A Windowed Green Function method for elastic scattering problems on a half-space

TL;DR

This paper introduces a windowed Green function method for efficiently solving elastic scattering problems on a half-space, achieving high accuracy and fast convergence without expensive layer Green function evaluations.

Contribution

The paper develops a novel WGF method that simplifies elastic scattering computations on a half-space, avoiding complex Green function evaluations and ensuring rapid convergence.

Findings

Achieves super-algebraic convergence with increasing window size.

Demonstrates high accuracy in 2D and 3D elastic scattering problems.

Avoids the need for layer Green function evaluations.

Abstract

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.