Advances in Computational Mathematics

, Volume 34, Issue 1, pp 83–103 | Cite as

Solution to the Neumann problem exterior to a prolate spheroid by radial basis functions

  • Q. T. Le Gia
  • E. P. Stephan
  • T. TranEmail author


We consider the exterior Neumann problem of the Laplacian with boundary condition on a prolate spheroid. We propose to use spherical radial basis functions in the solution of the boundary integral equation arising from the Dirichlet–to–Neumann map. Our approach is particularly suitable for handling of scattered data, e.g. satellite data. We also propose a preconditioning technique based on domain decomposition method to deal with ill-conditioned matrices arising from the approximation problem.


Exterior Neumann problem Boundary integral equation Prolate spheroid Radial basis function 

Mathematics Subject Classifications (2010)

65N30 65N38 65N55 


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© Springer Science+Business Media, LLC. 2010

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsUniversity of New South WalesSydneyAustralia
  2. 2.Institut für Angewandte Mathematik and QUEST (Centre for Quantum Engineering and Space-Time Research)Leibniz Universität HannoverHannoverGermany

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