Determination of an Extremal in Two-Dimensional Variational Problems Based on the RBF Collocation Method
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...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-09-01
|
| Series: | Entropy |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1099-4300/24/10/1345 |
| _version_ | 1797473435568308224 |
|---|---|
| author | Ahmad Golbabai Nima Safaei Mahboubeh Molavi-Arabshahi |
| author_facet | Ahmad Golbabai Nima Safaei Mahboubeh Molavi-Arabshahi |
| author_sort | Ahmad Golbabai |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-09T20:15:26Z |
| format | Article |
| id | doaj.art-57d03d03f05c4c109f8b7c061b964c9d |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-09T20:15:26Z |
| publishDate | 2022-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-57d03d03f05c4c109f8b7c061b964c9d2023-11-24T00:02:04ZengMDPI AGEntropy1099-43002022-09-012410134510.3390/e24101345Determination of an Extremal in Two-Dimensional Variational Problems Based on the RBF Collocation MethodAhmad Golbabai0Nima Safaei1Mahboubeh Molavi-Arabshahi2School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 16846-13114, IranSchool of Mathematics, Iran University of Science and Technology, Narmak, Tehran 16846-13114, IranSchool of Mathematics, Iran University of Science and Technology, Narmak, Tehran 16846-13114, IranThis 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.https://www.mdpi.com/1099-4300/24/10/1345two-dimensional variational problemradial basis functionsLagrange multipliers |
| spellingShingle | Ahmad Golbabai Nima Safaei Mahboubeh Molavi-Arabshahi Determination of an Extremal in Two-Dimensional Variational Problems Based on the RBF Collocation Method Entropy two-dimensional variational problem radial basis functions Lagrange multipliers |
| title | Determination of an Extremal in Two-Dimensional Variational Problems Based on the RBF Collocation Method |
| title_full | Determination of an Extremal in Two-Dimensional Variational Problems Based on the RBF Collocation Method |
| title_fullStr | Determination of an Extremal in Two-Dimensional Variational Problems Based on the RBF Collocation Method |
| title_full_unstemmed | Determination of an Extremal in Two-Dimensional Variational Problems Based on the RBF Collocation Method |
| title_short | Determination of an Extremal in Two-Dimensional Variational Problems Based on the RBF Collocation Method |
| title_sort | determination of an extremal in two dimensional variational problems based on the rbf collocation method |
| topic | two-dimensional variational problem radial basis functions Lagrange multipliers |
| url | https://www.mdpi.com/1099-4300/24/10/1345 |
| work_keys_str_mv | AT ahmadgolbabai determinationofanextremalintwodimensionalvariationalproblemsbasedontherbfcollocationmethod AT nimasafaei determinationofanextremalintwodimensionalvariationalproblemsbasedontherbfcollocationmethod AT mahboubehmolaviarabshahi determinationofanextremalintwodimensionalvariationalproblemsbasedontherbfcollocationmethod |