Abstract
AbstractIn 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.
Highlights
Isolated conductors exist in a wide range of electrical and electronic systems, such as electrode cores of high-voltage inductors,[1] metallic separators of IEC surge arresters,[2] defects in ultra-high-voltage gas-insulated switchgear,[3] passive electrodes of earthing systems,[4] conductors of floating-gate transistors,[5] and, more recently, metallic nanostructures extensively used in optoelectronic devices.[6]
In electrostatic simulations of these systems, these conductors result in equipotential surfaces with unfixed electric potential values and are referred to as floating potential conductors (FPCs)
charge simulation method (CSM) can account for charge conditions since it enforces a specific charge distribution on an FPC but this requires a priori knowledge of simulation results or multiple iterative simulations.[10,11,12,13]
Summary
Isolated conductors exist in a wide range of electrical and electronic systems, such as electrode cores of high-voltage inductors,[1] metallic separators of IEC surge arresters,[2] defects in ultra-high-voltage gas-insulated switchgear,[3] passive electrodes of earthing systems,[4] conductors of floating-gate transistors,[5] and, more recently, metallic nanostructures extensively used in optoelectronic devices.[6]. The local problem is formulated with a Dirichlet boundary condition and the electric potential is chosen as the hybrid variable in the global problem.
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