A general purpose tool for restoring inter-element continuity

Maréchal, Yves; Meunier, G.; Coulomb, J.L.; Magnin, H.

doi:10.1109/20.124037

Cited by 35 publications

(14 citation statements)

References 2 publications

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“…We will focus our attention on the description of the magnetic field distribution in a domain composed of two solid parts separated by an interface. We aim at describing the three-dimensional mortar edge element method and its main implementation aspects.The general problem of dealing with nonmatching grids in magneto-mechanical applications has been faced for a long time (see [15,16,17,20,24,29,31,32] for the main arguments that have been proposed since 1980 and [25] for further references on the subject). None of the existing methods is simultaneously characterized by involving positive definite matrices, avoiding remeshing and difficult intersection…”

mentioning

confidence: 99%

The Mortar Edge Element Method in Three Dimensions: Application to Magnetostatics

Bouillault¹,

Buffa²,

Maday³

et al. 2003

SIAM J. Sci. Comput.

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The subject presented in this paper concerns the approximation of a magnetostatic problem, where the primary unknown is the magnetic vector potential in a three-dimensional system composed of two solid parts separated by an interface. The approximation of the problem here is based on the mortar element method combined with edge elements on tetrahedral meshes that do not match at the interface. In this paper we describe the proposed method and its implementation aspects together with some numerical results that illustrate how the method works.Introduction. The flexibility and performance of a numerical method for the simulation of electromagnetic field distributions in electrotechnical devices relies, in several cases, on the possibility of working with nonmatching grids at the interface between adjacent subdomains. One example is given by the treatment of moving structures. We can choose to work in Eulerian coordinates, adding a convective term in the equations, or in Lagrangian coordinates, dealing with nonconforming discretizations. The second choice can be computationally more convenient whenever it is possible to avoid remeshing or interpolation procedures. Another example is the optimization of the structure shape. We can remesh either the whole domain or only a region containing the shape to be optimized: in the second case it can be useful to work with nonmatching grids to simplify the local remeshing task and successive solution of the problem. A third example consists of the possibility of coupling variational methods of different orders and types.In this paper we deal with the edge element approximation on nonmatching grids of a given magnetostatic problem in three dimensions. We will focus our attention on the description of the magnetic field distribution in a domain composed of two solid parts separated by an interface. We aim at describing the three-dimensional mortar edge element method and its main implementation aspects.The general problem of dealing with nonmatching grids in magneto-mechanical applications has been faced for a long time (see [15,16,17,20,24,29,31,32] for the main arguments that have been proposed since 1980 and [25] for further references on the subject). None of the existing methods is simultaneously characterized by involving positive definite matrices, avoiding remeshing and difficult intersection

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mentioning

confidence: 99%

The Mortar Edge Element Method in Three Dimensions: Application to Magnetostatics

Bouillault¹,

Buffa²,

Maday³

et al. 2003

SIAM J. Sci. Comput.

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“…The matching constraint at the interface between the rotor and stator is weakly imposed on the discrete solution by means of Lagrange multipliers. Note that our approach differs radically from that proposed in [21,26] even if the terminology is quite similar. Indeed, here, the Lagrange multiplier is never interpreted in terms of the primal unknown.…”

Section: Introductionmentioning

confidence: 94%

“…Then there is no interest in dealing with decompositions of very different sizes. Nevertheless, if one wants to use meshes that do not satisfy (21), then the results that follow still hold through a much more technical procedure.…”

Section: The Spatial Discretizationmentioning

confidence: 99%

A Slideing Mesh-Mortar Method for a two Dimensional Currents Model of Electric Engines

Buffa

2001

ESAIM: M2AN

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Abstract. The paper deals with the application of a non-conforming domain decomposition method to the problem of the computation of induced currents in electric engines with moving conductors. The eddy currents model is considered as a quasi-static approximation of Maxwell equations and we study its two-dimensional formulation with either the modified magnetic vector potential or the magnetic field as primary variable. Two discretizations are proposed, the first one based on curved finite elements and the second one based on iso-parametric finite elements in both the static and moving parts. The coupling is obtained by means of the mortar element method (see [7]) and the approximation on the whole domain turns out to be non-conforming. In both cases optimal error estimates are provided. Numerical tests are then proposed in the case of standard first order finite elements to test the reliability and precision of the method. An application of the method to study the influence of the free part movement on the currents distribution is also provided.Mathematics Subject Classification. 35Q60, 65N15, 65M55, 68U20, 78A30.

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“…In the paper, the problems of the 3-D analysis for the 0885-8969/96/$05.00 Q 1996 IEEE induction motor were overcome by using the new engineering work station with the large memory and a solution to mesh division using the sliding elements [9] [IO]. We study the effects of rotor skew, the rotor end-rings and distributions of electro-magnetic field toward the axial direction.…”

Section: Introductionmentioning

confidence: 99%

3-D electro-magnetic analyses of a cage induction motor with rotor skew

Kometani

Sakabe

Nakanishi

1996

IEEE Trans. On energy Conversion

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A b s t r a c t -The paper studied the performance characteristics of a 3-phase cage induction motor using 3-D finite element technique. Especially, the effects of rotor skew and the rotor end-rings and the distribution of the electro-magnetic field toward the axial direction, which have not been able to be analyzed accurately by 2-D analysis, were investigated. Since the 3-D analysis enabled 11s to analyze the continuity of the air gap flux density a t t h e core ends a n d t o take into consideration the rotor end-ring impedance, the motor parameters were calculated with high accuracy, compared with 2-D analysis. Firstly, we made the relation of the rotor end-ring current with the rotor b a r current clear, by analyzing the harmonics of the rotor bar current and the rotor end-ring current in the cases of motors without rotor skew and with rotor skew. Secondly, the torque and the rotor axial force were calculated from the distribution of the electro-magnetic field obtained by the 3-D analysis in the case of rotor skew. We also calculated the axial forces on the both end-rings in the case of rotor skew. The results obtained i n t h e p a p e r showed t h e importance of 3-D analysis for the design of the induction motors.

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A general purpose tool for restoring inter-element continuity

Cited by 35 publications

References 2 publications

The Mortar Edge Element Method in Three Dimensions: Application to Magnetostatics

The Mortar Edge Element Method in Three Dimensions: Application to Magnetostatics

A Slideing Mesh-Mortar Method for a two Dimensional Currents Model of Electric Engines

3-D electro-magnetic analyses of a cage induction motor with rotor skew

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