Eddy-current calculations in three-dimensional moving structures

Rapetti, Francesca; Maday, Yvon; Bouillault, Frédéric; Razek, A.

doi:10.1109/20.996160

Cited by 19 publications

(14 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Based on the mortar edge element method, this approximation has allowed us to work in a very elegant way with domain discretizations that do not match at the interface. The interest of the proposed method is focused on the following issues: (1) the imposition at a discrete level of the transmission condition for the tangential component of the magnetic vector potential field across the interface is done without any constraint between the spatial discretization steps h 1 and h 2 ; (2) the use of second order edge elements on the interface is mandatory to have an optimal approximation of the problem solution; (3) nonmatching grids can be easily intersected by means of a projection procedure based on the introduction of an independent third surface mesh; (4) the system of the discretized problem can be efficiently inverted by a preconditioned conjugate gradient procedure (see [27]). Numerical results confirm the theoretical ones and demonstrate the ability of the proposed method.…”

Section: Discussionmentioning

confidence: 99%

“…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. Moreover, the present analysis is an unavoidable preliminary step to [27] and [11], where the magnetodynamic problem in three-dimensional moving structures is addressed.…”

Section: Domain Decomposition Approachmentioning

confidence: 99%

“…Numerical results are obtained by a conjugate gradient algorithm that brings the residual under 10 −6 . We refer to [27], where a block Jacobi preconditioned conjugate gradient algorithm has been used for a magnetodynamic problem with a sensible Downloaded 12/30/12 to 138. 26.31.3.…”

Section: Meshesmentioning

confidence: 99%

See 2 more Smart Citations

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

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

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Domain Decomposition Approachmentioning

confidence: 99%

See 1 more Smart Citation

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

show abstract

“…A different but symmetric approach relies on the introduction of a third discretization on the skeleton, totally independent of those on the mortar and non-mortar sides. A quadrature formula is then defined on the mesh triangles of this third mesh and projected on those of the mortar and non-mortar sides (see [81] for a concrete application of this approach in three dimensions). We refer to [80] for a detailed analysis of the discretization relying on the previous considerations.…”

Section: Construction Of a Basis Of The Constrained Spacesmentioning

confidence: 99%

Basics and some applications of the mortar element method

2005

View full text Add to dashboard Cite

Key words Mortar element method, spectral methods, finite elements.We describe the main characteristics of the mortar element method, together with the usual arguments for its numerical analysis in an abstract framework. We illustrate this presentation by focussing on mortar spectral element and mortar finite element methods. We give three examples of recent applications, concerning the treatment of non homogeneous media, eddy currents in moving conductors, and finite element mesh adaptivity.

show abstract

“…It can provide an efficient formulation for analysis of rotating machinery using a sliding mesh [3] but efficient linear solvers for practical mortar finite element analyses have not been studied sufficiently. This study examines two types of linear systems of equations with and without Lagrange multipliers.…”

Section: Introductionmentioning

confidence: 99%