This paper presents a windowed Green function (WGF) method for the numerical solution of problems of elastic scattering by “locally-rough surfaces” (i.e., local perturbations of a half space), under either Dirichlet or Neumann boundary conditions, and in both two and three spatial dimensions. The proposed WGF method relies on an integral-equation formulation based on the free-space Green function, together with smooth operator windowing (based on a “slow-rise” windowing function) and efficient high-order singular-integration methods. The approach avoids the evaluation of the expensive layer Green function for elastic problems on a half-space, and it yields uniformly fast convergence for all incident angles. Numerical experiments for both two and three dimensional problems are presented, demonstrating the accuracy and super-algebraically fast convergence of the proposed method as the window-size grows.

本文提出了一种窗口格林函数（WGF）方法，用于在Dirichlet或Neumann边界条件下以及在两个条件下通过“局部粗糙表面”（即半空间的局部扰动）对弹性散射问题进行数值求解。和三个空间维度。所提出的WGF方法依赖于基于自由空间Green函数的积分方程公式，平滑的操作员加窗（基于“慢升”加窗功能）以及有效的高阶奇异积分方法。该方法避免了针对半空间上的弹性问题评估昂贵的层格林函数，并且对于所有入射角均产生了均匀快速的收敛。给出了针对二维和三维问题的数值实验，证明了所提方法随着窗口尺寸的增长的准确性和超代数快速收敛性。