Kansa radial basis function method with fictitious centres for solving nonlinear boundary value problems
| Autor: | Andreas Karageorghis, Andreas Katsiamis |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Discretization
Applied Mathematics General Engineering Boundary (topology) Basis function 02 engineering and technology Computer Science::Numerical Analysis 01 natural sciences Shape parameter Domain (mathematical analysis) 010101 applied mathematics Computational Mathematics Nonlinear system 020303 mechanical engineering & transports 0203 mechanical engineering Computer Science::Computational Engineering Finance and Science Collocation method Applied mathematics Boundary value problem 0101 mathematics Analysis Mathematics |
| Zdroj: | Engineering Analysis with Boundary Elements. 119:293-301 |
| ISSN: | 0955-7997 |
| DOI: | 10.1016/j.enganabound.2020.08.001 |
| Popis: | A Kansa–radial basis function (RBF) collocation method is applied to two–dimensional second and fourth order nonlinear boundary value problems. The solution is approximated by a linear combination of RBFs, each of which is associated with a centre and a different shape parameter. As well as the RBF coefficients in the approximation, these shape parameter values are taken to be among the unknowns. In addition, the centres are distributed within a larger domain containing the physical domain of the problem. The size of this larger domain is controlled by a dilation parameter which is also included in the unknowns. In fourth order problems where two boundary conditions are imposed, two sets of (different) boundary centres are selected. The Kansa–RBF discretization yields a system of nonlinear equations which is solved by standard software. The proposed technique is applied to four problems and the numerical results are analyzed and discussed. |
| Databáze: | OpenAIRE |
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