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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.