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Fast and oblivious algorithms for dissipative and two-dimensional wave equations. (English) Zbl 1362.65140

Summary: The use of time-domain boundary integral equations has proved very effective and efficient for three-dimensional acoustic and electromagnetic wave equations. In even dimensions and when some dissipation is present, time-domain boundary equations contain an infinite memory tail. Due to this, computation for longer times becomes exceedingly expensive. In this paper we show how oblivious quadrature, initially designed for parabolic problems, can be used to significantly reduce both the cost and the memory requirements of computing this tail. We analyze Runge-Kutta-based quadrature and conclude the paper with numerical experiments.

MSC:

65R20 Numerical methods for integral equations
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
65M38 Boundary element methods for initial value and initial-boundary value problems involving PDEs

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