Hyperviscosity-based stabilization for radial basis function-finite difference (RBF-FD) discretizations of advection–diffusion equations

Journal of Computational Physics ◽

10.1016/j.jcp.2018.06.036 ◽

2018 ◽

Vol 372 ◽

pp. 616-639 ◽

Author(s):

Varun Shankar ◽

Aaron L. Fogelson

Keyword(s):

Finite Difference ◽

Radial Basis Function ◽

Basis Function ◽

Diffusion Equations ◽

Advection Diffusion ◽

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Meshless upwind local radial basis function-finite difference technique to simulate the time- fractional distributed-order advection–diffusion equation

Engineering With Computers ◽

10.1007/s00366-019-00861-7 ◽

2019 ◽

Author(s):

Mostafa Abbaszadeh ◽

Mehdi Dehghan

Keyword(s):

Finite Difference ◽

Diffusion Equation ◽

Radial Basis Function ◽

Basis Function ◽

Finite Difference Technique ◽

Advection Diffusion Equation ◽

Advection Diffusion ◽

Radial Basis ◽

Distributed Order

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A Radial Basis Function (RBF) Compact Finite Difference (FD) Scheme for Reaction-Diffusion Equations on Surfaces

SIAM Journal on Scientific Computing ◽

10.1137/16m1095457 ◽

2017 ◽

Vol 39 (5) ◽

pp. A2129-A2151 ◽

Author(s):

Erik Lehto ◽

Varun Shankar ◽

Grady B. Wright

Keyword(s):

Finite Difference ◽

Radial Basis Function ◽

Basis Function ◽

Reaction Diffusion ◽

Reaction Diffusion Equations ◽

Diffusion Equations ◽

Compact Finite Difference ◽

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A Radial Basis Function (RBF)-Finite Difference (FD) Method for Diffusion and Reaction–Diffusion Equations on Surfaces

Journal of Scientific Computing ◽

10.1007/s10915-014-9914-1 ◽

2014 ◽

Vol 63 (3) ◽

pp. 745-768 ◽

Author(s):

Varun Shankar ◽

Grady B. Wright ◽

Robert M. Kirby ◽

Aaron L. Fogelson

Keyword(s):

Finite Difference ◽

Radial Basis Function ◽

Basis Function ◽

Reaction Diffusion ◽

Reaction Diffusion Equations ◽

Diffusion Equations ◽

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A radial basis function (RBF) finite difference method for the simulation of reaction-diffusion equations on stationary platelets within the augmented forcing method

International Journal for Numerical Methods in Fluids ◽

10.1002/fld.3880 ◽

2014 ◽

Vol 75 (1) ◽

pp. 1-22 ◽

Author(s):

Varun Shankar ◽

Grady B. Wright ◽

Aaron L. Fogelson ◽

Robert M. Kirby

Keyword(s):

Finite Difference ◽

Finite Difference Method ◽

Radial Basis Function ◽

Basis Function ◽

Difference Method ◽

Reaction Diffusion ◽

Reaction Diffusion Equations ◽

Diffusion Equations ◽

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An Upwind Scheme to Solve Unsteady Convection-Diffusion Equations Using Radial Basis Function Based Local Hermitian Interpolation Method with PDE Centres

Procedia Engineering ◽

10.1016/j.proeng.2015.11.390 ◽

2015 ◽

Vol 127 ◽

pp. 418-423 ◽

Author(s):

K. Monysekar ◽

Y.V.S.S. Sanyasiraju

Keyword(s):

Radial Basis Function ◽

Basis Function ◽

Interpolation Method ◽

Upwind Scheme ◽

Diffusion Equations ◽

Convection Diffusion ◽

Radial Basis ◽

Hermitian Interpolation

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On a high-order Gaussian radial basis function generated Hermite finite difference method and its application

CALCOLO ◽

10.1007/s10092-021-00443-4 ◽

2021 ◽

Vol 58 (4) ◽

Author(s):

Fazlollah Soleymani ◽

Shengfeng Zhu

Keyword(s):

Finite Difference ◽

Finite Difference Method ◽

Radial Basis Function ◽

Basis Function ◽

Difference Method ◽

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Numerical investigation based on radial basis function–finite-difference (RBF–FD) method for solving the Stokes–Darcy equations

Engineering With Computers ◽

10.1007/s00366-019-00863-5 ◽

2019 ◽

Author(s):

Mansour Safarpoor ◽

Ahmad Shirzadi

Keyword(s):

Finite Difference ◽

Radial Basis Function ◽

Numerical Investigation ◽

Basis Function ◽

Radial Basis ◽

Darcy Equations

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The overlapped radial basis function-finite difference (RBF-FD) method: A generalization of RBF-FD

Journal of Computational Physics ◽

10.1016/j.jcp.2017.04.037 ◽

2017 ◽

Vol 342 ◽

pp. 211-228 ◽

Author(s):

Varun Shankar

Keyword(s):

Finite Difference ◽

Radial Basis Function ◽

Basis Function ◽

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A Least Squares Radial Basis Function Finite Difference Method with Improved Stability Properties

SIAM Journal on Scientific Computing ◽

10.1137/20m1320079 ◽

2021 ◽

Vol 43 (2) ◽

pp. A1441-A1471

Author(s):

Igor Tominec ◽

Elisabeth Larsson ◽

Alfa Heryudono

Keyword(s):

Finite Difference ◽

Finite Difference Method ◽

Radial Basis Function ◽

Least Squares ◽

Basis Function ◽

Difference Method ◽

Stability Properties ◽

Radial Basis ◽

Improved Stability

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Implementation of a scalable, performance portable shallow water equation solver using radial basis function-generated finite difference methods

The International Journal of High Performance Computing Applications ◽

10.1177/1094342018797170 ◽

2018 ◽

Vol 33 (4) ◽

pp. 619-631

Author(s):

Samuel Elliott ◽

Raghu Raj Prasanna Kumar ◽

Natasha Flyer ◽

Tuan Ta ◽

Richard Loft

Keyword(s):

Finite Difference ◽

Radial Basis Function ◽

Shallow Water ◽

Basis Function ◽

Shallow Water Equation ◽

Finite Difference Methods ◽

Radial Basis ◽

Difference Methods

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