Generalized finite element method using mesh-based handbooks: application to problems in domains with many voids Original Research Article

This paper describes a new version of the generalized finite element method, originally developed [Int. J. Numer. Methods Engrg. 47 (2000) 1401; Comput. Methods Appl. Mech. Engrg. 181 (2000) 43; The design and implementation of the generalized finite element method, Ph.D. thesis, Texas A&M University, College Station, Texas, August 2000; Comput. Methods Appl. Mech. Engrg. 190 (2001) 4081], which is well suited for problems set in domains with a large number of internal features (e.g. voids, inclusions, cracks, etc.). The main idea is to employ handbook functions constructed on subdomains resulting from the mesh-discretization of the problem domain. The proposed new version of the GFEM is shown to be robust with respect to the spacing of the features and is capable of achieving high accuracy on meshes which are rather coarse relative to the distribution of the features.