Rapid computation of far-field statistics for random obstacle scattering

TL;DR

This paper presents a fast boundary integral method for computing statistical properties of acoustic scattering by random obstacles, enabling efficient evaluation of expected far-field patterns and variances.

Contribution

It introduces an artificial interface and low-rank approximation techniques to efficiently compute far-field statistics in random obstacle scattering problems.

Findings

Rapid computation of expected far-field patterns.

Effective variance estimation using low-rank approximation.

Numerical results confirm computational efficiency.

Abstract

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.