Classification and Overview of Meshfree Methods

By Thomas-Peter Fries, Hermann G. Matthies. 2004

351 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/8a970bac104097feed4f8427508dd5906de611f4

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Citations in the corpus

The extended/generalized finite element method: An overview of the method and its applications (2010, methodology): “We note also that many meshfree shape functions rely on the approximation properties of polynomials [27, 80], so there is a great flexibility in the construction of polynomial approximation spaces.”
Cohesive and non‐cohesive fracture by higher‐order enrichment of XFEM (2012, methodology): “x,y/, as is carried out in coupling of mesh-free methods and the FEM [36, 37].”
Numerical integration over arbitrary polygonal domains based on Schwarz–Christoffel conformal mapping (2009, unknown): “These methods have been recently reviewed and classified in [5].”
Strain smoothing in FEM and XFEM (2010, background): “1 See [63] for a very recent review and details on k well as [38] for an excellent overview and classificatio We present in this paper recent achievements realised on the application of strain smoothing in finite elements and propose suitable extensions to problems with discontinuities and singulari”
Accurate fracture modelling using meshless methods, the visibility criterion and level sets: Formulation and 2D modelling (2011, methodology): “Since the inception of smoothed particle hydrodynamics [1], a wide variety of meshless (or meshfree) methods [2, 3] have been proposed, as outlined in recent surveys [4, 5].”
Studied X-FEM enrichment to handle material interfaces with higher order finite element (2010, methodology): “These kinds of methods are called Meshfree Methods [8].”
Aspects of the use of orthogonal basis functions in the element‐free Galerkin method (2009, methodology): “A wide variety of methods have been proposed as outlined in recent surveys [1–3].”
Point based animation of elastic, plastic and melting objects (2004, methodology): “For a more extensive and up-to-date classification and overview of mesh free methods, see [ FM03 , Liu02, BKO ∗ 96].”
Convergence and stabilization of stress‐point integration in mesh‐free and particle methods (2008, methodology): “We consider mesh-free shape functions based on the MLS method [28, 29], although conclusions also apply to the reproducing kernel particle method [30], which is an alternative representation of MLS functions [24, 25, 31].”
Physically Based Deformable Models in Computer Graphics (2006, unknown): “For an extensive and up-to-date classification and overview of mesh-free methods, see [136], [137] and also the excellent review paper [138].”
An improved meshless Shepard and least squares method possessing the delta property and requiring no singular weight function (2014, methodology): “A wide variety of meshless methods have been proposed as outlined in recent surveys [1-3].”
A new weight‐function enrichment in meshless methods for multiple cracks in linear elasticity (2012, background): “Updated reviews on meshfree methods can be found in [22] and [23].”
On the optimum support size in meshfree methods: A variational adaptivity approach with maximum‐entropy approximants (2010, background): “Unfortunately, the optimal support size of the basis functions is problem-dependent, and even depends on the level of refinement [3, 6, 12].”
Free-surface flows solved by means of SPH schemes with numerical diffusive terms (2010, methodology): “In the SPH scheme, the field of a generic quantity f is interpolated through a convolution integral [8]:”