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

  • Wolfgang Hackbusch
  • Wendy Kress
  • Stefan A. Sauter
Part of the Lecture Notes in Applied and Computational Mechanics book series (LNACM, volume 29)


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.


Boundary Element Method Convolution Quadrature Versus B95L Galerkin Boundary Element Method Convolution Quadrature Method 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Wolfgang Hackbusch
    • 1
  • Wendy Kress
    • 1
  • Stefan A. Sauter
    • 2
  1. 1.Max-Planck-Institut für Mathematik in den NaturwissenschaftenLeipzigGermany
  2. 2.Institut für MathematikUniversität ZürichZürichSwitzerland

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