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When the flux distribution of a magnetic circuit is analyzed by using the conventional finite element method, the magnetizing currents must be given. Therefore, if the flux distribution is specified, it is difficult to obtain the distributions of magnetomotive forces or configuration of magnets producing the specified field distribution by the conventional finite element method. New methods which are called the "finite element method taking account of external power source" and the "finite element method with shape modification" have been developed. The processes of calculation in these methods are contrary to the conventional technique. These new methods have the following advantages: (a) If there are many unknown independent magnetizing currents, these currents are directly calculated by the new method. (b) When a flux distribution is specified, the optimum shapes of the magnets can be directly calculated. (c) As these new methods need no repetition, computing time can be considerably reduced. The principles and the finite element formulations of these new methods are described, and a few examples of application of these methods are shown. These new methods make it possible to design the optimum magnetic circuits by using the finite element method.