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, 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.

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，该区域可能包含散射体。在初始条件与强迫项具有径向对称性且紧支撑的假设下，我们提出将传播波近似为若干特殊时空函数的叠加。该求和中的每一项对应特定的场分量，用于建模单次反射或衍射效应。基于域几何特征，我们描述了一种自动识别此类分量的算法。为展示所提方法，我们给出若干数值算例，包括楔形散射及含障碍物房间内的波传播问题。