Simulation of floating potentials in industrial applications by boundary element methods

We consider the electrostatic field computations with floating potentials in a multi-dielectric setting. A floating potential is an unknown equipotential value associated with an isolated perfect electric conductor, where the flux through the surface is zero. The floating potentials can be integrated into the formulations directly or can be approximated by a dielectric medium with high permittivity. We apply boundary integral equations for the solution of the electrostatic field problem. In particular, an indirect single layer potential ansatz and a direct formulation based on the Steklov-Poincaré interface equation are considered. All these approaches are discussed in detail and compared for several examples including some industrial applications. In particular, we will demonstrate that the formulations involving constraints are vastly superior to the penalized formulations with high permittivity, which are widely used in practice.