An Implementation of Fast Wavelet Galerkin Methods for Integral Equations of the Second Kind

Authors:
Weifu Fang;Yi Wang;Yuesheng Xu
Affiliations:
Department of Mathematics, West Virginia University, Morgantown, West Virginia 26506, U.S.A. wfang@math.wvu.edu;Department of Mathematics, West Virginia University, Morgantown, West Virginia 26506, U.S.A. yiwang@math.wvu.edu;Department of Mathematics, West Virginia University, Morgantown, West Virginia 26506, U.S.A. Institute of Mathematics, Academy of Mathematics and System Sciences, the Chinese Academy of Sciences, ...
Venue:
Journal of Scientific Computing
Year:
2004

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Abstract

We present a numerical implementation of the fast Galerkin method for Fredholm integral equations of the second kind using the piecewise polynomial wavelets. We focus on addressing critical issues for the numerical implementation of such a method. They include a choice of practical truncation strategy, numerical integration of weakly singular integrals and the error control of the numerical quadrature. We also implement a multiscale iteration method for solving the resulting compressed linear system. Numerical examples are given to demonstrate the proposed ideas and methods.