Geometry-based approximation of waves in complex domains

We consider wave propagation problems over 2-dimensional domains with piecewise-linear boundaries, possibly including scatterers. Under the assumption that the initial conditions and forcing terms are radially symmetric and compactly supported (which is common in applications), we propose an approximation of the propagating wave as the sum of some special nonlinear space-time functions: each term in this sum identifies a particular ray, modeling the result of a single reflection or diffraction effect. We describe an algorithm for identifying such rays 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.