Domain Decomposition Methods (DDM) are a set of numerical techniques that efficiently implement parallel computing for the structural analysis of large domains. This work presents the implementation of mixed DDM for linear elasticity problems along with non-linear problems such as crack propagation. In addition, optimization algorithms have been used to find the optimal parameters of the mixed domain decomposition method. Finally, a strategy is proposed in order to implement the optimization methods to obtain a good approximation of the Search Direction parameter at a low computational cost.

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