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Title of Journal: Numer Math

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Abbravation: Numerische Mathematik

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Springer-Verlag

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DOI

10.1002/uog.2350

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0945-3245

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Preconditioners for pseudodifferential equations o

Authors: T Tran Q T Le Gia I H Sloan E P Stephan
Publish Date: 2009/10/14
Volume: 115, Issue: 1, Pages: 141-163
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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 illconditioned 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

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