Fast and oblivious algorithms for dissipative and 2D wave equations

TL;DR

This paper introduces oblivious quadrature methods to efficiently compute dissipative and 2D wave equations using boundary integral equations, significantly reducing computational cost and memory for long-time simulations.

Contribution

It adapts oblivious quadrature techniques to wave equations with dissipation, enabling efficient long-time boundary integral computations.

Findings

Oblivious quadrature reduces computational cost for long-time simulations.

The method effectively handles dissipative and 2D wave equations.

Numerical experiments confirm the efficiency and accuracy of the approach.

Abstract

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.