T-Ω method using hierarchal edge elements

The edge-element version of the T-Ω method is a 3D finite-element method for computing the fields in and around conducting and magnetic materials at power frequencies. The magnetic field is represented as the sum of two parts: the gradient of a scalar potential and, in the conductors, an additional vector field represented by Whitney edge elements. The method is powerful but uses only a low-order approximation of the magnetic field. The paper describes a version using higher-order polynomials. Three sets of trial function spaces are defined: a set of irrotational spaces and two sets of rotational spaces (one for the impressed coil field and one for the induced eddy currents). By combining spaces from the three sets, a number of representations for the magnetic field is possible on the same mesh. The simplest representation corresponds to the Whitney element; the most accurate is fully quadratic in each tetrahedron. Furthermore, as the spaces are hierarchically constructed, it is possible to mix elements of different types on the same mesh without violating continuity requirements. Results for two test problems are presented: an infinite, current-carrying copper plate, and a copper block in the airgap of a magnetic circuit. The results demonstrate that the higher-order elements give greater accuracy for a given computational cost