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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.


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Adaptive hybrid finite element/difference methods: application to inverse elastic scattering

L. Beilina

Department of Mathematics, Chalmers University of Technology, S-412 96 Göteborg, Sweden. E-mail:

Citation Information: Journal of Inverse and Ill-posed Problems jiip. Volume 11, Issue 6, Pages 585–618, ISSN (Online) 1569-3953, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/156939403322759660,

Publication History

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We use an optimal control approach for solution of inverse problem for time-dependent scattering of elastic waves in , d = 2, 3 where we seek a density ρ and Lamé coefficients λ and μ which minimize the difference between computed and measured output data in a discrete L 2 norm. We solve the optimization problem by a quasi-Newton method, where in each step we compute the gradient by solving a forward and an adjoint elastic wave propagation problem.

We develop a posteriori error estimator for the error in Lagrangian and apply it to solution of inverse problem for time-dependent scattering of elastic waves in , d = 2, 3.

For implementation of the inverse problem we use an adaptive hybrid finite element/difference methods, where we combine the flexibility of finite elements and the efficiency of finite differences. We present computational results for three dimensional inverse scattering and use an adaptive mesh refinement algorithm based on an a posteriori error estimate, to improve the accuracy of the identification.

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[1]
Jingzhi Li, Jianli Xie, and Jun Zou
Inverse Problems, 2011, Volume 27, Number 7, Page 075009
[2]
Larisa Beilina and Christian Clason
SIAM Journal on Scientific Computing, 2006, Volume 28, Number 1, Page 382

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