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MiS Preprint

Sparse Convolution Quadrature for Time Domain Boundary Integral Formulations of the Wave Equation by Cutoff and Panel-Clustering

Wolfgang Hackbusch, Wendy Kress and Stefan A. Sauter


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 $N\log^2 N M^2$, 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.

MSC Codes:
35L05, 74S15
boundary integral equations, wave equation, convolution quadrature, panel-clustering

Related publications

2007 Repository Open Access
Wolfgang Hackbusch, Wendy Kress and Stefan A. Sauter

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

In: Boundary element analysis / Martin Schanz... (eds.)
Berlin : Springer, 2007. - pp. 113-134
(Lecture notes in applied and computational mechanics ; 29)