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A fast direct solver for nonlocal operators in wavelet coordinates
JournalArticle (Originalarbeit in einer wissenschaftlichen Zeitschrift) |
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ID |
4615261 |
Author(s) |
Harbrecht, Helmut; Multerer, Michael D. |
Author(s) at UniBasel |
Harbrecht, Helmut
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Year |
2021 |
Title |
A fast direct solver for nonlocal operators in wavelet coordinates |
Journal |
Journal of computational physics |
Volume |
428 |
Pages / Article-Number |
110056 |
Keywords |
Nonlocal operator; direct solver; wavelet matrix compression; polarizable continuum model; fractional Laplacian; Gaussian random fields |
Abstract |
In this article, we consider fast direct solvers for nonlocal operators. The pivotal idea is to combine a wavelet representation of the system matrix, yielding a quasi-sparse matrix, with the nested dissection ordering scheme. The latter drastically reduces the fill-in during the factorization of the system matrix by means of a Cholesky decomposition or an LU decomposition, respectively. This way, we end up with the exact inverse of the compressed system matrix with only a moderate increase of the number of nonzero entries in the matrix.
To illustrate the efficacy of the approach, we conduct numerical experiments for different highly relevant applications of nonlocal operators: We consider (i) the direct solution of boundary integral equations in three spatial dimensions, issuing from the polarizable continuum model, (ii) a parabolic problem for the fractional Laplacian in integral form and (iii) the fast simulation of Gaussian random fields. |
Publisher |
ACADEMIC PRESS INC ELSEVIER SCIENCE |
ISSN/ISBN |
0021-9991 |
Full Text on edoc |
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Digital Object Identifier DOI |
10.1016/j.jcp.2020.110056 |
ISI-Number |
WOS:000612234200011 |
Document type (ISI) |
Article |
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25/04/2024
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