  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.
