A gauged A, V-A-Ψ formulation without A·n=0 on conductor boundaries

In the present paper a new A, V-A-Ψ formulation for transient quasi-static eddy current problems using V=0, instead of A·n=0, on conductor boundaries is proposed. This choice appears to advantageous for finite element solution problems without any symmetry plane or involving curved boundaries, even though unsuitable if the fields change very slowly. The differential formulation is carefully defined; the ways in which the Coulomb gauge is imposed and the existence and the uniqueness of the solution are discussed. A new method to obtain the symmetry of the final algebraic system is introduced. This symmetrisation technique leads to an indefinite system of algebraic equations with peculiar structure, that led to the development of a special solver. The results are extremely encouraging, the formulation is based on thorough theoretical basis, and it is fairly easy to impose the conditions on conductor boundaries