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We consider the numerical algorithm for the two-dimensional time-harmonicelastic wave scattering by unbounded rough surfaces with Dirichlet boundarycondition. A Nystr\"{o}m method is proposed for the scattering problem based onthe integral equation method. Convergence of the Nystr\"{o}m method isestablished with convergence rate depending on the smoothness of the roughsurfaces. In doing so, a crucial role is played by analyzing the singularitiesof the kernels of the relevant boundary integral operators. Numericalexperiments are presented to demonstrate the effectiveness of the method.

The Nystr\"{o}m method for elastic wave scattering by unbounded rough surfaces