半空间弹性散射问题的加窗格林函数法
A Windowed Green Function method for elastic scattering problems on a half-space
摘要：
本文提出了一种加窗格林函数（WGF）方法，用于数值求解“局部粗糙面”（即，半空间的局部扰动），在Dirichlet或Neumann边界条件下，以及在二维和三维空间中。所提出的WGF方法依赖于基于自由空间格林函数的积分方程制定，连同平滑算子加窗（基于“慢升”加窗函数）和高效的高阶奇异积分方法。该方法避免了昂贵的层格林函数的弹性问题的半空间上的评估，它产生一致的快速收敛的所有入射角。二维和三维问题的数值实验，证明了所提出的方法的精度和超代数快速收敛的窗口大小的增长。
英文摘要：
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.
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