Development of an electrical calculation method plays the leading role in simulating induction devices. In modeling electrical devices and complexes, it is often necessary to simultaneously solve both chain and field problems, i.e., to deal with both lumped and distributed parameters. The article considers the method of integral equations for induction systems with non-magnetic and ferromagnetic loading, which is based on the theory of long-range action. The method’s key statement is that the field at any point is determined as the sum of the fields produced by all sources, including primary and secondary ones. Another finite element method is based on the theory of short-range action, which describes the electromagnetic wave propagation from point to point, its refraction and reflection at the boundaries of media. The article substantiates the development of a combined method based on using the method of integral equations for calculating the input parameters of inductors (an external problem) and the finite element method for calculating the field distribution in the load (an internal problem). The combined method has well proven itself in modeling induction heating and melting of metals and oxides, heating a tape in a transverse magnetic field, induction plasmatrons, and casting aluminum into an electromagnetic crystallizer.
A finite element method for the solution of singular integral equations