Fast and oblivious algorithms for dissipative and 2D wave equations
This work provides a practical solution for reducing computational burden in wave propagation simulations with memory effects, benefiting researchers in computational acoustics and electromagnetics.
The paper addresses the computational cost and memory requirements of time-domain boundary integral equations for dissipative and 2D wave equations, which suffer from an infinite memory tail. By applying oblivious quadrature originally designed for parabolic problems, they significantly reduce both cost and memory, as demonstrated through numerical experiments.
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 analyse Runge-Kutta based quadrature and conclude the paper with numerical experiments.