Low-rank approximation of integral operators by using the Green formula and quadrature.

Börm, Steffen and Gördes, Jessica (2013) Low-rank approximation of integral operators by using the Green formula and quadrature. Numerical Algorithms, 64 (3). pp. 567-592. DOI 10.1007/s11075-012-9679-2.

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Abstract

Approximating integral operators by a standard Galerkin discretisation typically leads to dense matrices. To avoid the quadratic complexity it takes to compute and store a dense matrix, several approaches have been introduced including H-matrices. The kernel function is approximated by a separable function, this leads to a low rank matrix. Interpolation is a robust and popular scheme, but requires us to interpolate in each spatial dimension, which leads to a complexity of m^d for m-th order. Instead of interpolation we propose using quadrature on the kernel function represented with Green’s formula. Due to the fact that we are integrating only over the boundary, we save one spatial dimension compared to the interpolation method and get a complexity of m^(d-1).

Document Type: Article
Keywords: Integral equations Data-sparse approximation Quadrature Green’s formula Hierarchical matrices
Research affiliation: Kiel University > Kiel Marine Science
OceanRep > The Future Ocean - Cluster of Excellence
Kiel University
Refereed: Yes
Open Access Journal?: Yes
DOI etc.: 10.1007/s11075-012-9679-2
ISSN: 1017-1398
Projects: Future Ocean
Date Deposited: 31 Jan 2018 11:14
Last Modified: 16 Jul 2019 09:25
URI: http://oceanrep.geomar.de/id/eprint/41771

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