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

Authors:
Q. T. Le Gia;E. P. Stephan;T. Tran
Affiliations:
School of Mathematics and Statistics, University of New South Wales, Sydney, Australia 2052;Institut für Angewandte Mathematik and QUEST (Centre for Quantum Engineering and Space-Time Research), Leibniz Universität Hannover, Hannover, Germany 30167;School of Mathematics and Statistics, University of New South Wales, Sydney, Australia 2052
Venue:
Advances in Computational Mathematics
Year:
2011

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Abstract

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.