On the optimal shape parameters of radial basis functions used for 2-D meshless methods

By Jian-Guo Wang, Guirong Liu. 2002

589 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/505a67439d5d2f26088a28d6db450753dfa3ce66

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In Civil and Structural Engineering

In Mechanics of Materials

Citations in the corpus

Solving high order ordinary differential equations with radial basis function networks (2005, methodology): “In this regard, many attempts based on high order approximation schemes were made (e.g. Viecelli [3]; Sallam and El-Hawary [4]; Esmail et al [5]; Gutierrez and Laura [6]; Wu and Liu [7,8,9]).”
A LINEARLY CONFORMING RADIAL POINT INTERPOLATION METHOD FOR SOLID MECHANICS PROBLEMS (2006, methodology): “…(MLPG) that uses the local Petrov-Galerkin weak form [Atluri and Zhu (1998); Atluri et al. (1999)], the point interpolation method (PIM) and radial point interpolation method (RPIM) based on both Galerkin weak form and Petrov-Galerkin weak form [Liu and Gu (2001); Wang and Liu (2002)].”
A local Heaviside weighted meshless method for two-dimensional solids using radial basis functions (2003, methodology): “In the research by Wang and Liu (2002b) an optimal value of 1.03 was identified for the shape parameter b when using the extended MQ in an element-free Galerkin scheme.”
A nodal integration technique for meshfree radial point interpolation method (NI-RPIM) (2007, background): “It is consistent with the previous conclusions obtained by other authors (Wang and Liu, 2002b; Liu et al., 2005b).”
Static deformations and vibration analysis of composite and sandwich plates using a layerwise theory and multiquadrics discretizations (2005, methodology): “[49–51] and by Ferreira [52–54] for composite laminated plates and beams using the first-order and the third-order shear deformation theory.”
Free vibration analysis of functionally graded shells by a higher-order shear deformation theory and radial basis functions collocation, accounting for through-the-thickness deformations (2013, unknown): “The use of radial basis function for the analysis of structures and materials has been previously studied [15–29].”
A meshfree Hermite‐type radial point interpolation method for Kirchhoff plate problems (2006, methodology): “The choice of optimal parameters for the RPI method was studied by Wang and Liu in detail [12].”
Recent Advances in Radial Basis Function Collocation Methods (2013, background): “In recent decades, various RBF-based methods have gained fast growing attention from a broad range of scientific computing and engineering applications, such as multivariate scattered data processing [1], numerical solutions of partial differential equations (PDEs), neural networks [2], and machine ”