Radial basis function collocation method for an elliptic problem with nonlocal multipoint boundary condition

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Abstract

Radial basis function domain-type collocation method is applied for an elliptic partial differential equation with nonlocal multipoint boundary condition. A geometrically flexible meshless framework is suitable for imposing nonclassical boundary conditions which relate the values of unknown function on the boundary to its values at a discrete set of interior points. Some properties of the method are investigated by a numerical study of a test problem with the manufactured solution. Attention is mainly focused on the influence of nonlocal boundary condition. The standard collocation and least squares approaches are compared. In addition to its geometrical flexibility, the examined method seems to be less restrictive with respect to parameters of nonlocal conditions than, for example, methods based on finite differences.
Original languageEnglish
Pages (from-to)164-172
JournalEngineering Analysis with Boundary Elements
Volume67
DOIs
Publication statusPublished - 2016

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Collocation Method
Radial Functions
Elliptic Problems
Basis Functions
Boundary conditions
Nonlocal Conditions
Nonlocal Boundary Conditions
Meshless
Elliptic Partial Differential Equations
Interior Point
Collocation
Test Problems
Partial differential equations
Least Squares
Numerical Study
Finite Difference
Flexibility
Unknown

Keywords

  • Elliptic problem
  • Nonlocal multipoint boundary condition
  • Meshless method
  • Radial basis function
  • Collocation
  • Least squares

Cite this

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title = "Radial basis function collocation method for an elliptic problem with nonlocal multipoint boundary condition",
abstract = "Radial basis function domain-type collocation method is applied for an elliptic partial differential equation with nonlocal multipoint boundary condition. A geometrically flexible meshless framework is suitable for imposing nonclassical boundary conditions which relate the values of unknown function on the boundary to its values at a discrete set of interior points. Some properties of the method are investigated by a numerical study of a test problem with the manufactured solution. Attention is mainly focused on the influence of nonlocal boundary condition. The standard collocation and least squares approaches are compared. In addition to its geometrical flexibility, the examined method seems to be less restrictive with respect to parameters of nonlocal conditions than, for example, methods based on finite differences.",
keywords = "Elliptic problem, Nonlocal multipoint boundary condition, Meshless method, Radial basis function, Collocation, Least squares",
author = "Svajūnas Sajavičius",
year = "2016",
doi = "10.1016/j.enganabound.2016.03.010",
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journal = "Engineering Analysis with Boundary Elements",
issn = "0955-7997",
publisher = "Elsevier Limited",

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AU - Sajavičius, Svajūnas

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N2 - Radial basis function domain-type collocation method is applied for an elliptic partial differential equation with nonlocal multipoint boundary condition. A geometrically flexible meshless framework is suitable for imposing nonclassical boundary conditions which relate the values of unknown function on the boundary to its values at a discrete set of interior points. Some properties of the method are investigated by a numerical study of a test problem with the manufactured solution. Attention is mainly focused on the influence of nonlocal boundary condition. The standard collocation and least squares approaches are compared. In addition to its geometrical flexibility, the examined method seems to be less restrictive with respect to parameters of nonlocal conditions than, for example, methods based on finite differences.

AB - Radial basis function domain-type collocation method is applied for an elliptic partial differential equation with nonlocal multipoint boundary condition. A geometrically flexible meshless framework is suitable for imposing nonclassical boundary conditions which relate the values of unknown function on the boundary to its values at a discrete set of interior points. Some properties of the method are investigated by a numerical study of a test problem with the manufactured solution. Attention is mainly focused on the influence of nonlocal boundary condition. The standard collocation and least squares approaches are compared. In addition to its geometrical flexibility, the examined method seems to be less restrictive with respect to parameters of nonlocal conditions than, for example, methods based on finite differences.

KW - Elliptic problem

KW - Nonlocal multipoint boundary condition

KW - Meshless method

KW - Radial basis function

KW - Collocation

KW - Least squares

U2 - 10.1016/j.enganabound.2016.03.010

DO - 10.1016/j.enganabound.2016.03.010

M3 - Article

VL - 67

SP - 164

EP - 172

JO - Engineering Analysis with Boundary Elements

JF - Engineering Analysis with Boundary Elements

SN - 0955-7997

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