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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Keywords
- Boundary Element Method
- Convolution Quadrature
- Versus B95L
- Galerkin Boundary Element Method
- Convolution Quadrature Method
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Hackbusch, W., Kress, W., Sauter, S.A. (2007). Sparse Convolution Quadrature for Time Domain Boundary Integral Formulations of the Wave Equation by Cutoff and Panel-Clustering. In: Schanz, M., Steinbach, O. (eds) Boundary Element Analysis. Lecture Notes in Applied and Computational Mechanics, vol 29. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-47533-0_5
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