Investigation of a Boundary Integral Equation ${mbi n} \times {mbi H} = {mbi J}_{s}$ on Torus-Shaped Perfect Conductors

We have found that a boundary integral equation n times H = J_s results in an inaccurate solution on torus-shaped perfect conducting surfaces. Although, constraining a boundary condition n times H = J_s automatically satisfies E x n = 0 on a closed polyhedron-shaped conductor, there exists a solution which only satisfies the boundary condition n times H = J_s but not the other boundary condition E times n = 0 on a torus-shaped conductor. We have introduced a virtual magnetic current M_s in the system equation as another degree of freedom and employed E times n = 0 at one point on the perfect conducting surface so as to obtain the accurate solution. To verify the proposed discussion, we have formulated an axially-symmetric method of moments based on n times H = J_s and compared with other electromagnetic field solvers.