Rapid computation of far-field statistics for random obstacle scattering

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 twopoint 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.

Helmholtz Scattering by Random Domains: First-Order Sparse Boundary Element Approximation

“…General case [6], [7], [29], [30] BEM FEM [24] CT low-rank approximation FOSB Fig. 1: Background of the FOSB method (in blue) and nomenclature for alternative approaches.…”

Isogeometric multilevel quadrature for forward and inverse random acoustic scattering

“…In combination with low-rank techniques, this drastically reduces the high dimensionality of the random scattering problem, compare [25]. In order to speed up the computations of the Cauchy data's statistics even further, we employ the multilevel quadrature method, see e.g.…”