MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Analysis and numerical simulation of magnetic forces between rigid polygonal bodies. Part I: Analysis

Nikola Popović , Dirk Praetorius and Anja Schlömerkemper


The mathematical and physical analysis of magnetoelastic phenomena is a topic of ongoing research. Different formulae have been proposed to describe the magnetic forces in macroscopic systems. We discuss several of these formulae in the context of rigid magnetized bodies. In case the bodies are in contact, we consider formulae both in the framework of macroscopic electrodynamics and via a multiscale approach, i.e., in a discrete setting of magnetic dipole moments. We give mathematically rigorous proofs for domains of polygonal shape (as well as for more general geometries) in two and three space dimensions. In an accompanying second article, we investigate the formulae in a number of numerical experiments, where we focus on the dependence of the magnetic force on the distance between the bodies and on the case when the two bodies are in contact. The aim of the analysis as well as of the numerical simulation is to contribute to the ongoing debate about which formula describes the magnetic force between macroscopic bodies best and to stimulate corresponding real-life experiments.

MSC Codes:
78A30, 35J05, 40A30
41.20.Gz, 45.20.da, 02.30.Em
magnetostatics, magnetic force formulae, potential theory, lattice-to-continuum limit

Related publications

2007 Repository Open Access
Nikola Popovic, Dirk Praetorius and Anja Schlömerkemper

Analysis and numerical simulation of magnetic forces between rigid polygonal bodies. Pt. 1 : Analysis

In: Continuum mechanics and thermodynamics, 19 (2007) 1/2, pp. 67-80