An adaptive finite element method for magnetostatic force computations

An adaptive finite element method for magnetostatic force computations using Maxwell's stress tensor is presented. In a coarse mesh, there are large high-frequency errors in the distribution of force density on the integration path for force computation. The force density errors of the elements on the integration path are estimated from the differences between the computed force density and the smoothed one obtained by taking some low-frequency terms from the Fourier series expansion of the computed force density. The elements with relatively large errors are refined. Three integration paths are chosen for force density computation. In a coarse mesh, the computed forces for each integration path give great differences, but converge to certain values as mesh refinements are performed by the adaptive scheme. Good agreement has been obtained between analytic and numerical solutions in some typical models.<>