Numerical solution of Navier–Stokes equations using multiquadric radial basis function networks

By Nam Mai-Duy, Thanh Tran-Cong. 2001

141 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mechanics of Materials, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/a1f2fdac3401229c95c6402cd77f858f53adebed

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In Computational Mechanics

In Mechanics of Materials

In Statistical and Nonlinear Physics

Citations in the corpus

Radial basis function collocation method solution of natural convection in porous media (2004, unknown): “The streamfunction-vorticity formulation of the Navier-Stokes equations have been solved by RBFCM in the work of Mai-Dui and Tran-Cong (2001a).”
Results on meshless collocation techniques (2006, methodology): “This leads to the unsymmetric collocation technique started by Kansa [9,10] for the multiquadric kernel and used by many authors afterwards; for instance, see [4,11–13,16,18] and an overview in Ref.”
A novel application of radial basis functions for solving a model of first-order integro-ordinary differential equation (2011, methodology): “There are two basic approaches for obtaining new basis functions from RBFs, namely direct approach (DRBF) based on a differential process [20] and indirect approach (IRBF) based on an integration process [19,23,30].”
A volumetric integral radial basis function method for time-dependent partial differential equations. I. Formulation (2004, background): “Mai-Duy and Tran-Cong [31], [32] obtained very impressive computational results with singly or doubly integrated MQ RBFs that they cast as a minimization of the least-squares residual errors to find the expansion coefficients.”
Solving high order ordinary differential equations with radial basis function networks (2005, background): “There are two basic approaches for obtaining new basis functions from RBFs, namely the direct approach (DRBF) based on a differential process (Kansa [12]) and the indirect approach (IRBF) based on an integration process (Mai-Duy and Tran-Cong [15,18]).”