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Computational Methods in Applied Mathematics

Editor-in-Chief: Carstensen, Carsten

Managing Editor: Matus, Piotr

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1609-9389
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Volume 11, Issue 3 (Jan 2001)

Issues

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

Boris Khoromskij
  • Max-Planck-Institute for Mathematics in the Sciences, Inselstr. 22-26, D-04103 Leipzig, Germany.
  • Email:
Stefan Sauter
  • Institut für Mathematik Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland.
  • Email:
Alexander Veit
  • Email:

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.

Keywords: multi-dimensional problems; tensor approximation; quantized representation of vectors; model reduction; retarded potentials; 3D wave equation; quadrature rules

About the article

Received: 2011-07-29

Revised: 2011-08-11

Accepted: 2011-08-21

Published in Print:



Citation Information: Computational Methods in Applied Mathematics Comput. Methods Appl. Math., ISSN (Online) 1609-9389, ISSN (Print) 1609-4840, DOI: https://doi.org/10.2478/cmam-2011-0019. Export Citation

© Institute of Mathematics, NAS of Belarus. This article is distributed under the terms of the Creative Commons Attribution Non-Commercial License, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY-NC-ND 4.0)

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