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Generalized finite element method using mesh-based handbooks: application to problems in domains with many voids. (English) Zbl 1054.74059
Summary: This paper describes a new version of the generalized finite element method, originally developed [T. Strouboulis et al., Int. J. Numer. Methods Eng. 47, No. 8, 1401–1417 (2000; Zbl 0955.65080); Comput. Methods Appl. Mech. Eng. 181, No. 1-3, 43–69 (2000; Zbl 0983.65127); 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. Eng. 190, No. 32-33, 4081–4193 (2001; Zbl 0997.74069)], 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.

MSC:
74S05 Finite element methods applied to problems in solid mechanics
74E05 Inhomogeneity in solid mechanics
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