Numerical solution of eddy current problems in bounded domains using realistic boundary conditions

A multivalued magnetic scalar potential is introduced then to impose this curl-free condition. The discrete counterpart of this formulation leads to an important saving in computational effort. Problems related to the topology are also considered, more precisely, the possibility of having a non-simply connected dielectric domain is taken into account. Finally, the method is applied to solve two three-dimensional model problems: a test with a known analytical solution and the computation of the electromagnetic field in a metallurgical arc furnace.