Geometry-based approximation of waves in complex domains

TL;DR

This paper introduces a geometry-based method to approximate wave propagation in complex 2D domains with piecewise-linear boundaries, modeling reflections and diffractions through a sum of specialized functions.

Contribution

It presents an automatic algorithm to identify wave components related to reflections and diffractions based on domain geometry, with practical numerical examples.

Findings

Effective approximation of wave scattering in complex geometries

Automatic identification of wave components from domain features

Open-source software implementation provided

Abstract

We consider wave propagation problems over 2-dimensional domains with piecewise-linear boundaries, possibly including scatterers. We assume that the wave speed is constant, and that the initial conditions and forcing terms are radially symmetric and compactly supported. We propose an approximation of the propagating wave as the sum of some special space-time functions. Each term in this sum identifies a particular field component, modeling the result of a single reflection or diffraction effect. We describe an algorithm for identifying such components automatically, based on the domain geometry. To showcase our proposed method, we present several numerical examples, such as waves scattering off wedges and waves propagating through a room in presence of obstacles. Software implementing our numerical algorithm is made available as open-source code.