Fast and oblivious algorithms for dissipative and two-dimensional wave equations

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.