An overlapping additive Schwarz preconditioner for the Laplace-Beltrami equation using spherical splines
type: Item
instance of: scholarly article
title: An overlapping additive Schwarz preconditioner for the Laplace-Beltrami equation using spherical splines
zbMATH Open document ID: 1262.65190
author: M. C. Fu
published in: Advances in Computational Mathematics
publication date: 2012-12-21T00:00:00Z
review text: The paper deals with an overlapping domain decomposition technique based on a two-level mesh for solving the Laplace-Beltrami equation on the sphere. Spherical splines are used to solve the equation by Galerkin's method. The authors overcome the ill-conditionedness of the resulting linear system by preconditioning with additive Schwarz methods. The authors prove that the condition number of the additive Schwarz operator is bounded by \(O(H^{2}/h^{2})\) where \(H\) and \(h\) are the sizes of the coarse and fine meshes, respectively. A better bound is proved if the degree of the splines is even. Numerical experiments on large point sets taken from MAGSAT satellite data illustrate the method.
reviewed by: Adrian Carabineanu
Mathematics Subject Classification ID: 65N55
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65F08
Mathematics Subject Classification ID: 58J05
Mathematics Subject Classification ID: 35J05
zbMATH DE Number: 6117978
zbMATH Keywords: Laplace-Beltrami equation
zbMATH Keywords: sphere
zbMATH Keywords: spherical spline
zbMATH Keywords: domain decomposition
zbMATH Keywords: overlapping method
zbMATH Keywords: Galerkin's method
zbMATH Keywords: preconditioning
zbMATH Keywords: additive Schwarz method
zbMATH Keywords: condition number
zbMATH Keywords: numerical experiments
describes a project that uses: STRIPACK
MaRDI profile type: Publication
full work available at URL: s10444-011-9200-9
OpenAlex ID: W2056550748
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DOI: 10.1007/S10444-011-9200-9
description: scientific article; zbMATH DE number 6117978