A computational framework for a two-scale generalized/extended finite element method: generic imposition of boundary conditions

Purpose
This paper presents a computational framework to generate numeric enrichment functions for two-dimensional problems dealing with single/multiple local phenomenon. The two-scale generalized/extended finite element method (G/XFEM) approach used here is based on the solution decomposition, having a global and local scale components.
This strategy allows the use of a coarse mesh even when the problem produces complex local phenomena. For this purpose, local problems can be defined where these local phenomena are observed and are solved separately using fine meshes. The results of the local problems are used to enrich the global one improving the approximate solution.

Design/methodology/approach
The implementation of the two-scale G/XFEM formulation follows the object-oriented approach presented by the authors in a previous work, where it is possible to combine different kinds of elements and analysis models with the partition of unity enrichment scheme.
Beside the extension of the G/XFEM implementation to enclose the global-local strategy, the imposition of different boundary conditions is also generalized.

Findings
The generalization done for boundary conditions is very important since the global-local approach relies on the boundary information transferring process between the two scales of the analysis. The flexibility for the numerical analysis of the proposed framework is illustrated by several examples. Different analysis models, element formulations and enrichment functions are employed and the accuracy, robustness and computational efficiency are demonstrated.

Originality/value
This work shows a generalize imposition of different boundary conditions for global-local G/XFEM analysis through an object-oriented implementation. This generalization is very important since the global-local approach relies on the boundary information transferring process between the two scales of the analysis. Also, solving multiple local problem simultaneously and solving plate problems using global-local G/XFEM is another contributions of this work.