Numerical treatment of rounded and sharp corners in the modeling of 2D electrostatic fields

Krähenbühl, Laurent; Buret, François; Perrussel, Ronan; Voyer, Damien; Dular, Patrick; Péron, Victor; Poignard, Clair

doi:10.1590/s2179-10742011000100008

Cited by 10 publications

(15 citation statements)

References 6 publications

(12 reference statements)

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“…However, the maximum electric field strength at perfectly sharp edges is infinite [8]. The fact that simulations return a finite value is a consequence of the finite size of the grid cells used for simulation.…”

Section: Mesh-dependent Elecrtic Field Strengthmentioning

confidence: 99%

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Simulation of the electric field strength in the vicinity of metallization edges on dielectric substrates

Bayer

Baer

Waltrich

et al. 2015

IEEE Trans. Dielect. Electr. Insul.

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High electric field strengths at the edge of the metallization of insulated gate bipolar transistor (IGBT) power modules are, besides defects in the substrate or the potting gel, the main reason for partial discharge. These critical electric field strengths occur at the energized contact where it is bordered by the insulating ceramic and the cover (mostly silicone gel). The reduction of high electric field strengths for increasing the threshold voltage for partial discharge has been studied in several publications based on experiments as well as on simulations. Simulations allow the localization of the critical spots and the quantification of the maximum electric field strength. However, a systematic study of the singularities of the electric field strength at the sharp edges is lacking. Such singularities are investigated in this article. The calculation of an absolute electric field strength value is only possible for finite edge radii. For sharp edges, however, the maximum electric field strength returned by simulation depends on the grid size: Through the finite grid size a virtual edge radius is induced that suppresses the singularity at the edge. To get around this problem, a mesh-independent evaluation procedure is introduced. With this procedure it is possible to quantitatively evaluate the electric field strength in the vicinity of the sharp edge. As an example, the influence of the offset between the top and bottom metallization layer on the maximum electric field strength is studied. Moreover, the influence of the thickness of the involved layers and of the shape of the electrodes is discussed. Also, the impact of the material properties of the involved dielectrics is examined. In addition to electrostatic simulations we have carried out electric transient simulations, which show that the ratio of the conductivities of the involved dielectric materials plays a major role for determining the maximum electric field strength

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Section: Mesh-dependent Elecrtic Field Strengthmentioning

confidence: 99%

“…The correlation between the maximum electric field strength and the radius is described in the literature [8]: (2) and…”

Section: Mesh-dependent Elecrtic Field Strengthmentioning

confidence: 99%

Simulation of the electric field strength in the vicinity of metallization edges on dielectric substrates

Bayer

Baer

Waltrich

et al. 2015

IEEE Trans. Dielect. Electr. Insul.

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“…As it is common in practical engineering applications, the corners of the inclusion are rounded to eliminate the singularity induced by the re-entrant corners. 116 Specifically, a fillet defined using a small radius r is introduced to increase the regularity of the boundary. Figure 1 shows the intensity of the electric field for three different geometries, with a fillet of radius r=5, r=2 and r=1 respectively.…”

Section: Hdg-nefem: Exact Geometry and Degree Adaptivitymentioning

confidence: 99%

Discontinuous Galerkin approximations in computational mechanics: hybridization, exact geometry and degree adaptivity

Giacomini

Sevilla

2019

SN Appl. Sci.

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Discontinuous Galerkin (DG) discretizations with exact representation of the geometry and local polynomial degree adaptivity are revisited. Hybridization techniques are employed to reduce the computational cost of DG approximations and devise the hybridizable discontinuous Galerkin (HDG) method. Exact geometry described by non-uniform rational B-splines (NURBS) is integrated into HDG using the framework of the NURBS-enhanced finite element method (NEFEM). Moreover, optimal convergence and superconvergence properties of HDG-Voigt formulation in presence of symmetric second-order tensors are exploited to construct inexpensive error indicators and drive degree adaptive procedures. Applications involving the numerical simulation of problems in electrostatics, linear elasticity and incompressible viscous flows are presented. Moreover, this is done for both high-order HDG approximations and the lowest-order framework of face-centered finite volumes (FCFV).

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“…This numerical approach enables the simulation of the skin effect. Moreover, in order to evaluate the accuracy of the proposed asymptotic solutions, we establish a numerical comparison with the impedance boundary conditions (IBCs) solutions [17][18][19][20][21] that are among the most crucial methods for solving time-harmonic eddy current problems with a small skin depth denoted by δ. To shed a light on our approach, we emphasize that the IBCs method are no more efficient since the computational costs of the proposed method are less than the IBCs solutions regardless the number of physical parameters to be considered.…”

Section: Introductionmentioning

confidence: 99%

“…In this article, we employ an asymptotic approach that was previously involved in the context of the eddy current problem for highly conductive and non-magnetic materials. 1,12,17,22 More precisely, the solution of the eddy current problem is established previously 1 using a multiscale expansion in a bi-dimensional setting where the domain is considered unbounded and the solution grows logarithmically to infinity. Moreover, authors developed δ À parametrization in high frequency or high conductivity 12,17,22 that involves real asymptotics and family of Dirichlet problems for the Laplace operator set in the dielectric medium.…”

Section: Introductionmentioning

confidence: 99%

Numerical study of the magnetic skin effect: Efficient parameterization of 2D surface‐impedance solutions for linear ferromagnetic materials

Yafi

Péron

Perrussel

et al. 2022

Int J Numerical Modelling

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This work presents an efficient method based on asymptotic models in order to solve numerically eddy current problems in a bi-dimensional setting with a high contrast of linear relative magnetic permeability µr 1 between a conductor and a dielectric subdomain. We describe a magnetic skin effect by deriving a multiscale expansion for the magnetic potential in power series of a small parameter δ which represents the skin depth. We make explicit the first asymptotics up to the order three. Some numerical results based on the finite element method will be presented to illustrate the magnetic skin effect and to validate the performance of the proposed asymptotic models in the dielectric medium. We confirm that the proposed asymptotics provide reduced computational costs for a wide range of the physical parameters introduced in our problem.

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Numerical treatment of rounded and sharp corners in the modeling of 2D electrostatic fields

Cited by 10 publications

References 6 publications

Simulation of the electric field strength in the vicinity of metallization edges on dielectric substrates

Simulation of the electric field strength in the vicinity of metallization edges on dielectric substrates

Discontinuous Galerkin approximations in computational mechanics: hybridization, exact geometry and degree adaptivity

Numerical study of the magnetic skin effect: Efficient parameterization of 2D surface‐impedance solutions for linear ferromagnetic materials

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