Year: 2014
Communications in Mathematical Research , Vol. 30 (2014), Iss. 1 : pp. 71–80
Abstract
In this paper, we study, via variational methods, the problem of scattering of time harmonic acoustic waves by unbounded inhomogeneous layers above a sound soft rough surface. We first propose a variational formulation and exploit it as a theoretical tool to prove the well-posedness of this problem when the media is non-absorbing for arbitrary wave number and obtain an estimate about the solution, which exhibit explicitly dependence of bound on the wave number and on the geometry of the domain. Then, based on the non-absorbing results, we show that the variational problem remains uniquely solvable when the layer is absorbing by means of a priori estimate of the solution. Finally, we consider the finite element approximation of the problem and give an error estimate.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2014-CMR-18989
Communications in Mathematical Research , Vol. 30 (2014), Iss. 1 : pp. 71–80
Published online: 2014-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 10
Keywords: Helmholtz equation rough surface scattering problem.