Complementarity bilateral bounds on forces in magnet systems
Purpose - It is well known that complementarity can provide bilateral bounds on energy, in numerical approximations of non-linear magnetostatics. This study seeks to answer questions like whether 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 - This study finds that on the face of it, the answer is 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 non-linear magnetostatic systems.
magnetism non-linear control systems numerical analysis