On the boundary conditions for the vector potential formulation in electrostatics

Abstract

The vector potential formulation is a promising solution method for nonlinear electromechanically coupled boundary value problems. However, one of the drawbacks of this formulation is the non-uniqueness of the (electric) vector potential in three dimensions. The present paper focuses on the Coulomb gauging method to overcome this problem. In particular, the corresponding gauging boundary conditions and their consistency with the physical boundary conditions are examined in detail. Furthermore, certain topological features like cavities and multiply connectedness of the domain of analysis are taken into account. Different variational/weak formulations being appropriate for finite element implementation are described. Finally, the suitability of these formulations is demonstrated in several numerical examples. Copyright © 2015 John Wiley & Sons, Ltd.