A Hybrid Radial Basis Function–Finite Difference Matrix Operators (RBF–FDMO) Approach for Numerical Simulation of Grounding Systems on Non-Uniform FD Mesh.
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| Title: | A Hybrid Radial Basis Function–Finite Difference Matrix Operators (RBF–FDMO) Approach for Numerical Simulation of Grounding Systems on Non-Uniform FD Mesh. |
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| Authors: | Nguyen, Xuan-Binh1 (AUTHOR), Nguyen, Nhat-Nam1 (AUTHOR), Vu, Phan-Tu1 (AUTHOR) vptu@hcmut.edu.vn |
| Source: | Energies (19961073). May2026, Vol. 19 Issue 10, p2271. 23p. |
| Subject Terms: | *Radial basis functions, *Electric current grounding, *Engineering standards, *Differential operators, *Electromagnetic theory, *Laplace's equation, *Numerical analysis |
| Abstract: | This paper presents a hybrid numerical approach, termed the Radial Basis Function–Finite Difference Matrix Operator (RBF–FDMO) method, to enhance the accuracy and flexibility of the conventional FDMO technique for three-dimensional (3D) electromagnetic field analysis governed by the Laplace–Poisson equation. Conventional numerical methods often face challenges related to computational complexity and limited flexibility when handling non-uniform discretization and complex geometries. In the proposed method, spatial derivatives are approximated using RBF-based interpolation rather than finite difference schemes derived from Taylor series expansion. This formulation enables the construction of high-accuracy derivative operators on both uniform and non-uniform FD grids, thereby improving numerical robustness and adaptability to complex geometries. The performance of the proposed method is first compared with the FDMO in a 3D benchmark problem, with reductions of more than two orders of magnitude in both RMS and maximum errors. Furthermore, the RBF-FDMO approach is developed and, for the first time, applied to the analysis of grounding system (GS) configurations specified in IEEE Std. 80™, as well as a practical 110 kV substation GS in Vietnam. The obtained potential distributions, grounding resistances, and touch and step voltages confirm the effectiveness and reliability of the method. The results indicate that the proposed approach features a simple formulation and competitive computational efficiency, positioning it as a practical alternative to conventional methods like the finite element method (FEM) and the boundary element method (BEM) for GS analysis and design. [ABSTRACT FROM AUTHOR] |
| Database: | Energy & Power Source |
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| Header | DbId: enr DbLabel: Energy & Power Source An: 194141386 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: A Hybrid Radial Basis Function–Finite Difference Matrix Operators (RBF–FDMO) Approach for Numerical Simulation of Grounding Systems on Non-Uniform FD Mesh. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Nguyen%2C+Xuan-Binh%22">Nguyen, Xuan-Binh</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Nguyen%2C+Nhat-Nam%22">Nguyen, Nhat-Nam</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Vu%2C+Phan-Tu%22">Vu, Phan-Tu</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> vptu@hcmut.edu.vn</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Energies+%2819961073%29%22">Energies (19961073)</searchLink>. May2026, Vol. 19 Issue 10, p2271. 23p. – Name: Subject Label: Subject Terms Group: Su Data: *<searchLink fieldCode="DE" term="%22Radial+basis+functions%22">Radial basis functions</searchLink><br />*<searchLink fieldCode="DE" term="%22Electric+current+grounding%22">Electric current grounding</searchLink><br />*<searchLink fieldCode="DE" term="%22Engineering+standards%22">Engineering standards</searchLink><br />*<searchLink fieldCode="DE" term="%22Differential+operators%22">Differential operators</searchLink><br />*<searchLink fieldCode="DE" term="%22Electromagnetic+theory%22">Electromagnetic theory</searchLink><br />*<searchLink fieldCode="DE" term="%22Laplace's+equation%22">Laplace's equation</searchLink><br />*<searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: This paper presents a hybrid numerical approach, termed the Radial Basis Function–Finite Difference Matrix Operator (RBF–FDMO) method, to enhance the accuracy and flexibility of the conventional FDMO technique for three-dimensional (3D) electromagnetic field analysis governed by the Laplace–Poisson equation. Conventional numerical methods often face challenges related to computational complexity and limited flexibility when handling non-uniform discretization and complex geometries. In the proposed method, spatial derivatives are approximated using RBF-based interpolation rather than finite difference schemes derived from Taylor series expansion. This formulation enables the construction of high-accuracy derivative operators on both uniform and non-uniform FD grids, thereby improving numerical robustness and adaptability to complex geometries. The performance of the proposed method is first compared with the FDMO in a 3D benchmark problem, with reductions of more than two orders of magnitude in both RMS and maximum errors. Furthermore, the RBF-FDMO approach is developed and, for the first time, applied to the analysis of grounding system (GS) configurations specified in IEEE Std. 80™, as well as a practical 110 kV substation GS in Vietnam. The obtained potential distributions, grounding resistances, and touch and step voltages confirm the effectiveness and reliability of the method. The results indicate that the proposed approach features a simple formulation and competitive computational efficiency, positioning it as a practical alternative to conventional methods like the finite element method (FEM) and the boundary element method (BEM) for GS analysis and design. [ABSTRACT FROM AUTHOR] |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=enr&AN=194141386 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.3390/en19102271 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 23 StartPage: 2271 Subjects: – SubjectFull: Radial basis functions Type: general – SubjectFull: Electric current grounding Type: general – SubjectFull: Engineering standards Type: general – SubjectFull: Differential operators Type: general – SubjectFull: Electromagnetic theory Type: general – SubjectFull: Laplace's equation Type: general – SubjectFull: Numerical analysis Type: general Titles: – TitleFull: A Hybrid Radial Basis Function–Finite Difference Matrix Operators (RBF–FDMO) Approach for Numerical Simulation of Grounding Systems on Non-Uniform FD Mesh. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Nguyen, Xuan-Binh – PersonEntity: Name: NameFull: Nguyen, Nhat-Nam – PersonEntity: Name: NameFull: Vu, Phan-Tu IsPartOfRelationships: – BibEntity: Dates: – D: 15 M: 05 Text: May2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 19961073 Numbering: – Type: volume Value: 19 – Type: issue Value: 10 Titles: – TitleFull: Energies (19961073) Type: main |
| ResultId | 1 |
