RBF Multiscale Collocation for Second Order Elliptic Boundary Value Problems
Type
ArticleKAUST Grant Number
KUK-C1-013-04Date
2013-01Permanent link to this record
http://hdl.handle.net/10754/599450
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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 multilevel 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. © 2013 Society for Industrial and Applied Mathematics.Citation
Farrell P, Wendland H (2013) RBF Multiscale Collocation for Second Order Elliptic Boundary Value Problems. SIAM J Numer Anal 51: 2403–2425. Available: http://dx.doi.org/10.1137/120898383.Sponsors
This work was supported in part by award KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).ae974a485f413a2113503eed53cd6c53
10.1137/120898383