A comparison analysis between unsymmetric and symmetric radial basis function collocation methods for the numerical solution of partial differential equations

By Henry Power, V. Barraco. 2002

122 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/062752e47ef2894b25f18fc612a1fc0813b1c2d1

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In Computational Mechanics

In Electrical and Electronic Engineering

In Mechanics of Materials

Citations in the corpus

Radial basis function collocation method solution of natural convection in porous media (2004, background): “The formulation shown can be upgraded by the collocation that gives symmetric matrices, as recently shown by Power and Barraco (2002).”
A collocation method based on one-dimensional RBF interpolation scheme for solving PDEs (2007, unknown): “…equations has received a great deal of attention over the past 15 years (see, for example, Kansa, 1990; Fasshauer, 1997; Zerroukat et al, 1998; Mai-Duy and Tran-Cong, 2001; Fedoseyev et al, 2002; Power and Barraco, 2002; Cheng et al, 2003; Larsson and Fornberg, 2003; Sarler et al, 2004).”
A stabilized least-squares radial point collocation method (LS-RPCM) for adaptive analysis (2006, background): “Since then many of the research woks have been carried out extensively [5,6,9,12,30,35].”
Kernel techniques: From machine learning to meshless methods (2006, background): “…collocation can be found in the literature (Wu 1992, Iske 1995, Franke and Schaback 1998a, 1998b), while reports on applications are somewhat scattered (Power and Barraco 2002, Larsson and Fornberg 2003, Fasshauer 2004, Šarler 2005) and often limited to small problems with regular solutions.”
Radial point interpolation collocation method (RPICM) for partial differential equations (2005, methodology): “I N T R O D U C T I O N In recent years, there has been great interest to improve meshfree methods based on radial basis functions (RBF) in the field of computational mathematics and mechanics [1-8].”
Solving PDEs with radial basis functions * (2015, background): “Shortly afterwards it was introduced a number of times independently, for instance by Shu, Ding and Yeo (2003), Wang and Liu (2002) and Wright (2003). Since this approach is still in rapid development, the present discussion will not attempt to be comprehensive but only highlight how it has already ”