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Numerische Mathematik

, Volume 115, Issue 1, pp 141–163 | Cite as

Preconditioners for pseudodifferential equations on the sphere with radial basis functions

  • T. TranEmail author
  • Q. T. Le Gia
  • I. H. Sloan
  • E. P. Stephan
Article

Abstract

In a previous paper a preconditioning strategy based on overlapping domain decomposition was applied to the Galerkin approximation of elliptic partial differential equations on the sphere. In this paper the methods are extended to more general pseudodifferential equations on the sphere, using as before spherical radial basis functions for the approximation space, and again preconditioning the ill-conditioned linear systems of the Galerkin approximation by the additive Schwarz method. Numerical results are presented for the case of hypersingular and weakly singular integral operators on the sphere \({\mathbb{S}^2}\) .

Mathematics Subject Classification (2000)

33F05 65N55 65N30 

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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • T. Tran
    • 1
    Email author
  • Q. T. Le Gia
    • 1
  • I. H. Sloan
    • 1
  • E. P. Stephan
    • 2
  1. 1.School of Mathematics and StatisticsThe University of New South WalesSydneyAustralia
  2. 2.Institut für Angewandte MathematikLeibniz Universität HannoverHannoverGermany

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