Sparsity of Runge-Kutta convolution weights for three-dimensional wave equation

Lehel Banjai and Maryna Kachanovska

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Submission date: 18. Dec. 2012
Pages: 27
published in: BIT : numerical mathematics, 54 (2014) 4, p. 901-936 
DOI number (of the published article): 10.1007/s10543-014-0498-9
Bibtex
MSC-Numbers: 65R20, 65L06, 35L05, 65M38
Keywords and phrases: convolution quadrature, Runge-Kutta methods, time-domain boundary integral equations, wave equation
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Abstract:
Wave propagation problems in unbounded homogeneous domains can be formulated as time-domain integral equations. An effective way to discretize such equations in time are Runge-Kutta based convolution quadratures. In this paper the behaviour of the weights of such quadratures are investigated. In particular approximate sparseness of their Galerkin discretization is analyzed. Application of these results in the construction of fast algorithms for the construction of the fully discrete systems is also briefly described.