International Journal for Numerical Methods in Engineering · 2010 · 1.4K citations · 192 references
EngineeringComputational EngineeringMechanical EngineeringComputational MechanicsFinite Element AnalysisFinite Element MethodsConvergence AnalysisFinite Element DiscretizationFinite Element FormulationSolid Mechanics ApplicationsStructural Finite Element AnalysisFinite Element ModelingFinite Element SimulationPiecewise Polynomial ApproximationShear Bands
The paper presents an overview of the extended/generalized finite element method (GEFM/XFEM) with a focus on methodological issues. GEFM/XFEM accurately approximates solutions with jumps, kinks, singularities, and other locally non‑smooth features by enriching the polynomial approximation space of the classical finite element method. GEFM/XFEM has demonstrated potential in numerous applications involving non‑smooth solutions near interfaces, including crack simulation, shear band modeling, dislocation analysis, solidification, and multi‑field problems. © 2010 John Wiley & Sons, Ltd.
Abstract An overview of the extended/generalized finite element method (GEFM/XFEM) with emphasis on methodological issues is presented. This method enables the accurate approximation of solutions that involve jumps, kinks, singularities, and other locally non‐smooth features within elements. This is achieved by enriching the polynomial approximation space of the classical finite element method. The GEFM/XFEM has shown its potential in a variety of applications that involve non‐smooth solutions near interfaces: Among them are the simulation of cracks, shear bands, dislocations, solidification, and multi‐field problems. Copyright © 2010 John Wiley & Sons, Ltd.
192
A two-dimensional interpolation function for irregularly-spaced data
Donald S. Shepard · 1968 · 5K citations