Shortcourse: Theory and Practice of the Generalized/eXtended Finite Element Method


Armando Duarte (University of Illinois at Urbana-Champaign)

Angelo Simone (TU Delft)

The Generalized or eXtended Finite Element Method (G/XFEM) has received increased attention and undergone substantial development during the last decade. This method offers unprecedented flexibility in the construction of shape functions and corresponding approximation spaces. With the proper selection of enrichment functions, the G/XFEM is able to address many shortcoming and limitations of the classical FEM while retaining its attractive features.

This short course will introduce participants to the approximation theory of G/XFEM and its formulation for three-dimensional fractures, polycrystalline and fiber-reinforced materials. The implementation of the G/XFEM in an existing FEM software as well as closed-source software, such as Abaqus, are discussed. Recent developments such as the Stable Generalized FEM (SGFEM) and GFEMs for problems with multiple spatial scales of interest (GFEMgl) are also presented. Hands-on practice sessions using a representative implementation of the G/XFEM in MATLAB will be used to illustrate the performance and practical aspects of the method.