Rapid computation of far-field statistics for random obstacle scattering
This work provides a computationally efficient approach for uncertainty quantification in wave scattering problems, relevant to engineering and physics applications involving random geometries.
The paper introduces a method for computing far-field statistics (expectation and variance) for acoustic scattering from random obstacles using an artificial interface and boundary integral equations, achieving rapid evaluation via low-rank approximation of the two-point correlation function.
In this article, we consider the numerical approximation of far-field statistics for acoustic scattering problems in the case of random obstacles. In particular, we consider the computation of the expected far-field pattern and the expected scattered wave away from the scatterer as well as the computation of the corresponding variances. To that end, we introduce an artificial interface, which almost surely contains all realizations of the random scatterer. At this interface, we directly approximate the second order statistics, i.e., the expectation and the variance, of the Cauchy data by means of boundary integral equations. From these quantities, 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 employing a low-rank approximation of the Cauchy data's two-point correlation function, we drastically reduce the cost of the computation of the scattered wave's variance. Numerical results are provided in order to demonstrate the feasibility of the proposed approach.