Harbrecht, Helmut Multerer, Michael 2020-12-16 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. application/pdf https://susi.usi.ch/global/documents/319364 https://n2t.net/ark:/12658/srd1319364 https://susi.usi.ch/documents/319364/files/Multerer_2020_Else_jcp.pdf eng info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jcp.2020.110056 info:eu-repo/semantics/altIdentifier/ark/12658/srd1319364 info:eu-repo/semantics/openAccess CC BY Journal of computational physics. - 2021, vol. 428, p. 15 p Nonlocal operator Direct solver Wavelet matrix compression Polarizable continuum model Fractional Laplacian Gaussian random fields info:eu-repo/classification/udc/51 A fast direct solver for nonlocal operators in wavelet coordinates http://purl.org/coar/resource_type/c_6501