A hybridizable discontinuous Galerkin method for simulation of electrostatic problems with floating potential conductors

TL;DR

This paper introduces a hybridizable discontinuous Galerkin (HDG) method for electrostatic simulations involving floating potential conductors, improving computational efficiency while maintaining accuracy compared to traditional DG methods.

Contribution

A novel HDG approach is developed to efficiently handle floating potential boundary conditions in electrostatics, reducing unknowns and computational cost.

Findings

HDG method matches DG accuracy

Significant reduction in unknowns and computational time

Effective enforcement of floating potential conditions

Abstract

In an electrostatic simulation, an equipotential condition with an undefined/floating potential value has to be enforced on the surface of an isolated conductor. If this conductor is charged, a nonzero charge condition is also required. While implementation of these conditions using a traditional finite element method (FEM) is not straightforward, they can be easily discretized and incorporated within a discontinuous Galerkin (DG) method. However, DG discretization results in a larger number of unknowns as compared to FEM. In this work, a hybridizable DG (HDG) method is proposed to alleviate this problem. Floating potential boundary conditions, possibly with different charge values, are introduced on surfaces of each isolated conductor and are weakly enforced in the global problem of HDG. The unknowns of the global HDG problem are those only associated with the nodes on the mesh skeleton and their number is much smaller than the total number of unknowns required by DG. Numerical examples show that the proposed method is as accurate as DG while it improves the computational efficiency significantly.