Determination of an Extremal in Two-Dimensional Variational Problems Based on the RBF Collocation Method

Autor: Ahmad Golbabai, Nima Safaei, Mahboubeh Molavi-Arabshahi
Jazyk: angličtina
Rok vydání: 2022
Předmět:
Zdroj: Entropy, Vol 24, Iss 10, p 1345 (2022)
Druh dokumentu: article
ISSN: 1099-4300
DOI: 10.3390/e24101345
Popis: This paper introduces a direct method derived from the global radial basis function (RBF) interpolation over arbitrary collocation nodes occurring in variational problems involving functionals that depend on functions of a number of independent variables. This technique parameterizes solutions with an arbitrary RBF and transforms the two-dimensional variational problem (2DVP) into a constrained optimization problem via arbitrary collocation nodes. The advantage of this method lies in its flexibility in selecting between different RBFs for the interpolation and parameterizing a wide range of arbitrary nodal points. Arbitrary collocation points for the center of the RBFs are applied in order to reduce the constrained variation problem into one of a constrained optimization. The Lagrange multiplier technique is used to transform the optimization problem into an algebraic equation system. Three numerical examples indicate the high efficiency and accuracy of the proposed technique.
Databáze: Directory of Open Access Journals
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