Nonlinear localization strategies for domain decomposition methods: Application to post-buckling analyses

In this paper, we explore the capabilities of some nonlinear strategies based on domain decomposition for nonlinear analyses, and more particularly for post-buckling analyses of large slender structures. After having recalled the classical Newton–Krylov–Schur methods, chosen here to serve as a reference, we propose two versions specifically developed to treat nonlinear phenomena at the most relevant scale through nonlinear localizations per substructure. All these different strategies lead to solving similar condensed problems on which we apply classical Domain Decomposition Methods. Performances are discussed and comparative results in terms of convergence are presented in the case of beam frames with large rotations and local buckling.