Calculation of stationary magnetic fields based on the improved quadrature formulas for a simple layer potential

Reznichenko, Igor (author), Podržaj, Primož (author), Peperko, Aljoša (author)

This research deals with precision calculations of stationary magnetic fields of volumetric bodies. The electrostatics analogy allows for the use of a scalar magnetic potential, which reformulates the original task as a boundary value problem for the Laplace equation. We approach this with the boundary element method, specifically in distance ranges close to the magnetized surface, where existing standard numerical methods are known to struggle. This work presents an approach based on the improved quadrature formulas for the simple layer potential and its normal derivative. Numerical tests confirm significant improvements in calculating the field at any distance from the surface of the magnet.

• Language: English
• Keywords: boundary element method, magnetic fields, numerical integration, Laplace equation, Fredholm integral equation
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FS - Faculty of Mechanical Engineering
• Publication status: Published
• Publication version: Version of Record
• Year: 2024
• Number of pages: 16 str.
• Numbering: Vol. 12, iss. 1, [article no.] 21
• PID: 20.500.12556/RUL-154324-4549f4aa-3146-2b6e-2b9d-5bad2241f33e
• UDC: 519.62
• ISSN on article: 2227-7390
• DOI: 10.3390/math12010021
• COBISS.SI-ID: 184054275
• Publication date in RUL: 07.02.2024

Record is a part of a journal

• Title: Mathematics
• Shortened title: Mathematics
• Publisher: MDPI AG
• ISSN: 2227-7390
• COBISS.SI-ID: 523267865

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

• Language: Slovenian
• Keywords: metoda robnih elementov, magnetna polja, numerična integracija, Laplaceova enačba, Fredholmova integralna enačba