Sparse Convolution Quadrature for Time Domain Boundary Integral Formulations of the Wave Equation

Wolfgang Hackbusch, Wendy Kress, and Stefan A. Sauter

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Submission date: 09. Dec. 2005 (revised version: February 2006)
Pages: 23
published in: IMA journal of numerical analysis, 29 (2009) 1, p. 158-179 
DOI number (of the published article): 10.1093/imanum/drm044
Bibtex
MSC-Numbers: 35L05, 74S15, 65N38
Keywords and phrases: boundary integral equations, wave equation, convolution quadrature, time domain, stability
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Abstract:
Many important physical applications are governed by the wave equation. The formulation as time domain boundary integral equations involves retarded potentials. For the numerical solution of this problem we employ the convolution quadrature method for the discretization in time and the Galerkin boundary element method for the space discretization. We will introduce a simple a-priori cutoff strategy where small entries of the system matrix are replaced by zero. The threshold for the cutoff is determined by an a-priori analysis which will be developed in this paper. This method reduces the storage requirements from O(M² N log² N) to O(M^1+s N log² N) for some s between 0 and 1 where N denotes the number of time steps and M is the dimension of the boundary element space.