A fast direct solver for nonlocal operators in wavelet coordinates
Additional information
Authors
Harbrecht H.,
Multerer M.
Type
Journal Article
Language
English
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.
Keywords
Nonlocal operator, Direct solver, Wavelet matrix compression, Polarizable continuum model, Fractional Laplacian, Gaussian random fields
Journal
Journal of computational physics
Volume
428
Pages (or article number)
15 p
Diffusion
License
CC BY
Visibility
Public
Status open access
Hybrid
