A tunable volume integration formulation for force calculation in finite-element based computational magnetostatics

A generalized formulation for net magnetostatic loading force calculation is derived from the Maxwell stress expression. The formulation yields a combined surface and volume integration method based on the magnetic flux density and an arbitrary scalar function g. The most interesting feature of the technique is its flexibility. For one choice of g, the method reduces to a distributed Maxwell stress scheme; for another, it yields a generalized version of the Coulomb virtual work implementation. With the introduction of an intelligent g-function based on local field-error, the new formulation yields a fully automatic method suitable for extracting accurate and consistent forces from imperfect numerical solutions. It is implemented for two-dimensional first-order finite elements, and two illustrative test problems are analyzed. The performance of the scheme is compared to the Maxwell stress and Coulomb approaches