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International Journal for Uncertainty Quantification
IF: 0.967 5-Year IF: 1.301 SJR: 0.531 SNIP: 0.8 CiteScore™: 1.52

ISSN Print: 2152-5080
ISSN Online: 2152-5099

Open Access

International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.v1.i2.10
pages 99-117


Paul Tsuji
ICES, University of Texas at Austin, Austin, TX 78712
Dongbin Xiu
Mathematics and Scientific Computing and Imaging (SCI) Institute, The University of Utah, Utah, USA
Lexing Ying
Department of Mathematics and ICES, University of Texas at Austin, TX 78712


This paper is concerned with the uncertainty quantification of high-frequency acoustic scattering from objects with random shape in two-dimensional space. Several new methods are introduced to efficiently estimate the mean and variance of the random radar cross section in all directions. In the physical domain, the scattering problem is solved using the boundary integral formulation and Nyström discretization; recently developed fast algorithms are adapted to accelerate the computation of the integral operator and the evaluation of the radar cross section. In the random domain, it is discovered that due to the highly oscillatory nature of the solution, the stochastic collocation method based on sparse grids does not perform well. For this particular problem, satisfactory results are obtained by using quasi-Monte Carlo methods. Numerical results are given for several test cases to illustrate the properties of the proposed approach.