Complete radiation boundary conditions for acoustic waves

Abstract

The radiation of energy to the far field is a central feature of acoustics. As such, efficient, convergent domain truncation algorithms are a necessary component of any software for simulating acoustic waves in the time domain. Complete radiation boundary conditions are, in our view, an ideal solution to this problem. In particular, they are provably spectrally convergent, depending on parameters which can be chosen automatically to guarantee any required accuracy; as they directly approximate both propagating and evanescent modes, the computational boundary can be placed arbitrarily close to scatterers or other inhomogeneities. In this talk we will outline the theory behind the method for scattering and waveguide problems with a homogeneous far field, discuss the simple implementation of the method via the solution of a coupled system wave equations in a thin double absorbing boundary layer, and consider its application in more complex settings including advective acoustics, stratified media, and random media. Numerical experiments in three space dimensions using high-order methods will be shown.