Overlapping additive Schwarz preconditioners for elliptic PDEs on the unit sphere

Le Gia, Q.; Sloan, I.; Tran, T.

doi:10.1090/S0025-5718-08-02150-9

Overlapping additive Schwarz preconditioners for elliptic PDEs on the unit sphere
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by Q. T. Le Gia, I. H. Sloan and T. Tran;

Math. Comp. 78 (2009), 79-101

DOI: https://doi.org/10.1090/S0025-5718-08-02150-9

Published electronically: July 28, 2008

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Abstract:

We present an overlapping domain decomposition technique for solving elliptic partial differential equations on the sphere. The approximate solution is constructed using shifts of a strictly positive definite kernel on the sphere. The condition number of the Schwarz operator depends on the way we decompose the scattered set into smaller subsets. The method is illustrated by numerical experiments on relatively large scattered point sets taken from MAGSAT satellite data.

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