A relaxed Robin-Robin algorithm for solving a Cauchy problem in linear elasticity

This work deals with an iterative approach for solving a Cauchy inverse problem in linear elasticity. The proposed method is based on a fixed point approach, it allows us to use domain decomposition methods like algorithms to solve the Cauchy inverse problem. The suggested method is described in detail and a relaxation procedure is developed in order to increase its rate of convergence. The boundary element method is used for implementation of the proposed algorithm then the technique to obtain its corresponding algebraic system is discussed. Finally, a numerical study is presented which shows the efficiency and stability of the proposed algorithm when the data is perturbed by noise.