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Mathematics of Computation

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Overlapping additive Schwarz preconditioners for elliptic PDEs on the unit sphere


Authors: Q. T. Le Gia, I. H. Sloan and T. Tran
Journal: Math. Comp. 78 (2009), 79-101
MSC (2000): Primary 33F05, 65N55; Secondary 65N30
DOI: https://doi.org/10.1090/S0025-5718-08-02150-9
Published electronically: July 28, 2008
MathSciNet review: 2448698
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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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Additional Information

Q. T. Le Gia
Affiliation: School of Mathematics and Statistics, The University of New South Wales, Sydney 2052, Australia
Email: qlegia@maths.unsw.edu.au

I. H. Sloan
Affiliation: School of Mathematics and Statistics, The University of New South Wales, Sydney 2052, Australia
Email: I.Sloan@unsw.edu.au

T. Tran
Affiliation: School of Mathematics and Statistics, The University of New South Wales, Sydney 2052, Australia
Email: Thanh.Tran@unsw.edu.au

DOI: https://doi.org/10.1090/S0025-5718-08-02150-9
Keywords: Sphere, spherical basis function, domain decomposition, elliptic partial differential equation
Received by editor(s): December 15, 2006
Received by editor(s) in revised form: January 31, 2008
Published electronically: July 28, 2008
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.