Optimizing the search directions of a mixed DDM applied on cracks

Abstract

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.

Global-Local non intrusive analysis with robin parameters: application to plastic hardening behavior and crack propagation in 2D and 3D structures

“…Within this range, an optimum that minimizes the number of iterations can be found. However, as presented in [34,13], the value depends on the problem type, the applied loads, the boundary conditions and the form of the Robin operator used in the analysis. Therefore, in order to find the Robin operator that guarantees convergence and also minimizes the number of iterations until convergence, an optimization process is performed for the different problems presented.…”

“…The values of the Robin operator assuring the convergence of the non-intrusive method with Robin conditions can be estimated analytically for simple examples with few degrees of freedom. For industrial/real structures, the range of the values are not easily found directly, so these values are found by iterative methods as presented in [20,13] or by using two scale strategies as shown in [27,15].…”

“…This is useful to study the convergence of the method in structures with strong modifications in the stiffness. Consequently, the original approximation of the Robin parameter may not be the best for each interface and these factors could be different for each analysis direction, as presented in [13].…”