

Preprint 72/2012
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.