Floating-Potential Boundary Conditions using Discontinuous Galerkin Method

Isolated conductors appear in various electrostatic problems. In simulations, an equipotential condition with a floating (undefined) potential value is enforced on the surface of an isolated conductor. In this work, a numerical scheme making use of the discontinuous Galerkin (DG) method is proposed to model such conductors in electrostatic simulations. A floating-potential boundary condition, which involves the equipotential condition together with a total charge condition, is “weakly” enforced on the conductor surface through the numerical flux. Compared to adaptations of the finite element method used for modeling conductors, the proposed method is more accurate, capable of imposing nonzero charge conditions, and simpler to implement. Numerical results, which demonstrate the accuracy and applicability of the proposed method, are provided.