On finite element force computation from two- and three-dimensional magnetostatic fields

The mathematics of force computation is well known. However, little literature exists on the practical aspects of its implementation in finite element methods. This paper takes up the issue and shows that the convergence of force with finite element mesh refinement is far behind that of flux density or vector potential. Likewise, the effect of remote boundaries placed at far, but finite, distances is shown to be greater on force. Algorithms are given for the extraction of forces from a field solution for an interactive environment and the force density and Maxwell stress methods compared.