Commun. Comput. Phys., 2 (2007), pp. 54-72.


An Efficient Spectral Method for Acoustic Scattering from Rough Surfaces

Dongbin Xiu 1*, Jie Shen 1

1 Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA.

Received 3 February 2006; Accepted (in revised version) 9 May 2006
Available online 30 August 2006

Abstract

An efficient and accurate spectral method is presented for scattering problems with rough surfaces. A probabilistic framework is adopted by modeling the surface roughness as random process. An improved boundary perturbation technique is employed to transform the original Helmholtz equation in a random domain into a stochastic Helmholtz equation in a fixed domain. The generalized polynomial chaos (gPC) is then used to discretize the random space; and a Fourier-Legendre method to discretize the physical space. These result in a highly efficient and accurate spectral algorithm for acoustic scattering from rough surfaces. Numerical examples are presented to illustrate the accuracy and efficiency of the present algorithm.

AMS subject classifications: 65C20, 65C30, 78A45, 35J05

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Key words: Acoustic scattering, spectral methods, stochastic inputs, differential equations, uncertainty quantification.

*Corresponding author.
Email: dxiu@math.purdue.edu (D. Xiu), shen@math.purdue.edu (J. Shen)
 

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