On the stability and convergence of the finite section method for integral equation formulations of rough surface scattering (Q2714902)

The authors consider the two-dimensional Dirichlet and Robin boundary value problems for the Helmholtz equation modelling time harmonic acoustic scattering of an incident field by sound-soft and impedance infinite rough surfaces, respectively. Recent work by Chandler-Wilde et al on novel boundary integral formulations of these problems is reviewed. The main goal of the paper is studying the stability and convergence of finite section approximations to the corresponding second kind integral equations on the infinite rough surface \(\Gamma\). Stability and convergence of the finite section method is shown when \(\Gamma\) is sufficiently close to a straight line, whereas in the general case this is proved for a modified finite section procedure in which the truncated boundary is flattened near its two endpoints.