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We have decided to discontinue the publication of preprints on our preprint server end of 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
Fast Quadrature Techniques for Retarded Potentials Based on TT/QTT Tensor Approximation
Boris N. Khoromskij, Stefan A. Sauter and Alexander VeitAbstract
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.
- Received:
- 14.07.11
- Published:
- 14.07.11
- MSC Codes:
- 65F30, 65F50, 65N35
- Keywords:
- tensor approximation, quantized representation of vectors, retarded potentials, 3D wave equation, quadrature rules