A fast direct solver for nonlocal operators in wavelet coordinates

Harbrecht, Helmut and Multerer, Michael. (2020) A fast direct solver for nonlocal operators in wavelet coordinates. Preprints Fachbereich Mathematik, 2020 (04).


Official URL: https://edoc.unibas.ch/79041/

Downloads: Statistics Overview


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.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Computational Mathematics (Harbrecht)
12 Special Collections > Preprints Fachbereich Mathematik
UniBasel Contributors:Harbrecht, Helmut
Item Type:Preprint
Publisher:Universität Basel
edoc DOI:
Last Modified:03 Nov 2020 19:12
Deposited On:03 Nov 2020 19:12

Repository Staff Only: item control page