Comparison of different boundary integral formulations when coupled with finite elements in three dimensions

Ren, Zhuoxiang; Bouillault, Frédéric; Razek, A.; Verite, J.C.

doi:10.1049/ip-a-1.1988.0078

Cited by 15 publications

(20 citation statements)

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“…Concern about this problem has already been expressed [5,19,. Excessive such concern may be uncalled for, as theoretical results [28] as well as numerical experiments [29] show that this loss of symmetry may not be that critical. However, symmetry is still highly desirable.…”

Section: Introductionmentioning

confidence: 96%

“…But it is not so; the part of the matrix coming from the boundary stiffness is not symmetric, if one follows a straightforward approach to its discretization. Concern about this problem has already been expressed [5,19,25-271. Excessive such concern may be uncalled for, as theoretical results [28] as well as numerical experiments [29] show that this loss of symmetry may not be that critical. However, symmetry is still highly desirable.…”

Section: Introductionmentioning

confidence: 99%

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Mixed methods and the marriage between “mixed” finite elements and boundary elements

Bossavit

1991

Numerical Methods Partial

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When fields that describe a physical situation extend over the whole space, but with complex behavior (nonlinearity, coupling, etc.) only in a bounded region and simple behavior in the rest of space, it may be worthwhile to treat the inner field by a finite elements procedure and the outer field by boundary elements. We address this "marriage" problem in the case of mixed elements. The model problem adopted for this discussion is mugnetostutics. A new approach to the question of mixed elements is used, which emphasizes their parenthood with a classical concept of differential geometry, Whifney forms.

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Section: Introductionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

Mixed methods and the marriage between “mixed” finite elements and boundary elements

Bossavit

1991

Numerical Methods Partial

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“…Hybrid methods which solve the Poisson equation for the interior magnetostatic domains and the boundary integral form of the potential equation for the exterior magnetostatic domain have also been developed [11,12]. These hybrid methods can accurately take into account the unbounded regions with the boundary integral formulation and at the same time can treat nonlinearities such as saturation, non-isotropism or eddy currents in the magnetic materials [13]. Besides, only the interior domains and their boundaries need to be discretized in this case.…”

Section: Introductionmentioning

confidence: 99%

A hybrid full-Lagrangian technique for the static and dynamic analysis of magnetostatic MEMS

De¹,

Aluru²

2006

J. Micromech. Microeng.

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Magnetostatic microelectromechanical systems (MEMS) are based on the electromagnetic interactions between magnetic microstructures and active (coils) or passive (permanent magnets) magnetic field sources. They offer distinct advantages at the micrometer scale in strength, polarity and distance of actuation, when compared to other methods of actuation in MEMS. For proper understanding and detailed exploration of magnetostatic MEMS, it is important to have a reliable and efficient physical level simulation tool. In this paper, we propose an efficient technique, namely the hybrid full-Lagrangian technique for the static and dynamic analysis of magnetostatic MEMS. In this technique, the magnetostatic analysis needed to compute the magnetostatic force acting on the microstructure is performed using a hybrid BIE/Poisson approach. The Poisson equation is solved for the interior magnetostatic domains and the boundary integral equation (BIE) formulation of the potential equation is solved for the exterior magnetostatic domain and the different domains are coupled through interface conditions. A Lagrangian description of all the physical domains (magnetostatic, mechanical and fluidic) is used to eliminate geometry updates and rediscretization. The Lagrangian formulation along with the hybrid approach makes the proposed technique much more efficient than conventional tools for the analysis of magnetostatic MEMS. The new technique is used to simulate several magnetostatic MEMS switches and relays and validated by comparing numerical simulation results with experimental data. Dynamic analysis of a magnetostatic MEMS switch is performed using the new technique.

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“…Dans une telle situation il semble naturel d'associer aux éléments finis une autre technique de calcul afin d'effectuer une modélisation fidèle d'un dispositif avec un coût raisonnable. C'est un choix souvent judicieux dans le cas bidimensionnel [3][4][5][6]11] mais qui devient alors crucial en trois dimensions [1,7]. Nous effectuons dans ce qui suit deux types de couplage dans le cadre d'une géométrie axisymétri-Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/rphysap:0198900240110104900 que : 1) une combinaison éléments finis/éléments de frontière ; 2) une combinaison éléments finis/développement analytique.…”

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Comparaison de techniques mixtes pour le calcul de courants de Foucault en géométrie axisymétrique

Pichon

Ayoub

Razek

1989

Rev. Phys. Appl. (Paris)

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Nous présentons et comparons dans cet article deux types de méthodes mixtes pour le calcul des courants de Foucault lors de la modélisation de systèmes électromagnétiques présentant une symétrie de révolution. Dans ces deux techniques, les éléments finis sont réservés aux parties massives du dispositif tandis que l'espace environnant est considéré ou bien par la méthode des éléments de frontière ou bien par le développement d'une solution analytique. Après avoir exposé les formulations employées et explicité les couplages réalisés, nous appliquons ces méthodes au calcul des courants de Foucault et comparons nos résultats numériques à ceux de l'expérience

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Comparison of different boundary integral formulations when coupled with finite elements in three dimensions

Cited by 15 publications

References 1 publication

Mixed methods and the marriage between “mixed” finite elements and boundary elements

Mixed methods and the marriage between “mixed” finite elements and boundary elements

A hybrid full-Lagrangian technique for the static and dynamic analysis of magnetostatic MEMS

Comparaison de techniques mixtes pour le calcul de courants de Foucault en géométrie axisymétrique

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