In this paper a new method for solving nonlinear inverse problems is presented. In order to overcome severe nonlinear behaviors, the domain is divided into several sub-domains. In each sub-domain, by using an optimization method and finite element method and also by employing the information obtained by the previous sub-domain, the unknown boundary conditions are determined.
To show the efficiency of the proposed method, an inverse non-linear heat conduction problem and an inverse non-linear thermoelastic problem are analyzed by both the whole domain and the present methods. According to the obtained results, it is shown that the presented domain decomposition method is more efficient and accurate than the whole domain method.