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Advances in Computational Mathematics

, Volume 11, Issue 4, pp 271–286 | Cite as

Boundary element preconditioners for a hypersingular integral equation on an interval

  • W. McLean
  • O. Steinbach
Article

Abstract

We propose an almost optimal preconditioner for the iterative solution of the Galerkin equations arising from a hypersingular integral equation on an interval. This preconditioning technique, which is based on the single layer potential, was already studied for closed curves [11,14]. For a boundary element trial space, we show that the condition number is of order (1 + | log hmin|)2, where hmin is the length of the smallest element. The proof requires only a mild assumption on the mesh, easily satisfied by adaptive refinement algorithms.

preconditioning techniques boundary element methods 65F35 65N22 65N38 

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Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • W. McLean
    • 1
  • O. Steinbach
    • 2
  1. 1.School of MathematicsThe University of New South WalesSydneyAustralia
  2. 2.Mathematisches Institut AUniversität StuttgartStuttgartGermany

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