This paper describes the role and meaning of the gauge condition of magnetic vector potential, and also a new formulation of the finite-element analysis. The relation between the Coulomb gauge and the condition for outer boundary, symmetrical boundary and the boundary of different materials are clarified. It is found that the gauge condition is essential for solving the three-dimensional magnetostatic field problems. The vector-Poissons equation including the gauge is discretized using the Galerkin method which in turn yields a new formulation. In this paper, The three components of A(AX, AY, AZ) are formulated separately. By the separation of the components, memory size and calculating time can be reduced greatly. To confirm the theory and the formulation, the IEE model is examined. In the examination, it is found that the measured and calculated results are in close agreement and it is also confirmed that the divergence of A at every node which is on the boundary of different materials equals zero in the volume. These show that the theory and the formulation in this paper are valid.
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