|Publisher DOI:||10.1016/j.camwa.2018.10.042||Title:||Domain decomposition methods in scattered data interpolation with conditionally positive definite radial basis functions||Language:||English||Authors:||Le Borne, Sabine
|Issue Date:||15-Feb-2019||Source:||Computers and Mathematics with Applications 4 (77): 1178-1196 (2019-02-15)||Abstract (english):||
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.
|URI:||http://hdl.handle.net/11420/2327||ISSN:||0898-1221||Journal:||Computers and mathematics with applications||Institute:||Mathematik E-10||Document Type:||Article|
|Appears in Collections:||Publications without fulltext|
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