The Mathematical Institute, University of Oxford, Eprints Archive

RBF multiscale collocation for second order elliptic boundary value problems

Farrell, P. and Wendland, H. (2013) RBF multiscale collocation for second order elliptic boundary value problems. SIAM Journal on Numerical Analysis . (Submitted)

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Abstract

In this paper, we discuss multiscale radial basis function collocation methods for solving elliptic partial differential equations on bounded domains. The approximate solution is constructed in a multi-level fashion, each level using compactly supported radial basis functions of smaller scale on an increasingly fine mesh. On each level, standard symmetric collocation is employed. A convergence theory is given, which builds on recent theoretical advances for multiscale approximation using compactly supported radial basis functions. We are able to show that the convergence is linear in the number of levels. We also discuss the condition numbers of the arising systems and the effect of simple, diagonal preconditioners, now proving rigorously previous numerical observations.

Item Type:Article
Subjects:D - G > General
Research Groups:Oxford Centre for Collaborative Applied Mathematics
ID Code:1720
Deposited By: Peter Hudston
Deposited On:30 Jul 2013 13:14
Last Modified:29 May 2015 19:24

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