Block preconditioners for linear systems arising from multiscale collocation with compactly supported RBFs

Patricio Farrell, Jennifer Pestana

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

© 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.
Original languageEnglish (US)
Pages (from-to)731-747
Number of pages17
JournalNumerical Linear Algebra with Applications
Volume22
Issue number4
DOIs
StatePublished - Apr 30 2015
Externally publishedYes

Fingerprint Dive into the research topics of 'Block preconditioners for linear systems arising from multiscale collocation with compactly supported RBFs'. Together they form a unique fingerprint.

Cite this