We introduce a new class of computationally tractable scattering problems in unbounded domains, which we call decomposable problems. In these decomposable problems, the computational domain can be split into a finite collection of subdomains in which the scatterer has a "simple" structure. A subdomain is simple if the domain Green's function for this subdomain is either available analytically or can be computed numerically with arbitrary accuracy by a tractable method. These domain Green's functions are then used to reformulate the scattering problem as a system of boundary integral equations on the union of the subdomain boundaries. This reformulation gives a practical numerical method, as the resulting integral equations can then be solved, to any desired degree of accuracy, by using coordinate complexification over a finite interval, and standard discretization techniques.

翻译：本文引入了一类新的计算可处理的散射问题，我们称之为可分解问题。在这些可分解问题中，计算域可以被分割成有限个子域集合，其中散射体具有“简单”结构。若某个子域的域格林函数能够解析获得，或可通过一种可处理方法以任意精度数值计算，则该子域被视为简单的。这些域格林函数随后被用于将散射问题重新表述为子域边界并集上的边界积分方程组。这种重构提供了一种实用的数值方法，因为所得的积分方程可以通过在有限区间上进行坐标复化，并应用标准离散化技术，以任意期望的精度进行求解。