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

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Farrell, Patricio and Pestana, Jennifer (2015) Block preconditioners for linear systems arising from multiscale collocation with compactly supported RBFs. Numerical Linear Algebra with Applications, 22 (4). pp. 731-747. ISSN 1070-5325 (https://doi.org/10.1002/nla.1984)

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Abstract

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.

ORCID iDs

Farrell, Patricio and Pestana, Jennifer ORCID logoORCID: https://orcid.org/0000-0003-1527-3178;
  • Item type:Article
    ID code:54750
    Dates:
    Date
    Event
    August 2015
    Published
    30 April 2015
    Published Online
    6 March 2015
    Accepted
    Subjects:Science > Mathematics
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Pure Administrator
    Date deposited:11 Dec 2015 01:26
    Last modified:18 Dec 2024 01:18
    URI:https://strathprints.strath.ac.uk/id/eprint/54750
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