Parallel Numerical Computing of Finite Element Model of Conductors and Floating Potentials

Dong, Wang; Ruan, Jiangjun; Zhang, Du; Liu, Shoubao; Zhang, Yujiao

doi:10.1109/ispa.2010.32

Cited by 5 publications

(12 citation statements)

References 12 publications

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“…In (13) and 14,M is the mass matrix, which is a K ×K block diagonal matrix, with each diagonal block being a 3 × 3 block diagonal matrix with 3 identical…”

Section: B Discontinuous Galerkin Formulationmentioning

confidence: 99%

“…Several techniques have been introduced to the traditional FEM so that FPCs can be accounted for. These include the virtual permittivity method (VPM) [10], the matrix reduction method (MRM) [13], and the charge simulation method (CSM) [11], [12], [16]. These methods' accuracy, ease of implementation (or amount of modifications required for implementation in legacy FEM codes), ability to account for charges on FPCs, and savings in the number of unknowns have recently been compared in [15].…”

Section: Introductionmentioning

confidence: 99%

“…Accurate representation of an FPC requires a very high virtual permittivity value but this in return reduces the solution accuracy since it makes the FEM matrix illconditioned. MRM does not suffer from this problem but it requires considerable modifications to the original FEM code [13]- [15]. Additionally, both VPM and MRM lack the ability to enforce nonzero charge conditions on the surface of an FPC [13]- [15].…”

Section: Introductionmentioning

confidence: 99%

“…MRM does not suffer from this problem but it requires considerable modifications to the original FEM code [13]- [15]. Additionally, both VPM and MRM lack the ability to enforce nonzero charge conditions on the surface of an FPC [13]- [15]. CSM can account for charge conditions but setting a specific charge distribution on an FPC calls for a priori knowledge often acquired heuristically by running multiple simulations [13]- [16].…”

Section: Introductionmentioning

confidence: 99%

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Modeling Floating Potential Conductors Using Discontinuous Galerkin Method

2020

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Isolated conductors appear in various electrostatic problems. In simulations, an equipotential condition with an undefined/floating potential value is enforced on the surface of isolated conductors. In this work, a numerical scheme making use of the discontinuous Galerkin (DG) method is proposed to model such conductors in electrostatic problems. A floating-potential boundary condition, which involves the equipotential condition together with a total charge condition, is ''weakly'' enforced on the conductor surfaces through the numerical flux of the DG method. Compared to adaptations of the finite element method used for modeling conductors, this proposed method is more accurate, capable of imposing charge conditions, and simpler to implement. Numerical results, which demonstrate the accuracy and applicability of the proposed method, are presented. INDEX TERMS Discontinuous Galerkin method, electrostatics, finite element method, floating potential conductors, magnetostatics, plasmonic-enhanced photoconductive antenna.

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“…In (13) and 14,M is the mass matrix, which is a K ×K block diagonal matrix, with each diagonal block being a 3 × 3 block diagonal matrix with 3 identical…”

Section: B Discontinuous Galerkin Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Modeling Floating Potential Conductors Using Discontinuous Galerkin Method

2020

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“…In addition, when an FPC is charged, a nonzero charge condition must be imposed on its surface. Both VPM and MRM cannot account for this nonzero charge condition 10‐12 . 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 10‐13 .…”

Section: Introductionmentioning

confidence: 99%

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

Chen

Dong

et al. 2020

Int J Numerical Modelling

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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.

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