Approximation of integral operators by Green quadrature and nested cross approximation

Börm, Steffen and Christophersen, Sven (2016) Approximation of integral operators by Green quadrature and nested cross approximation Numerische Mathematik, 133 (3). pp. 409-442. DOI 10.1007/s00211-015-0757-y.

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Abstract

We present a fast algorithm that constructs a data-sparse approximation of matrices arising in the context of integral equation methods for elliptic partial differential equations. The new algorithm uses Green’s representation formula in combination with quadrature to obtain a first approximation of the kernel function, and then applies nested cross approximation to obtain a more efficient representation. The resulting {\mathcal H}^2
-matrix representation requires {\mathcal O}(n k)
units of storage for an n\times n
matrix, where k depends on the prescribed accuracy.

Document Type: Article
Keywords: 65N38 65N80 65D30 45B05
Research affiliation: OceanRep > The Future Ocean - Cluster of Excellence
Kiel University
Refereed: Yes
DOI etc.: 10.1007/s00211-015-0757-y
ISSN: 0029-599X
Date Deposited: 14 Dec 2017 13:51
Last Modified: 24 Sep 2019 03:48
URI: http://eprints.uni-kiel.de/id/eprint/40654

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