The finite element modeling of conductors and floating potentials

In both electrostatic and magnetostatic finite element analysis the need occasionally arises for the inclusion of isolated perfect electric and magnetic conductors, respectively. The surfaces of such conductors represent equipotentials but do not constitute a Dirichlet boundary condition. Existing methods for constraining such surface potentials to be constant, without giving specific values, are fairly complicated. This paper presents a simple approach which requires no modifications to existing finite element programs that can solve Laplace's and Poisson's equation subject to the usual Dirichlet and Neumann boundary conditions. The paper also addresses the dual problem of voids in conductors and shows how the floating potential concept can be exploited to obtain streamlines of current flow.