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.
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Communicated by Juan Manuel Peña.
Dedicated to R.S. Anderssen on the occasion of his 70th birthday.
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Le Gia, Q.T., Stephan, E.P. & Tran, T. Solution to the Neumann problem exterior to a prolate spheroid by radial basis functions. Adv Comput Math 34, 83–103 (2011). https://doi.org/10.1007/s10444-010-9145-4
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DOI: https://doi.org/10.1007/s10444-010-9145-4