The numerical solution of scattering by infinite rough interfaces based on the integral equation method

In this paper, we describe a Nyström integration method for the integral operator TT which is the normal derivative of the double-layer potential arising in problems of two-dimensional acoustic scattering by infinite rough interfaces. The hypersingular kernel and unbounded integral interval of TT are the key difficulties. By using a mollifier, we separately deal with these two difficulties and propose its Nyström integration method. Furthermore, we establish convergence of the method. Finally, we apply the method to the scattering problem by infinite rough interfaces and carry out some numerical experiments to show the validity.