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.

翻译：本文研究具有分段线性边界的二维区域上的波传播问题，可能包含散射体。我们假设波速恒定，且初始条件和强迫项具有径向对称性与紧支集特性。我们提出将传播波近似表示为若干特殊时空函数之和。该求和式中的每一项对应特定场分量，用于模拟单次反射或衍射效应的结果。我们描述了一种基于域几何自动识别此类分量的算法。为展示所提方法，我们给出了若干数值算例，例如楔形散射波与存在障碍物时室内传播波的情况。实现本数值算法的软件已作为开源代码发布。