A new approach to SP Computation-vector potential approach

The steady current field is guided by two fundamental principles, i.e., the vanishing of the curl of the field strength and the vanishing of the divergence of current density, which originate from the conservation of energy and charge, respectively. In the prevailing approach, the first principle is assumed to be generally valid and, hence, the field strength is equated to the negative gradient of a scalar potential. The second principle is dropped at certain points, which are called current sources, that current is supposed to be injected from the outside. In the present paper, a different approach is proposed, in which the density of current is equated to the curl of a vector potential so that its divergence vanishes unconditionally while the curl of field strength assumes nonvanishing value at some points that are called curl sources. It is called the vector potential theory approach and shows its advantage over scalar potential theory in spontaneous potential (SP) computation. In the vector potential approach, the dipole layer disappears and SP is supposed to be generated by the curl source rather than the dipole layer. In the numerical computation, the numerical mode-matching method (NMM) is used. Hermite cubic interpolation rather than linear interpolation is employed in the basis function expansion of the simulated function. Eigenvectors to be solved for are composed of, not only the amplitudes, but also the slopes of the simulated function at nodal points