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An innovative method for fast analysis of electromagnetic problems comprising nonlinear dielectrics is proposed. The method is based on the combination of finite elements and domain decomposition methods. This latter technique allows for the separation of the problem in multiple subproblems which can be solved separately. By appropriately defining one of such subdomains as containing all the nonlinear dielectrics it is possible to restrict the application of an iterative algorithm for the numerical solution of nonlinear equations only to this latter, smaller, domain. Numerical results showing the accuracy and efficiency of this technique are presented in few 2D cases.