weakly singular integral equations. The preconditioners, which are of the type of hierarchical basis preconditioners, are based on the decomposition of the piecewise-linear (respectively piecewise-constant) functions as the sum of prewavelets (respectively derivatives of prewavelets). We prove that with these preconditioners the preconditioned systems have condition numbers uniformly bounded with respect to the degrees of freedom. Numerical experiments support our analysis.
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页码：233 / 249
页数：16
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