This paper introduces a computational strategy to collaboratively develop the Galerkin Finite Volume Method (GFVM) as one of the most straightforward and efficient explicit numerical methods to solve structural problems encountering material nonlinearity in a small limited area, while the remainder of the domain represents a linear elastic behavior. In this regard, the Element Free Galerkin method (EFG), which is remarkably robust and accurate, but presumably more expensive, has locally been employed as a nonlinear sub-model to cover the shortcomings of the GFVM in the elastoplastic analysis. Since the formulations of these two methods are fundamentally different, the iterative zonal coupling has been accomplished using overlapping Multi-Grid (MG) patches with a non-matching interface and Iterative Global/Local (IGL) approach. The main property of such an algorithm is its non-intrusiveness, which means the complex nonlinear EFG solver is locally utilized over an elastic global GFVM without any geometric modification. This method is verified and investigated with available analytical and numerical solutions which gave quiet promising results showing the robustness and accuracy of the method. The Moving Least-Square approximation (MLS) has widely been applied on transfer level due to the non-conforming interface at the patch edges, and easily allows us to attach complex geometries with different mesh patterns. The new type of Quasi-Newtonian accelerator is adopted on the global material constitutive matrices and its convergence property and accuracy is compared with dynamic Aitken accelerators for two-dimensional problems in MATLAB. Finally, various accelerator types and mapping strategies are also concerned in the examination.
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