1 research outputs found
A hybridizable discontinuous Galerkin method for simulation of electrostatic problems with floating potential conductors
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