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Article
Publication date: 30 April 2019

Mohammad Issa, Jean-René Poirier, Ronan Perrussel, Olivier Chadebec and Victor Péron

Thin conducting sheets are used in many electric and electronic devices. Solving numerically the eddy current problems in presence of these thin conductive sheets requires…

Abstract

Purpose

Thin conducting sheets are used in many electric and electronic devices. Solving numerically the eddy current problems in presence of these thin conductive sheets requires a very fine mesh which leads to a large system of equations, and it becomes more problematic in case of higher frequencies. The purpose of this paper is to show the numerical pertinence of equivalent models for 3D eddy current problems with a conductive thin layer of small thickness e based on the replacement of the thin layer by its mid-surface with equivalent transmission conditions that satisfy the shielding purpose, and by using an efficient discretization using the boundary element method (BEM) to reduce the computational work.

Design/methodology/approach

These models are solved numerically using the BEM and some numerical experiments are performed to assess the accuracy of the proposed models. The results are validated by comparison with an analytical solution and a numerical solution by the commercial software Comsol.

Findings

The error between the equivalent models and analytical and numerical solutions confirms the theoretical approach. In addition to this accuracy, the computational work is reduced by considering a discretization method that requires only a surface mesh.

Originality/value

Based on a hybrid formulation, the authors present briefly a formal derivation of impedance transmission conditions for 3D thin layers in eddy current problems where non-conductive materials are considered in the interior and the exterior domain of the sheet. BEM is adopted to discretize the problem as there is no need for volume discretization.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 38 no. 2
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 1 June 2004

B. Butrylo, F. Musy, L. Nicolas, R. Perrussel, R. Scorretti and C. Vollaire

This paper presents new trends in parallel methods used to solve finite element matrix systems: standard iterative and direct solving methods first, and then domain…

Abstract

This paper presents new trends in parallel methods used to solve finite element matrix systems: standard iterative and direct solving methods first, and then domain decomposition methods. For example, the current status and properties of two prevailing programming environments (PVM and MPI) are finally given and compared when implemented together with a finite element time domain formulation.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 23 no. 2
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 9 May 2008

D. Voyer, F. Musy, L. Nicolas and R. Perrussel

The aim is to apply probabilistic approaches to electromagnetic numerical dosimetry problems in order to take into account the variability of the input parameters.

Abstract

Purpose

The aim is to apply probabilistic approaches to electromagnetic numerical dosimetry problems in order to take into account the variability of the input parameters.

Design/methodology/approach

A classic finite element method is coupled with probabilistic methods. These probabilistic methods are based on the expansion of the random parameters in two different ways: a spectral expansion and a nodal expansion.

Findings

The computation of the mean and the variance on a simple scattering problem shows that only a few hundreds calculations are required when applying these methods while the Monte Carlo method uses several thousands of samples in order to obtain a comparable accuracy.

Originality/value

The number of calculations is reduced using several techniques: a regression technique, sparse grids computed from Smolyak algorithm or a suited coordinate system.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 27 no. 3
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 3 May 2016

Israel Tuval, Dan Givoli and Ehud Behar

The purpose of this paper is to propose a computational model for thin layers, for problems of linear time-dependent heat conduction. The thin layer is replaced by a…

Abstract

Purpose

The purpose of this paper is to propose a computational model for thin layers, for problems of linear time-dependent heat conduction. The thin layer is replaced by a zero-thickness interface. The advantage of the new model is that it saves the need to construct and use a fine mesh inside the layer and in regions adjacent to it, and thus leads to a reduction in the computational effort associated with implicit or explicit finite element schemes.

Design/methodology/approach

Special asymptotic models have been proposed for linear heat transfer and linear elasticity, to handle thin layers. In these models the thin layer is replaced by an interface with zero thickness, and specific jump conditions are imposed on this interface in order to represent the special effect of the layer. One such asymptotic interface model is the first-order Bövik-Benveniste model. In a paper by Sussmann et al., this model was incorporated in a FE formulation for linear steady-state heat conduction problems, and was shown to yield an accurate and efficient computational scheme. Here, this work is extended to the time-dependent case.

Findings

As shown here, and demonstrated by numerical examples, the new model offers a cost-effective way of handling thin layers in linear time-dependent heat conduction problems. The hybrid asymptotic-FE scheme can be used with either implicit or explicit time stepping. Since the formulation can easily be symmetrized by one of several techniques, the lack of self-adjointness of the original formulation does not hinder an accurate and efficient solution.

