Volume 22, Issue 5
An Adaptive Finite Element PML Method for the Acoustic-Elastic Interaction in Three Dimensions

Xue Jiang & Peijun Li

Commun. Comput. Phys., 22 (2017), pp. 1486-1507.

Published online: 2017-11

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  • Abstract

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.

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@Article{CiCP-22-1486, author = {}, title = {An Adaptive Finite Element PML Method for the Acoustic-Elastic Interaction in Three Dimensions}, journal = {Communications in Computational Physics}, year = {2017}, volume = {22}, number = {5}, pages = {1486--1507}, abstract = {

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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2017-0047}, url = {http://global-sci.org/intro/article_detail/cicp/10450.html} }
TY - JOUR T1 - An Adaptive Finite Element PML Method for the Acoustic-Elastic Interaction in Three Dimensions JO - Communications in Computational Physics VL - 5 SP - 1486 EP - 1507 PY - 2017 DA - 2017/11 SN - 22 DO - http://doi.org/10.4208/cicp.OA-2017-0047 UR - https://global-sci.org/intro/article_detail/cicp/10450.html KW - AB -

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.

Xue Jiang & Peijun Li. (2020). An Adaptive Finite Element PML Method for the Acoustic-Elastic Interaction in Three Dimensions. Communications in Computational Physics. 22 (5). 1486-1507. doi:10.4208/cicp.OA-2017-0047
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