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

By Boris N. Khoromskij, Stefan A. Sauter, Alexander Veit. 2011

18 citations recorded by the source corpus.

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.

Subfields: Atomic and Molecular Physics, and Optics, Electrical and Electronic Engineering, Mechanics of Materials

Citations in the corpus

• A literature survey of low‐rank tensor approximation techniques (2013, neutral): “QTT has been applied to the solution of PDEs and eigenvalue problems [144, 154, 162], evaluation of boundary integrals in BEM [164], convolution [107] and the FFT [63, 108, 230].”