An Efficient Numerical Method for Acoustic Wave Scattering in Random Media

This paper is concerned with developing efficient numerical methods for acoustic wave scattering in random media which can be expressed as random perturbations of homogeneous media. We first analyze the random Helmholtz problem by deriving some wavenumber-explicit solution estimates. We then establish a multimodes representation of the solution as a power series of the perturbation parameter and analyze its finite modes approximations. Based on this multimodes representation, we develop a Monte Carlo interior penalty discontinuous Galerkin (MCIP-DG) method for approximating the mode functions, which are governed by recursively defined nearly deterministic Helmholtz equations. Optimal order error estimates are derived for the method, and an efficient algorithm, which is based on the LU direct solver, is also designed for efficiently implementing the proposed multimodes MCIP-DG method. It is proved that the computational complexity of the whole algorithm is comparable to that of solving one deterministic He...

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