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Fast quadrature techniques for retarded potentials based on TT/QTT tensor approximation


Khoromskij, B; Sauter, S; Veit, A (2011). 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 effciency 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 effciency 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:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Date:2011
Deposited On:21 Sep 2011 09:02
Last Modified:20 Sep 2018 03:24
Publisher:Vydavetstvo Belaruskaya Navuka
ISSN:1609-4840
OA Status:Green
Free access at:Official URL. An embargo period may apply.
Official URL:http://www.cmam.info/index.php?do=issues/art&vol=11&num=3&art=322

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