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 a very…
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.
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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 decomposition…
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.
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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.
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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.
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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.
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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.
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.
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Borja López-Alonso, Pablo Briz, Hector Sarnago, José M. Burdio and Oscar Lucia
This paper aims to study the feasibility of proposed method to focus the electroporation ablation by mean of multi-output multi-electrode system.
Abstract
Purpose
This paper aims to study the feasibility of proposed method to focus the electroporation ablation by mean of multi-output multi-electrode system.
Design/methodology/approach
The proposed method has been developed based on a previously designed electroporation system, which has the capabilities to modify the electric field distribution in real time, and to estimate the impedance distribution. Taking into consideration the features of the system and biological tissues, the problem has been addressed in three phases: modeling, control system design and simulation testing. In the first phase, a finite element analysis model has been proposed to reproduce the electric field distribution within the hepatic tissue, based on the characteristics of the electroporation system. Then, a control strategy has been proposed with the goal of ensuring complete ablation while minimizing the affected volume of healthy tissue. Finally, to check the feasibility of the proposal, several representative cases have been simulated, and the results have been compared with those obtained by a traditional system.
Findings
The proposed method achieves the proposed goal, as part of a complex electroporation system designed to improve the targeting, effectiveness and control of electroporation treatments and serve to demonstrate the feasibility of developing new electroporation systems capable of adapting to changes in the preplanning of the treatment in real-time.
Originality/value
The work presents a thorough study of control method to multi-output multi-electrode electroporation system by mean of a rigorous numerical simulation.
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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 the…
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.
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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.
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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 values…
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.