Circulant preconditioners for ill-conditioned boundary integral equations from potential equations

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journal

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Author(s)

Detail(s)

Original languageEnglish
Pages (from-to)1505-1521
Journal / PublicationInternational Journal for Numerical Methods in Engineering
Volume43
Issue number8
Online published21 Dec 1998
Publication statusPublished - 30 Dec 1998
Externally publishedYes

Abstract

In this paper, we consider solving potential equations by the boundary integral equation approach. The equations so derived are Fredholm integral equations of the first kind and are known to be ill-conditioned. Their discretized matrices are dense and have condition numbers growing like(n) where n is the matrix size. We propose to solve the equations by the preconditioned conjugate gradient method with circulant integral operators as preconditioners. These are convolution operators with periodic kernels and hence can be inverted efficiently by using fast Fourier transforms. We prove that the preconditioned systems are well conditioned, and hence the convergence rate of the method is linear. Numerical results for two types of regions are given to illustrate the fast convergence. 

Research Area(s)

  • Boundary integral equations, Circulant preconditioners, Fredholm integral equations, Preconditioned conjugate gradient method

Citation Format(s)

Circulant preconditioners for ill-conditioned boundary integral equations from potential equations. / Chan, Raymond H.; Sun, Hai-Wei; Ng, Wing-Fai.

In: International Journal for Numerical Methods in Engineering, Vol. 43, No. 8, 30.12.1998, p. 1505-1521.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journal