Preconditioners for pseudodifferential equations on the sphere with radial basis functions |
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Authors: | T Tran Q T Le Gia I H Sloan E P Stephan |
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Institution: | (1) School of Mathematics, University of New South Wales, Sydney, 2052, Australia;(2) Institut für Angewandte Mathematik, University of Hannover, Welfengarten 1, D-30167 Hannover, Germany |
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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
\mathbbS2{\mathbb{S}^2} . |
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Keywords: | |
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