Acoustic scattering in case of random obstacles

In this article, we deal with the numerical solution of acoustic scattering problems in case of random obstacles. We compute the second order statistics, i.e. the expectation and the variance, of the solution's Cauchy data on an artificial, deterministic interface by means of boundary integral equations. As a consequence, we are able to rapidly evaluate statistics of the scattered wave everywhere in the exterior domain, including the expectation and the variance of the far-field. By using a low-rank approximation of the Cauchy data's two-point correlation function, the cost of the computation of the scattered wave’s variance is drastically reduced. Numerical results are given to demonstrate the feasibility of the proposed approach.