edoc: No conditions. Results ordered -Date Deposited. 2024-06-22T05:37:05ZEPrintshttps://edoc.unibas.ch/images/uni-logo.jpghttps://edoc.unibas.ch/2019-04-11T15:20:58Z2020-05-27T09:29:55Zhttps://edoc.unibas.ch/id/eprint/70079This item is in the repository with the URL: https://edoc.unibas.ch/id/eprint/700792019-04-11T15:20:58ZAcoustic scattering in case of random obstaclesIn 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. Helmut HarbrechtNikola IlićMichael D. Multerer2019-02-26T13:13:19Z2021-05-01T01:30:05Zhttps://edoc.unibas.ch/id/eprint/69011This item is in the repository with the URL: https://edoc.unibas.ch/id/eprint/690112019-02-26T13:13:19ZRapid computation of far-field statistics for random obstacle scatteringIn 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. Helmut HarbrechtNikola IlićMichael D. Multerer