Originality/value

Most of the literature on asymptotic models for thin layers, replacing the layer by an interface, is analytic in nature. The proposed model is presented in a computational context, fitting naturally into a finite element framework, with both implicit and explicit time stepping, while saving the need for expensive mesh construction inside the layer and in its vicinity.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 26 no. 3/4
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 3 January 2017

Patrick Dular, Patrick Kuo-Peng, Mauricio Valencia Ferreira da Luz and Laurent Krahenbuhl

This paper aims to develop a methodology for progressive finite element (FE) modeling of transformers, from simple to complex models of both magnetic cores and windings.

Abstract

Purpose

This paper aims to develop a methodology for progressive finite element (FE) modeling of transformers, from simple to complex models of both magnetic cores and windings.

Design/methodology/approach

The progressive modeling of transformers is performed via a subproblem (SP) FE method. A complete problem is split into SPs with different adapted overlapping meshes. Model refinements are performed from ideal to real flux tubes, one-dimensional to two-dimensional to three-dimensional models, linear to nonlinear materials, perfect to real materials, single wire to volume conductor windings and homogenized to fine models of cores and coils, with any coupling of these changes.

Findings

The proposed unified procedure efficiently feeds each SP via interface conditions (ICs), which lightens mesh-to-mesh sources transfers and quantifies the gain given by each refinement on both local fields and global quantities, with a clear view on its significance to justify its usefulness, if any. It can also help in education with a progressive understanding of the various aspects of transformer designs.

Originality/value

Models of different accuracy levels are sequenced with successive additive corrections supported by different adapted meshes. The way the sources act at each correction step, up to the full models with their actual geometries, is given a particular care and generalized, allowing the proposed unified procedure. For all the considered corrections, the sources are always of IC type, thus only needed in layers of FE along boundaries, which lightens the required mesh-to-mesh projections between subproblems.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 36 no. 1
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 5 May 2015

Patrick Dular, Laurent Krähenbühl, Mauricio V. Ferreira da Luz, Patrick Kuo-Peng and Christophe Geuzaine

– The purpose of this paper is to develop a subproblem method (SPM) for progressive modeling of inductors, with model refinements of both source conductors and magnetic cores.

79

Abstract

Purpose

The purpose of this paper is to develop a subproblem method (SPM) for progressive modeling of inductors, with model refinements of both source conductors and magnetic cores.

Design/methodology/approach

The modeling of inductors is split into a sequence of progressive finite element (FE) SPs. The source fields (SFs) generated by the source conductors alone are calculated at first via either the Biot-Savart (BS) law or FEs. With a novel general way to define the SFs via interface conditions (ICs), to lighten their evaluation process, the associated reaction fields for each added or modified region, mainly the magnetic cores, and in return for the source conductor regions themselves when massive, are then calculated with FE models. Changes of magnetic regions go from perfect magnetic properties up to volume linear and nonlinear properties, and from statics to dynamics.

Findings

For any added or modified region, the novel proposed ICs to define the SFs appear of general usefulness, which opens the method to a wide range of model improvements.

Originality/value

The resulting SPM allows efficient solving of parameterized analyses thanks to a proper mesh for each SP and the reuse of previous solutions to be locally corrected, in association with novel SF ICs that strongly lighten the quantity of BS evaluations. Significant corrections are progressively obtained for the fields, up to nonlinear magnetic core properties and skin and proximity effects in conductors, and for the related inductances and resistances.

Details

COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, vol. 34 no. 3
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 26 October 2018

Luca G. Campana, Paolo Di Barba, Fabrizio Dughiero, Michele Forzan, Maria Evelina Mognaschi, Rudy Rizzo and Elisabetta Sieni

In electrochemotherapy, flexible electrodes, composed by an array of needles, are applied to human tissues to treat large surface tumors. The positioning of the needles in…

Abstract

Purpose

In electrochemotherapy, flexible electrodes, composed by an array of needles, are applied to human tissues to treat large surface tumors. The positioning of the needles in the tissue depends on the surface curvature. The parallel needle case is preferred, as their relative inclinations strongly affect the actual distribution of electric field. Nevertheless, in some case, small inclinations are unavoidable. The purpose of this paper is to study the electric field distribution for non-parallel needles.

