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An iterative approach to the solution of an inverse problem in linear elasticity

Author

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  • Ellabib, A.
  • Nachaoui, A.

Abstract

This paper presents an iterative alternating algorithm for solving an inverse problem in linear elasticity. A relaxation procedure is developed in order to increase the rate of convergence of the algorithm and two selection criteria for the variable relaxation factors are provided. The boundary element method is used in order to implement numerically the constructing algorithm. We discuss this implementation, mention the use of Krylov methods to solve the obtained linear algebraic systems of equations and investigate the convergence and the stability when the data is perturbed by noise.

Suggested Citation

  • Ellabib, A. & Nachaoui, A., 2008. "An iterative approach to the solution of an inverse problem in linear elasticity," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 77(2), pages 189-201.
    • Handle: RePEc:eee:matcom:v:77:y:2008:i:2:p:189-201
    DOI: 10.1016/j.matcom.2007.08.014
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    Cited by:

    1. Ellabib, Abdellatif & Nachaoui, Abdeljalil & Ousaadane, Abdessamad, 2021. "Mathematical analysis and simulation of fixed point formulation of Cauchy problem in linear elasticity," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 231-247.
    2. Bergam, A. & Chakib, A. & Nachaoui, A. & Nachaoui, M., 2019. "Adaptive mesh techniques based on a posteriori error estimates for an inverse Cauchy problem," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 865-878.

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