Mesh Free Methods: Moving Beyond the Finite Element Method

By Guirong Liu. 2002

1,774 citations recorded by the source corpus.

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Citations in the corpus

Upper bound solution to elasticity problems: A unique property of the linearly conforming point interpolation method (LC‐PIM) (2008, methodology): “This concept has also been applied to analyze mesh-free methods [9].”
A moving Kriging interpolation‐based meshless method for numerical simulation of Kirchhoff plate problems (2009, methodology): “We now consider a support domain =[0,1] with six uniformly distributed points of [0,0.”
Static analysis of functionally graded plates using third-order shear deformation theory and a meshless method (2005, unknown): “see [27].”
An n-sided polygonal smoothed finite element method (nSFEM) for solid mechanics (2007, methodology): “mesh-free techniques, such as MLS/RK methods [16,17], radial point interpolation method (RPIM) [18–21].”
Time‐dependent fractional advection–diffusion equations by an implicit MLS meshless method (2011, result): “The above two spline functions have been found [35, 41] to lead to very similar results for the problems studied.”
EDGE-BASED SMOOTHED POINT INTERPOLATION METHODS (2008, methodology): “The PIM shape functions (with either polynomial or radial basis functions) possess the Kronecker delta property, which facilitates simple implementations of essential boundary conditions [Liu (2002)].”
Radial point interpolation collocation method (RPICM) for partial differential equations (2005, methodology): “So far, there is no mathematical theory developed for determining the optimal value• Detailed guidelines on how to choose these parameters can be found in Liu's recent monograph [8].”
A gradient smoothing method (GSM) with directional correction for solid mechanics problems (2007, methodology): “Moreover, the GFDM falls into the wider class of so-called meshfree methods [ 16 ,17].”
Assessment of smoothed point interpolation methods for elastic mechanics (2010, methodology): “The detailed procedure of constructing shape functions using both polynomial functions and RBFs can be referred to in the meshfree method book by Liu [17].”
A node-based smoothed finite element method (NS-FEM) for upper bound solutions to solid mechanics problems (2009, unknown): “[27].”