论文标题
窗户的绿色功能方法，用于半空间上的弹性散射问题
A Windowed Green Function method for elastic scattering problems on a half-space
论文作者
论文摘要
本文提出了一种窗口的绿色函数（WGF）方法，用于通过“局部弯曲表面”（即半空间的局部扰动），dirichlet或neumann边界条件以及两个空间维度的数值解决方案（即半空间的局部扰动）。所提出的WGF方法依赖于基于自由空间绿色功能的积分方程式，以及平滑的操作员窗口（基于“慢速”窗口功能）和有效的高阶单数融合方法。该方法避免了对半空间弹性问题的昂贵层绿色函数的评估，并且对于所有入射角都会产生均匀的快速收敛。提出了两个和三维问题的数值实验，证明了随着窗口尺寸的增长，该方法的准确性和超级代数快速收敛。
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.
