Surface integrals on 3D and 2D finite element models for skin effect excitations and open boundaries

Surface integrals on three-dimensional finite-element models can be used to excite currents in conductors with skin effects and to approximate open boundaries. In both cases the surface integrals are shown to be inhomogeneous Neumann boundary integrals which do not increase matrix bandwidth or destroy its symmetry. To excite total conductor currents in skin effect problems, inhomogeneous Neumann excitations are used. To represent open boundaries, the surface integrals are transformed into asymptotic boundary conditions. Example analyses include a 3-D railgun with transient skin effects, a 2-D air core electromagnet with open boundaries, and three-phase AC bus bars having both closed and open boundaries. Results for the electromagnetic agree with theory within two parts per million