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L. Beilina

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

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.

Journal of Inverse and Ill-posed Problems, Walter de Gruyter

Print ISSN: 0928-0219
Volume: 11, 12/2003
Pages: 585 - 618

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