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Fast Quadrature Techniques for Retarded Potentials Based on TT/QTT Tensor Approximation


Khoromskij, Boris; Sauter, Stefan; Veit, Alexander (2001). Fast Quadrature Techniques for Retarded Potentials Based on TT/QTT Tensor Approximation. Computational Methods in Applied Mathematics, 11(3):342-362.

Abstract

We consider the Galerkin approach for the numerical solution of retarded boundary integral formulations of the three dimensional wave equation in unbounded domains. Recently smooth and compactly supported basis functions in time were introduced which allow the use of standard quadrature rules in order to compute the entries of the boundary element matrix. In this paper, we use TT and QTT tensor approximations to increase the efficiency of these quadrature rules. Various numerical experiments show the substantial reduction of the computational cost that is needed to obtain accurate approximations for the arising integrals

Abstract

We consider the Galerkin approach for the numerical solution of retarded boundary integral formulations of the three dimensional wave equation in unbounded domains. Recently smooth and compactly supported basis functions in time were introduced which allow the use of standard quadrature rules in order to compute the entries of the boundary element matrix. In this paper, we use TT and QTT tensor approximations to increase the efficiency of these quadrature rules. Various numerical experiments show the substantial reduction of the computational cost that is needed to obtain accurate approximations for the arising integrals

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:National licences > 142-005
Dewey Decimal Classification:510 Mathematics
Language:English
Date:1 January 2001
Deposited On:18 Oct 2018 14:06
Last Modified:31 Jul 2020 02:24
Publisher:De Gruyter
ISSN:1609-4840
OA Status:Green
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.2478/cmam-2011-0019
Related URLs:https://www.swissbib.ch/Search/Results?lookfor=nationallicencegruyter102478cmam20110019 (Library Catalogue)

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