Complementarity bilateral bounds on forces in magnet systems

Abstract

Purpose

It is well known that complementarity can provide bilateral bounds on energy, in numerical approximations of nonlinear magnetostatics. Questions whether like force is, up to sign, the derivative of energy, can such bounds also apply to forces, torques, and other concepts?

Design/methodology/approach

This is a discussion paper exploring the issues conceptually.

Findings

On the face of it, no, since inequalities are not preserved by differentiation. Yet, useful bounds can be given in some cases, as shown in the discussion, following an idea by Matagne.

Originality/value

The paper aids the understanding of nonlinear magnetostatic systems.

Citation

Bossavit, A. (2007), "Complementarity bilateral bounds on forces in magnet systems", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 26 No. 4, pp. 932-940. https://doi.org/10.1108/03321640710756276