Accuracy of force calculations using first order tetrahedra for electromagnetic devices with small air gaps

The accuracy of force calculations for three-dimensional electromagnetic devices with small air gaps is examined for the case of a first-order, tetrahedral finite-element model of a control solenoid. The air gap tetrahedra in this example have large aspect ratios and obtuse angles which adversely impact the Maxwell stress tensor based force calculations. Typical finite-element solutions of this problem produce force values which are considerably lower than those measured. A significant improvement in the accuracy of the force computations was achieved through successive stages of adaptive mesh refinement.