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Domain decomposition methods in scattered data interpolation with conditionally positive definite radial basis functions
Publikationstyp
Journal Article
Date Issued
2019-02-15
Sprache
English
Author(s)
Institut
TORE-URI
Volume
77
Issue
4
Start Page
1178
End Page
1196
Citation
Computers and Mathematics with Applications 4 (77): 1178-1196 (2019-02-15)
Publisher DOI
Scopus ID
Scattered data interpolation using conditionally positive definite radial basis functions (RBFs) requires the solution of a symmetric saddle-point system. Based on an approximation of the system matrix as a hierarchical matrix, we solve the system iteratively using the GMRes algorithm and a domain decomposition preconditioner. The novelty of our work lies in the proposed solution of the subdomain problems using the nullspace method with an orthogonal basis represented as a sequence of Householder reflectors. The resulting positive definite subdomain systems are solved either directly or using an inner GMRes iteration with H-Cholesky preconditioning. Numerical tests demonstrate the effectiveness of this solution process for up to N=160000 centers in two and three dimensions.