The Eggshell method in a nutshell.

The Eggshell method was introduced by F. Henrotte as a novel magnetic force computation method. It allows computation of the force by integrating the magnetic stress tensor over a shell surrounding the body of interest. We investigate the numerical properties of this method for current carrying wires, and permanent magnets immersed in two-dimensional stationary magnetic fields, discretized by first and second order isoparametric triangular finite elements. We do so by comparing the accuracy of the method, as a function of the mesh size and element order, with the result of three classical force computation methods: the Lorentz, the Virtual Work and the Maxwell Stress Tensor method. Our numerical results clearly show that for current carrying wires the Lorentz method is the method of choice. For permanent magnets (for which the Lorentz method no longer applies) the isoparametric second order Eggshell method is more accurate than the Virtual Work or the Maxwell Stress Tensor method. These results make the Eggshell method attractive for use in more complex problems. The Eggshell method is applied on second order isoparametric elements. Its implementation is presented in detail as a set of new MATLAB post-processing routines in the FEMLAB simulation environment