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Sparse convolution quadrature for time domain boundary integral formulations of the wave equation by cutoff and panel-clustering


Hackbusch, W; Kress, W; Sauter, S (2007). Sparse convolution quadrature for time domain boundary integral formulations of the wave equation by cutoff and panel-clustering. In: Schanz, M; Steinbach, O. Boundary element analysis. Berlin: Springer, 113-134.

Abstract

We consider the wave equation in a time domain boundary integral formulation. To obtain a stable time discretization, we employ the convolution quadrature method in time, developed by Lubich. In space, a Galerkin boundary element method is considered. The resulting Galerkin matrices are fully populated and the computational complexity is proportional to N log2 NM 2, where M is the number of spatial unknowns and N is the number of time steps.
We present two ways of reducing these costs. The first is an a priori cutoff strategy, which allows to replace a substantial part of the matrices by 0. The second is a panel clustering approximation, which further reduces the storage and computational cost by approximating subblocks by low rank matrices.

Abstract

We consider the wave equation in a time domain boundary integral formulation. To obtain a stable time discretization, we employ the convolution quadrature method in time, developed by Lubich. In space, a Galerkin boundary element method is considered. The resulting Galerkin matrices are fully populated and the computational complexity is proportional to N log2 NM 2, where M is the number of spatial unknowns and N is the number of time steps.
We present two ways of reducing these costs. The first is an a priori cutoff strategy, which allows to replace a substantial part of the matrices by 0. The second is a panel clustering approximation, which further reduces the storage and computational cost by approximating subblocks by low rank matrices.

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Additional indexing

Item Type:Book Section, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2007
Deposited On:11 Dec 2009 07:50
Last Modified:05 Apr 2016 13:23
Publisher:Springer
Series Name:Lecture Notes in Applied and Computational Mechanics
Number:29
ISBN:978-3-540-47465-4
Publisher DOI:https://doi.org/10.1007/978-3-540-47533-0
Related URLs:http://www.ams.org/mathscinet-getitem?mr=2307201

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