Block preconditioners for linear systems arising from multiscale collocation with compactly supported RBFs
Type
ArticleKAUST Grant Number
KUK- C1-013-04Date
2015-04-30Online Publication Date
2015-04-30Print Publication Date
2015-08Permanent link to this record
http://hdl.handle.net/10754/597686
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© 2015John Wiley & Sons, Ltd. Symmetric collocation methods with RBFs allow approximation of the solution of a partial differential equation, even if the right-hand side is only known at scattered data points, without needing to generate a grid. However, the benefit of a guaranteed symmetric positive definite block system comes at a high computational cost. This cost can be alleviated somewhat by considering compactly supported RBFs and a multiscale technique. But the condition number and sparsity will still deteriorate with the number of data points. Therefore, we study certain block diagonal and triangular preconditioners. We investigate ideal preconditioners and determine the spectra of the preconditioned matrices before proposing more practical preconditioners based on a restricted additive Schwarz method with coarse grid correction. Numerical results verify the effectiveness of the preconditioners.Citation
Farrell P, Pestana J (2015) Block preconditioners for linear systems arising from multiscale collocation with compactly supported RBFs. Numerical Linear Algebra with Applications 22: 731–747. Available: http://dx.doi.org/10.1002/nla.1984.Sponsors
We thank the referees for their helpful comments that improved the paper. This work was supported in part by award KUK- C1-013-04, made by King Abdullah University of Science and Technology (KAUST).Publisher
WileyDOI
10.1002/nla.1984ae974a485f413a2113503eed53cd6c53
10.1002/nla.1984