Finite‐Element Solution of Magnetic Circuits

This chapter presents the basic method of first‐order triangular finite elements to illustrate its use in both two‐dimensional linear and nonlinear magnetostatic problems. For a two‐dimensional magnetostatic problem, the magnetic vector potential concept is a useful approach which reduces the number of unknown functions. To the finite‐element discretization scheme, the variational approach is discussed in the chapter. The variational method consists of constructing a set of approximate functions which minimize the energy stored in the system. It is possible to show that the approximating function is the required solution to the differential equation which satisfies the given boundary conditions. The first‐order finite‐element solution technique described in the chapter assumes that the field excitation is a consequence of source currents in the region. Another possible source of excitation is that of permanent magnets. The chapter further shows the second quadrant of the B‐H characteristic of a permanent magnet.