T-Ω formulation for eddy-current problems in multiply connected regions

When using t-Ω formulation for solving eddy-current problems in multiply connected regions, cuts have to be introduced to avoid multivalued problems of scalar potential. In this paper, the vector potential is used in both the conducting region and cutting domains. The cutting domains are composed of one layer of elements that fill the holes of conductors. In the cutting domains, the zero curl condition of the vector potential is strongly imposed by a constraint function. Such a method avoids the introduction of a fake conductor in the holes. To generate the cutting domains, an automatic cut generation algorithm is developed