Calculation of eddy currents in moving structures using a finite element method on  non‐matching grids

Rapetti, Francesca; Santandréa, Laurent; Bouillault, Frédéric; Razek, A.

doi:10.1108/03321640010302762

Cited by 10 publications

(18 citation statements)

References 11 publications

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“…This method has already been proved to be efficient in treating two-dimensional problems combined with both nodal elements (see [10,28]) and edge ones (see [2,26]). The method we shall describe and implement here develops what is presented in [3], where the proper space of Lagrange multipliers is defined and optimality of the approximation is proven, and in [9], where a different version of the method is proposed.…”

Section: Domain Decomposition Approachmentioning

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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Section: Domain Decomposition Approachmentioning

confidence: 99%

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

Bouillault¹,

Buffa²,

Maday³

et al. 2003

SIAM J. Sci. Comput.

Self Cite

View full text Add to dashboard Cite

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“…The fact of using such finite elements changes the definition of the approximation space (24)(25). The constraint condition (25) no longer makes sense since, in general, neither v 1,h nor v 2,h in (25) are defined over Γ.…”

Section: Effects Of Using Iso-parametric Finite Elementsmentioning

confidence: 99%

“…where the bilinear form a is defined in (12), Ω = Ω 1 (0) ∪ Ω 2 as in Section 1 and where the discretization relies on a space U 0 h (see (24)(25)) that now takes into account the effect of using iso-parametric finite element approximations in both Ω 1 and Ω 2 .…”

Section: Effects Of Using Iso-parametric Finite Elementsmentioning

confidence: 99%

“…Further results on the influence of the rotor movement on the currents distribution as well as on the power losses in dependence of the rotor angular speed are presented in [24].…”

Section: A Realistic Simulationmentioning

confidence: 99%

“…In Section 5 we detail the implementation aspects of the proposed method in case of standard linear finite elements resulting in the solution of a symmetric and positive definite system. Finally, Section 6 is dedicated to some numerical results both of validation and application of the method to an academic concrete problem; we refer to [24] for more physical examples.…”

Section: Introductionmentioning

confidence: 99%

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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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The mortar edge element method on non‐matching grids for eddy current calculations in moving structures

Rapetti

2001

Int J Numerical Modelling

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SUMMARYThe subject presented in this paper concerns the approximation of the eddy current problem in nonstationary geometries with sliding interfaces. The physical system is supposed to be composed of two solid parts: a "xed one (stator) and a moving one (rotor) which slides in contact with the stator. We consider a two-dimensional mathematical model based on the transverse electric formulation of the eddy currents problem in the time domain and the primary unknown is the electric ,eld vector. The "rst-order approximation of the problem that we propose here is based on the mortar element method combined with the edge element discretization in space and an implicit Euler scheme in time. Numerical results illustrate the accuracy of the method and allow to understand the in#uence of the rotor movement on the currents distribution.

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Calculation of eddy currents in moving structures using a finite element method on non‐matching grids

Cited by 10 publications

References 11 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

The mortar edge element method on non‐matching grids for eddy current calculations in moving structures

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