Optimization, conditioning and accuracy of radial basis function method for partial differential equations with nonlocal boundary conditions

A case of two-dimensional Poisson equation

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

Various real-world processes usually can be described by mathematical models consisted of partial differential equations (PDEs) with nonlocal boundary conditions. Therefore, interest in developing computational methods for the solution of such nonclassical differential problems has been growing fast. We use a meshless method based on radial basis functions (RBF) collocation technique for the solution of two-dimensional Poisson equation with nonlocal boundary conditions. The main attention is paid to the influence of nonlocal conditions on the optimal choice of the RBF shape parameters as well as their influence on the conditioning and accuracy of the method. The results of numerical study are presented and discussed.
Original languageEnglish
Pages (from-to)788-804
JournalEngineering Analysis with Boundary Elements
Volume37
Issue number4
DOIs
Publication statusPublished - 2013

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Nonlocal Boundary Conditions
Poisson equation
Poisson's equation
Radial Functions
Conditioning
Partial differential equations
Basis Functions
Partial differential equation
Boundary conditions
Nonlocal Conditions
Optimization
Meshless Method
Shape Parameter
Computational methods
Collocation
Computational Methods
Numerical Study
Mathematical Model
Mathematical models
Influence

Keywords

  • Poisson equation
  • Nonlocal boundary condition
  • Meshless method
  • Radial basis function
  • Collocation
  • Shape parameter
  • Condition number

Cite this

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title = "Optimization, conditioning and accuracy of radial basis function method for partial differential equations with nonlocal boundary conditions: A case of two-dimensional Poisson equation",
abstract = "Various real-world processes usually can be described by mathematical models consisted of partial differential equations (PDEs) with nonlocal boundary conditions. Therefore, interest in developing computational methods for the solution of such nonclassical differential problems has been growing fast. We use a meshless method based on radial basis functions (RBF) collocation technique for the solution of two-dimensional Poisson equation with nonlocal boundary conditions. The main attention is paid to the influence of nonlocal conditions on the optimal choice of the RBF shape parameters as well as their influence on the conditioning and accuracy of the method. The results of numerical study are presented and discussed.",
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N2 - Various real-world processes usually can be described by mathematical models consisted of partial differential equations (PDEs) with nonlocal boundary conditions. Therefore, interest in developing computational methods for the solution of such nonclassical differential problems has been growing fast. We use a meshless method based on radial basis functions (RBF) collocation technique for the solution of two-dimensional Poisson equation with nonlocal boundary conditions. The main attention is paid to the influence of nonlocal conditions on the optimal choice of the RBF shape parameters as well as their influence on the conditioning and accuracy of the method. The results of numerical study are presented and discussed.

AB - Various real-world processes usually can be described by mathematical models consisted of partial differential equations (PDEs) with nonlocal boundary conditions. Therefore, interest in developing computational methods for the solution of such nonclassical differential problems has been growing fast. We use a meshless method based on radial basis functions (RBF) collocation technique for the solution of two-dimensional Poisson equation with nonlocal boundary conditions. The main attention is paid to the influence of nonlocal conditions on the optimal choice of the RBF shape parameters as well as their influence on the conditioning and accuracy of the method. The results of numerical study are presented and discussed.

KW - Poisson equation

KW - Nonlocal boundary condition

KW - Meshless method

KW - Radial basis function

KW - Collocation

KW - Shape parameter

KW - Condition number

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