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

Raymond H. CHAN*, Hai Wei SUN, Wing Fai NG

*Corresponding author for this work

Research output: Journal PublicationsJournal Article (refereed)peer-review

9 Citations (Scopus)


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 O(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.

Original languageEnglish
Pages (from-to)1505-1521
Number of pages17
JournalInternational Journal for Numerical Methods in Engineering
Issue number8
Publication statusPublished - 30 Dec 1998
Externally publishedYes


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


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