On the stability and convergence of the finite section method for integralequation formulations of rough surface scattering

We consider the Dirichlet and Robin boundary value problems for the Helmhol tz equation in a non-locally perturbed half-plane, modelling time harmonic acoustic scattering of an incident field by, respectively, sound-soft and i mpedance infinite rough surfaces. Recently proposed novel boundary integral equation formulations of these problems are discussed. It is usual in prac tical computations to truncate the infinite rough surface, solving a bounda ry integral equation on a finite section of the boundary, of length 2A, say . In the case of surfaces of small amplitude and slope we prove the stabili ty and convergence as A --> infinity of this approximation procedure. For s urfaces of arbitrarily large amplitude and/or surface slope we prove stabil ity and convergence of a modified finite section procedure in which the tru ncated boundary is 'flattened' in finite neighbourhoods of its two endpoint s. Copyright (C) 2001 John Wiley & Sons, Ltd.