Calculation of Stationary Magnetic Fields Based on the Improved Quadrature Formulas for a Simple Layer Potential

Igor Reznichenko, Primož Podržaj () and Aljoša Peperko
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Igor Reznichenko: Faculty of Mechanical Engineering, University of Ljubljana, 1000 Ljubljana, Slovenia
Primož Podržaj: Faculty of Mechanical Engineering, University of Ljubljana, 1000 Ljubljana, Slovenia
Aljoša Peperko: Faculty of Mechanical Engineering, University of Ljubljana, 1000 Ljubljana, Slovenia

Mathematics, 2023, vol. 12, issue 1, 1-16

Abstract: 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.

Keywords: boundary element method; magnetic fields; numerical integration; Laplace equation; Fredholm integral equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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