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.

翻译：我们考虑具有分段线性边界的二维区域（可能包含散射体）上的波传播问题。在初始条件和强迫项具有径向对称性且紧支撑（这在应用中很常见）的假设下，我们提出将传播波近似为若干特殊非线性时空函数的叠加：该求和中的每一项对应一条特定射线，用以刻画单次反射或衍射效应。我们描述了一种基于区域几何特性自动识别此类射线的算法。为展示所提方法，我们给出了若干数值算例，包括楔形波散射以及障碍物存在下房间内的波传播。