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

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.

A Locally-Implicit Discontinuous Galerkin Time-Domain Method to Simulate Metasurfaces Using Generalized Sheet Transition Conditions

“…Here, n ν k,g represents the component of nk,g along the direction ν ∈ {x, ŷ, ẑ}, γ ab,νη k,g , a, b ∈ {E, H}, µ, η ∈ {x, y, z} is the νη component of the tensor γ ab k,g , and I and O are identity and zero matrices. Note that F k,g has the same matrix entries as F k,g but with its columns re-organized such that it operates on the unknowns of element k , i.e., if node j of element k is connected to node j element k , column j of F k,g is equal to column j of F k,g [61].…”

Analysis of Screening Effects on Terahertz Photoconductive Devices Using a Fully-Coupled Multiphysics Approach

“…The Poisson-DD system (1)-( 2) is solved iteratively using the Gummel method [40] and the linearized set of equations at every iteration are discretized using a stationary discontinuous Galerkin (DG) scheme [37], [43]- [47]. The steady-state solutions are used as inputs in the transient solver [36].…”

“…For the Poisson equation, a potential-drop boundary condition is used along the x direction to mimic the bias voltage, periodic boundary conditions (PBCs) are used along the y direction, and a homogeneous Neumann boundary condition is used along the z direction. For the stationary DD equations, PBCs are used along x and y directions, and a homogeneous Robin boundary condition is used on the surfaces of the LT-GaAs layer (transverse to the z direction) [46], [47]. PBCs are used along the x and y directions for the timedependent Maxwell and DD equations.…”

Analysis of Screening Effects on Terahertz Photoconductive Devices using a Fully-Coupled Multiphysics Approach

“…The Poisson-DD system (1)-( 2) is solved iteratively using the Gummel method [40] and the linearized set of equations at every iteration are discretized using a stationary discontinuous Galerkin (DG) scheme [37,[43][44][45][46][47]. The steady-state solutions are used as inputs in the transient solver [36].…”

“…For the Poisson equation, a potential-drop boundary condition is used along the x direction to mimic the bias voltage, periodic boundary conditions (PBCs) are used along the y direction, and a homogeneous Neumann boundary condition is used along the z direction. For the stationary DD equations, PBCs are used along x and y directions, and a homogeneous Robin boundary condition is used on the surfaces of the LT-GaAs layer (transverse to the z direction) [46,47]. PBCs are used along the x and y directions for the time-dependent Maxwell and DD equations.…”