A meshless radial basis function method for 2D steady-state heat conduction problems in anisotropic and inhomogeneous media

DOI10.1016/j.enganabound.2016.01.013zbMath1403.80038OpenAlexW2282397481MaRDI QIDQ1655005

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.2016.01.013

zbMATH Keywords

radial basis functionsirregular domainmeshless methodinhomogeneous mediaanisotropic problems

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Boundary element methods applied to problems in thermodynamics and heat transfer (80M15) Spectral, collocation and related (meshless) methods applied to problems in thermodynamics and heat transfer (80M22)

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Cites Work

• Unnamed Item
• Recent advances on radial basis function collocation methods
• Particular solutions of splines and monomials for polyharmonic and products of Helmholtz operators
• The method of approximate particular solutions for solving anisotropic elliptic problems
• 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
• The backward substitution method for multipoint problems with linear Volterra-Fredholm integro-differential equations of the neutral type
• 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
• Numerical investigation of the meshless radial basis integral equation method for solving 2D anisotropic potential problems
• 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
• Asymptotic behaviors of heat transfer in porous passages with axial conduction
• Modeling groundwater flow and contaminant transport
• Method of particular solutions for solving PDEs of the second and fourth orders with variable coefficients
• A new meshless method for steady-state heat conduction problems in anisotropic and inhomogeneous media
• 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
• A Novel Semi-Analytic Meshless Method for Solving TwoandThree-Dimensional Elliptic Equations of GeneralForm with Variable Coefficients in Irregular Domains
• Particular Solutions of Chebyshev Polynomials for Polyharmonic and Poly-Helmholtz Equations
• The boundary element solution of the Cauchy steady heat conduction problem in an anisotropic medium
• Polynomial particular solutions for certain partial differential operators