The generalized finite element method: an example of its implementation and illustration of its performance

By Theofanis Strouboulis, K. Copps, I. Ka. 2000

388 citations recorded by the source corpus.

Subfields: Computational Mechanics, Electrical and Electronic Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/a4da0e6df16d33f4088b173612816d755fa9646c

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In Computational Mechanics

In Electrical and Electronic Engineering

In Mechanics of Materials

Citations in the corpus

A computational library for multiscale modeling of material failure (2013, methodology): “separation methods [139], extended finite element method (XFEM)/generalized finite element method (GFEM) [17, 86,126], extended element free Galerkin method (XEFG)”
A review of extended/generalized finite element methods for material modeling (2009, background): “When the approximation space is enriched by singular or discontinuous functions, these quadrature techniques need to be modified because inaccurate quadrature can lead to inaccuracy and poor convergence of the XFEM/GFEM solutions [95, 96, 10, 75].”
Computational homogenization for the multi-scale analysis of multi-phase materials (2002, methodology): “Approaches of this type have been recently applied for unit cell modelling (Strouboulis et al. (2000); Sukumar et al. (2001)).”
The 3D Numerical Simulation for the Propagation Process of Multiple Pre-existing Flaws in Rock-Like Materials Subjected to Biaxial Compressive Loads (2016, methodology): “The extended finite element method (XFEM) (Paluszny and Matthai 2009), the generalized finite element method (GFEM) (Strouboulis et al. 2000a, b) and the particle finite element method (PFEM) (Aubry et al. 2005; Pin et al. 2007) are three very commonly used methods that were developed from the FEM,…”
The extended/generalized finite element method: An overview of the method and its applications (2010, methodology): “The structure of the enrichment term plays a crucial role in the PUM, GFEM, and XFEM: The functions N⋆i build a partition of unity over the domain, i.e. Ω, ∑ i∈I N⋆i (x) = 1.”
A hybrid extended finite element/level set method for modeling phase transformations (2002, methodology): “Finally, we note that the method shares many common elements with the Generalized Finite Element Method [ 16 ; 17].”
A Meshfree Thin Shell for Arbitrary Evolving Cracks Based on An Extrinsic Basis (2006, methodology): “We will pursue another idea rst proposed by Song, Areias, and Belytschko (2006) in the context of nite elements and modify the quadrature weights.”
Multiscale enrichment based on partition of unity (2005, methodology): “In GFEM, which uses special handbook function [ 36 , 37], the resulting space is not linearly independent and the computational overhead (needed for either reorthogonalization or for using an indefinite solver) might be quite significant.”
Meshless methods: A review and computer implementation aspects (2008, methodology): “[91] pointed out in their generalized finite element method (GFEM) that different partition of unities can be used for the usual approximation and the so-called enrichment.”
Arbitrarily smooth generalized finite element approximations (2006, neutral): “, [4,16,18,19,53,55,56, 68,70,71].”
Three-dimensional crack initiation, propagation, branching and junction in non-linear materials by an extended meshfree method without asymptotic enrichment (2008, neutral): “The discontinuous part of the displacement approximation due to crack a 2 E writes 8X 2 X0; 8t > 0; ueaðX; tÞ ¼ X I2Wa UIðXÞWaI ðXÞaaI ðtÞ ð8Þ Note that the shape functions UI in Eq.”
An improved stable XFEM (Is-XFEM) with a novel enrichment function for the computational modeling of cohesive cracks (2015, methodology): “Among them, the eXtended/generalized finite element method (XFEM/GFEM) [11, 43, 63, 64] has been widely accepted and applied with great successes; see the review papers [4, 14] for the details.”
Modeling bimaterial interface cracks using the numerical manifold method (2013, methodology): “Typical examples include the cloud-based hp FEM [1], the extended finite element method (XFEM) [2–4], the generalized finite element method (GFEM) [5,6], the phantom node method [7] and the improved finite element method [8].”