T-OMEGA METHOD USING HIERARCHICAL EDGE ELEMENTS

The edge-element version of the T-Omega 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 t he sum of two parts: the gradient of a scalar potential and, in the co nductors, an additional vector held represented by Whitney edge elemen ts. The method is powerful but uses only a low-order approximation of the magnetic held. The paper describes a version using higher-order po lynomials. Three sets of trial function spaces are defined: a set of i rrotational spaces and two sets of rotational spaces (one for the impr essed coil held and one for the induced eddy currents). By combining s paces from the three sets, a number of representations for the magneti c field is possible on the same mesh. The simplest representation corr esponds to the Whitney element; the most accurate is fully quadratic i n each tetrahedron. Furthermore, as the spaces are hierarchally constr ucted, it is possible to mix elements of different types on the same m esh without violating continuity requirements. Results for two test pr oblems are presented: an infinite, current-carrying copper plate, and a copper block in the airgap of a magnetic circuit. The results demons trate that the higher-order elements give greater accuracy for a given computational cost.