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
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Submission date: 24. Feb. 2006
published in: Boundary element analysis / M.Schanz ... (eds.)
Berlin : Springer, 2007. - P. 113 - 134
(Lecture notes in applied and computational mechanics ; 29)
DOI number (of the published article): 10.1007/978-3-540-47533-0_5
MSC-Numbers: 35L05, 74S15
Keywords and phrases: boundary integral equations, wave equation, convolution quadrature, panel-clustering
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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 , 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.