Application of essential boundary conditions in mesh-free methods: a corrected collocation method

By Gregory J. Wagner, Wing Kam Liu. 2000

140 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/f299703817a4ce247c9f97c1ad19222d92e25513

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In Computational Mechanics

In Electrical and Electronic Engineering

In Mechanics of Materials

Citations in the corpus

Moving kriging interpolation and element‐free Galerkin method (2003, methodology): “Attempts have been made to impose essential boundary conditions such as point collocation [3], Lagrange multipliers [1], singular weighting functions [4], and coupling with FEM [5].”
Reproducing kernel element method. Part I: Theoretical formulation (2004, methodology): “, Lagrangian multiplier technique [2], transformation technique [6], hierarchical enrichment technique [13,29], reproducing kernel interpolation technique [5], singular kernel function technique [6,17], collocation technique [30], window or correction function [10], and use of D Alembert s principle”
The method of finite spheres (2000, methodology): “, 1994), corrected collocation techniques (Wagner and Liu, 1999) and transformation methods (Atluri et al.”
Consistent element‐free Galerkin method (2014, methodology): “Strategies developed for this purpose are the penalty method [11], coupling methods [12, 13], corrected collocation method [14] and so on.”
A point interpolation meshless method based on radial basis functions (2002, methodology): “For the rst issue, many schemes have been proposed such as Lagrangian [5], penalty [11] and collocation [12].”
Optimization of natural frequencies of bidirectional functionally graded beams (2006, methodology): “We use the corrected collocation method proposed by Wagner and Liu (2000) , which does not require any penalty parameters.”
Meshfree Methods: Progress Made after 20 Years (2017, unknown): “…boundary conditions at nodes is to utilize the relationship between nodal coefficients and field values at the nodes (Atluri et al. 1999; Chen and Wang 2000b; Chen et al. 1996; Günther and Liu 1998; Wagner and Liu 2000; Zhu and Atluri 1998), called the transformation method or collocation method .”
Lagrangian Meshfree Formulation for Analysis of Geotechnical Materials (2001, unknown): “study by Wagner and Liu (2000) has shown that the collocation method, if done correctly, can converge with a correct rate.”