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An Adaptive Finite Element PML Method for the Acoustic-Elastic Interaction in Three Dimensions

Part of:Partial differential equations, boundary value problemsEquations of mathematical physics and other areas of applicationOptics, electromagnetic theory - Basic methods

Published online by Cambridge University Press:  31 October 2017

Xue Jiang and
Peijun Li
Xue Jiang*
Affiliation:
School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China
Peijun Li*
Affiliation:
Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA
*
*Corresponding author. Email addresses:jxue@lsec.cc.ac.cn(X. Jiang), lipeijun@math.purdue.edu(P. Li)
*Corresponding author. Email addresses:jxue@lsec.cc.ac.cn(X. Jiang), lipeijun@math.purdue.edu(P. Li)

Abstract

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Consider the scattering of a time-harmonic acoustic incident wave by a bounded, penetrable, and isotropic elastic solid, which is immersed in a homogeneous compressible air or fluid. The paper concerns the numerical solution for such an acoustic-elastic interaction problem in three dimensions. An exact transparent boundary condition (TBC) is developed to reduce the problem equivalently into a boundary value problem in a bounded domain. The perfectly matched layer (PML) technique is adopted to truncate the unbounded physical domain into a bounded computational domain. The well-posedness and exponential convergence of the solution are established for the truncated PML problem by using a PML equivalent TBC. An a posteriori error estimate based adaptive finite element method is developed to solve the scattering problem. Numerical experiments are included to demonstrate the competitive behavior of the proposed method.

Keywords

Acoustic-elastic interactionperfectly matched layeradaptive finite element methodtransparent boundary condition

MSC classification

Secondary:65N30: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods78M10: Finite element methods35Q99: None of the above, but in this section

Information

Type
Research Article
Information
Communications in Computational Physics , Volume 22 , Issue 5 , November 2017, pp. 1486 - 1507
Copyright
Copyright © Global-Science Press 2017 

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