A mesh free approach using radial basis functions and parallel domain decomposition for solving three-dimensional diffusion equations

2004 ◽  
Vol 60 (13) ◽  
pp. 2183-2201 ◽  
Author(s):  
M. S. Ingber ◽  
C. S. Chen ◽  
J. A. Tanski
Keyword(s):  
Domain Decomposition ◽  
Radial Basis Functions ◽  
Three Dimensional ◽  
Basis Functions ◽  
Diffusion Equations ◽  
Dimensional Diffusion ◽  
Mesh Free ◽  
Radial Basis

Solving PDEs with radial basis functions

Acta Numerica ◽  
2015 ◽  
Vol 24 ◽  
pp. 215-258 ◽  
Author(s):  
Bengt Fornberg ◽  
Natasha Flyer
Keyword(s):  
Radial Basis Functions ◽  
Finite Differences ◽  
Large Scale ◽  
Numerical Approach ◽  
Basis Functions ◽  
Integration Time ◽  
Small Scale ◽  
Major Step ◽  
Mesh Free ◽  
Radial Basis

Finite differences provided the first numerical approach that permitted large-scale simulations in many applications areas, such as geophysical fluid dynamics. As accuracy and integration time requirements gradually increased, the focus shifted from finite differences to a variety of different spectral methods. During the last few years, radial basis functions, in particular in their ‘local’ RBF-FD form, have taken the major step from being mostly a curiosity approach for small-scale PDE ‘toy problems’ to becoming a major contender also for very large simulations on advanced distributed memory computer systems. Being entirely mesh-free, RBF-FD discretizations are also particularly easy to implement, even when local refinements are needed. This article gives some background to this development, and highlights some recent results.

scholarly journals Three-Dimensional Swirl Flow Velocity-Field Reconstruction Using a Neural Network With Radial Basis Functions

2001 ◽  
Vol 123 (4) ◽  
pp. 920-927 ◽  
Author(s):  
J. Pruvost ◽  
J. Legrand ◽  
P. Legentilhomme
Keyword(s):  
Neural Network ◽  
Velocity Field ◽  
Radial Basis Functions ◽  
Swirling Flow ◽  
Interpolation Method ◽  
Measurement Techniques ◽  
Three Dimensional ◽  
Basis Functions ◽  
Hydrodynamic Characteristics ◽  
Radial Basis

For many studies, knowledge of continuous evolution of hydrodynamic characteristics is useful but generally measurement techniques provide only discrete information. In the case of complex flows, usual numerical interpolating methods appear to be not adapted, as for the free decaying swirling flow presented in this study. The three-dimensional motion involved induces a spatial dependent velocity-field. Thus, the interpolating method has to be three-dimensional and to take into account possible flow nonlinearity, making common methods unsuitable. A different interpolation method is thus proposed, based on a neural network algorithm with Radial Basis Functions.

scholarly journals Solving the forward-backward heat equation in two-dimension by Radial basis functions mesh free method

2020 ◽  
Vol 22 (2) ◽  
pp. 305-318
Author(s):  
Siamak Banei ◽  
◽  
Kamal Shanazari ◽  
Yaqub Azari ◽  
◽  
...  
Keyword(s):  
Heat Equation ◽  
Radial Basis Functions ◽  
Basis Functions ◽  
Two Dimension ◽  
Mesh Free ◽  
Radial Basis ◽  
Mesh Free Method
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