A meshless radial basis function method for steady-state advection-diffusion-reaction equation in arbitrary 2D domains

DOI10.1016/j.enganabound.2017.03.004zbMath1403.65172OpenAlexW2604368509MaRDI QIDQ1655340

Ji Lin, Sergiy Y. Reutskiy

Publication date: 9 August 2018

Published in: Engineering Analysis with Boundary Elements (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.enganabound.2017.03.004

zbMATH Keywords

radial basis functionsirregular domainmeshless methodnonlinear problemadvection-diffusion-reaction equation

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35)

Related Items (10)

The Hermit-Type Reproducing Kernel Particle Method for Elasticity Problems ⋮ Radial basis reproducing kernel particle method for piezoelectric materials ⋮ A meshfree method with a non-overlapping domain decomposition method based on TPS for solving the forward-backward heat equation in two-dimension ⋮ An energy regularization of the MQ-RBF method for solving the Cauchy problems of diffusion-convection-reaction equations ⋮ Polynomial Particular Solutions for the Solutions of PDEs with Variables Coefficients ⋮ A Novel Method for Solving Time-Dependent 2D Advection-Diffusion-Reaction Equations to Model Transfer in Nonlinear Anisotropic Media ⋮ A RBF-based technique for 3D convection-diffusion-reaction problems in an anisotropic inhomogeneous medium ⋮ Simulation of linear and nonlinear advection-diffusion-reaction problems by a novel localized scheme ⋮ A space-time backward substitution method for three-dimensional advection-diffusion equations ⋮ The radial basis reproducing kernel particle method for geometrically nonlinear problem of functionally graded materials

Cites Work

• Recent advances on radial basis function collocation methods
• Particular solutions of splines and monomials for polyharmonic and products of Helmholtz operators
• Compact local integrated-RBF approximations for second-order elliptic differential problems
• Multiquadrics - a scattered data approximation scheme with applications to computational fluid-dynamics. I: Surface approximations and partial derivative estimates
• A numerical study of some radial basis function based solution methods for elliptic PDEs
• A comparison of efficiency and error convergence of multiquadric collocation method and finite element method.
• Circumventing the ill-conditioning problem with multiquadric radial basis functions: Applications to elliptic partial differential equations
• Particular solutions of Laplacian, Helmholtz-type, and polyharmonic operators involving higher order radial basis functions
• Numerical comparisons of two meshless methods using radial basis functions
• A multiple-scale Pascal polynomial triangle solving elliptic equations and inverse Cauchy problems
• A meshless radial basis function method for 2D steady-state heat conduction problems in anisotropic and inhomogeneous media
• A new meshless method for solving steady-state nonlinear heat conduction problems in arbitrary plane domain
• Perturbation technique and method of fundamental solution to solve nonlinear Poisson problems
• Solving the nonlinear Poisson-type problems with F-Trefftz hybrid finite element model
• Error estimate, optimal shape factor, and high precision computation of multiquadric collocation method
• Some recent results and proposals for the use of radial basis functions in the BEM
• A meshless numerical method based on the local boundary integral equation (LBIE) to solve linear and nonlinear boundary value problems
• Method of particular solutions for solving PDEs of the second and fourth orders with variable coefficients
• Method of particular solutions for nonlinear Poisson-type equations in irregular domains
• The method of approximate particular solutions for solving certain partial differential equations
• THE METHOD OF APPROXIMATE PARTICULAR SOLUTIONS FOR SOLVING ELLIPTIC PROBLEMS WITH VARIABLE COEFFICIENTS
• Fictitious Time Integration Method of Fundamental Solutions with Chebyshev Polynomials for Solving Poisson-type Nonlinear PDEs
• A Fictitious Time Integration Method for a Quasilinear Elliptic Boundary Value Problem, Defined in an Arbitrary Plane Domain
• Particular Solutions of Chebyshev Polynomials for Polyharmonic and Poly-Helmholtz Equations
• Polynomial particular solutions for certain partial differential operators
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: A meshless radial basis function method for steady-state advection-diffusion-reaction equation in arbitrary 2D domains