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

Boris N. Khoromskij, Stefan A. Sauter, and Alexander Veit

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Submission date: 14. Jul. 2011
Pages: 22
published in: Computational methods in applied mathematics, 11 (2011) 3, p. 342-362 
DOI number (of the published article): 10.2478/cmam-2011-0019
Bibtex
MSC-Numbers: 65F30, 65F50, 65N35
Keywords and phrases: tensor approximation, quantized representation of vectors, retarded potentials, 3D wave equation, quadrature rules
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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.