Design/methodology/approach

The effect of electrode position is evaluated systematically by means of numerical models and experiments on phantoms for two different angles (5° and 30°) and compared with the case of parallel needles. Potato model was used as phantom, as this tissue becomes dark after few hours from electroporation. The electroporation degree was gauged from the color changings on the potatoes.

Findings

The distribution of electric field in different needle configuration is found by means of finite element analysis (FEA) and experiments on potatoes. The electric field level of inclined needles was compared with parallel needle case. In particular, the electric field distribution in the case of inclined needles could be very different with respect to the one in the case of parallel needles. The degree of enhancement for different inclinations is visualized by potato color intensity. The FEA suggested that the needle parallelism has to be maintained as possible as if the tips are closer to each other, the electric field intensity could be different with respect to the one in the case of parallel needles.

Originality/value

This paper analyzes the effect of inclined electrodes considering also the non-linearity of tissues.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 38 no. 1
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 3 May 2013

Liang Li, Stéphane Lanteri and Ronan Perrussel

This work is concerned with the development and the numerical investigation of a hybridizable discontinuous Galerkin (HDG) method for the simulation of two‐dimensional…

Abstract

Purpose

This work is concerned with the development and the numerical investigation of a hybridizable discontinuous Galerkin (HDG) method for the simulation of two‐dimensional time‐harmonic electromagnetic wave propagation problems.

Design/methodology/approach

The proposed HDG method for the discretization of the two‐dimensional transverse magnetic Maxwell equations relies on an arbitrary high order nodal interpolation of the electromagnetic field components and is formulated on triangular meshes. In the HDG method, an additional hybrid variable is introduced on the faces of the elements, with which the element‐wise (local) solutions can be defined. A so‐called conservativity condition is imposed on the numerical flux, which can be defined in terms of the hybrid variable, at the interface between neighbouring elements. The linear system of equations for the unknowns associated with the hybrid variable is solved here using a multifrontal sparse LU method. The formulation is given, and the relationship between the considered HDG method and a standard upwind flux‐based DG method is also examined.

Findings

The approximate solutions for both electric and magnetic fields converge with the optimal order of p+1 in L2 norm, when the interpolation order on every element and every interface is p and the sought solution is sufficiently regular. The presented numerical results show the effectiveness of the proposed HDG method, especially when compared with a classical upwind flux‐based DG method.

Originality/value

The work described here is a demonstration of the viability of a HDG formulation for solving the time‐harmonic Maxwell equations through a detailed numerical assessment of accuracy properties and computational performances.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 32 no. 3
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 1 December 2005

Christian Vollaire, François Musy and Ronan Perrussel

Propose post processing methods for the edge finite element (FE) method on a tetrahedral mesh. They make it possible to deduce vector values on the vertices from scalar…

Abstract

Purpose

Propose post processing methods for the edge finite element (FE) method on a tetrahedral mesh. They make it possible to deduce vector values on the vertices from scalar values defined on the edges of the tetrahedra.

Design/methodology/approach

The new proposed techniques are based on a least squares formulation leading to a sparse matrix system to be solved. They are compared in terms of accuracy and CPU time on a FEs formulation for open boundary – frequency domain problems.

Findings

A significant improvement of vector values accuracy on the vertices of the tetrahedra is obtained compared to a classical approach with a very small additional computation time.

Originality/value

This work presents techniques: to obtain the values at the initial nodes of the mesh and not inside the tetrahedra; and to take into account the discontinuity to the interface between two media of different electromagnetic properties.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 24 no. 4
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 16 November 2010

Riccardo Scorretti, Ronan Perrussel, Laurent Morel, Noël Burais and Laurent Nicolas

The classical ϕa formulations for numerical dosimetry of currents induced by extremely low frequency magnetic fields requires that the source field is provided through a…

Abstract

Purpose

The classical ϕa formulations for numerical dosimetry of currents induced by extremely low frequency magnetic fields requires that the source field is provided through a vector potential. The purpose of this paper is to present a new formulation tb which directly takes the flux density as source term.

Design/methodology/approach

This formulation is implemented through finite element and validated by comparison with analytical solutions. The results obtained by both formulations are compared in the case of an anatomical computational phantom exposed to a vertical uniform field.

Findings

A good agreement between the tb formulation and both numerical and analytical computations was found.

Originality/value

This new formulation seems to be more accurate than the ϕa formulation, and is more suited for situations where the magnetic field is known from experimental measurements, as there is no need for a magnetic vector potential.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 29 no. 6
Type: Research Article
ISSN: 0332-1649

Keywords

1 – 10 of 13