Numerical treatment of floating conductors based on the traditional finite element formulation

Rincon, David J.; Aguilera, Eduardo; Chacón, J. C.

doi:10.7716/aem.v7i3.720

Cited by 6 publications

(15 citation statements)

References 7 publications

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“…We should note here that VMP does not produce a single value for the floating potential (especially for low values of v ), therefore ϕ f for VMP is selected as the value that produces the maximum diff f . The table shows that, for DG and MRM, the errors are on the same level while the accuracy of VPM depends on the choice of v (as reported in [15]). For smaller values of v , the virtual material does not behave like a perfect conductor.…”

Section: Numerical Examples a Coaxial Capacitor With Fpcmentioning

confidence: 74%

“…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]. Among all the schemes used for analyzing problems involving FPCs, VPM is perhaps the easiest one to implement since it does not require any modifications to the traditional FEM code.…”

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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Section: Numerical Examples a Coaxial Capacitor With Fpcmentioning

confidence: 74%

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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“…contacts are modeled as floating conductors with the virtual permittivity method [10] (relative permittivity is set to 10 9 ).…”

Section: Plos Computational Biologymentioning

confidence: 99%

OSS-DBS: Open-source simulation platform for deep brain stimulation with a comprehensive automated modeling

et al. 2020

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In this study, we propose a new open-source simulation platform that comprises computeraided design and computer-aided engineering tools for highly automated evaluation of electric field distribution and neural activation during Deep Brain Stimulation (DBS). It will be shown how a Volume Conductor Model (VCM) is constructed and examined using Pythoncontrolled algorithms for generation, discretization and adaptive mesh refinement of the computational domain, as well as for incorporation of heterogeneous and anisotropic properties of the tissue and allocation of neuron models. The utilization of the platform is facilitated by a collection of predefined input setups and quick visualization routines. The accuracy of a VCM, created and optimized by the platform, was estimated by comparison with a commercial software. The results demonstrate no significant deviation between the models in the electric potential distribution. A qualitative estimation of different physics for the VCM shows an agreement with previous computational studies. The proposed computational platform is suitable for an accurate estimation of electric fields during DBS in scientific modeling studies. In future, we intend to acquire SDA and EMA approval. Successful incorporation of open-source software, controlled by in-house developed algorithms, provides a highly automated solution. The platform allows for optimization and uncertainty quantification (UQ) studies, while employment of the open-source software facilitates accessibility and reproducibility of simulations.

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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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Numerical treatment of floating conductors based on the traditional finite element formulation

Cited by 6 publications

References 7 publications

Modeling Floating Potential Conductors Using Discontinuous Galerkin Method

Modeling Floating Potential Conductors Using Discontinuous Galerkin Method

OSS-DBS: Open-source simulation platform for deep brain stimulation with a comprehensive automated modeling

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

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