Multipole theory for 3D magnetic vector potential magneto-static field problems using the second order vector potential

A MT (Multipole Theory) method for 3D magnetic vector potential magneto-static field problems formulated in terms of the second order vector potential is presented. The result of the mathematical analysis shows that the MT can get the unique solution for magnetic vector potential boundary-value problems that has a unique solution. Using the MT method, it is unnecessary to discrete the field domain or the boundary, the number of the variables is much less than that of the other method and a minimum computer resource is needed. By calculating two examples, it is shown that the MT is reliable, has better computation accuracy and can be used to compute the 3D magnetic vector potential magneto-static boundary value problems.