Eddy Currents and Non-Conforming Sliding Interfaces for Motion in 3-D Finite Element Analysis of Electrical Machines

Böhmer, Stefan; Kruttgen, Christian; Riemer, Björn; Hameyer, Kay

doi:10.1109/tmag.2014.2359155

Cited by 4 publications

(5 citation statements)

References 13 publications

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“…Originally introduced for coupling of spectral and FE methods [3], the analysis of Mortar methods has been extended to 3-D problems, together with advances in efficiently solving these types of problems (see [4]). Toward 3-D electromagnetics, special care has to be taken to achieve appropriate Lagrange multipliers, as described in [5] and [6] as well as [7] for electrical machines.…”

Section: Introductionmentioning

confidence: 99%

Non-Conforming Nitsche Interfaces for Edge Elements in Curl–Curl-Type Problems

2020

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In this article, a methodology to incorporate non-conforming interfaces between several conforming mesh regions is presented for Maxwell's curl-curl problem. The derivation starts from a general interior penalty discontinuous Galerkin formulation of the curl-curl problem and eliminates all interior jumps in the conforming parts but retains them across non-conforming interfaces. Therefore, it is possible to think of this Nitsche approach for interfaces as a specialization of discontinuous Galerkin on meshes, which are conforming nearly everywhere. The applicability of this approach is demonstrated in two numerical examples, including parameter jumps at the interface. A convergence study is performed for h-refinement, including the investigation of the penalization-(Nitsche-) parameter.

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Section: Introductionmentioning

confidence: 99%

Non-Conforming Nitsche Interfaces for Edge Elements in Curl–Curl-Type Problems

2020

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“…Three kinds of non-conforming techniques have already been proposed: (1) the discontinuous Galerkin method [8], (2) the mortar FEM [9], and (3) the mesh interpolating method [10], and in this paper we use the third one.…”

Section: Proposed Meshing Refinement Methods Utilizing Nonconforminmentioning

confidence: 99%

“…(10) where C is the constitutional matrix derived from the relation between the master and slave edges [10]. The following system of equations needs to be solved:…”

Section: Proposed Meshing Refinement Methods Utilizing Nonconforminmentioning

confidence: 99%

A New Adaptive Mesh Refinement Method in FEA Based on Magnetic Field Conservation at Elements Interfaces and Non-Conforming Mesh Refinement Technique

et al. 2017

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Mesh quality strongly affects the solution accuracy in electromagnetic finite-element analysis. Hence, the realization of adequate mesh generation becomes a very important task. Several adaptive meshing methods for automatic adjustments of the mesh density in accordance with the shape and complexity of the analyzed problem have been proposed. However, the most of them are not enough robust, some are quite laborious and could not be universally used for adaptive meshing of complex analysis models. In this paper, a new adaptive mesh refinement method based on magnetic field conservation at the border between finite elements is proposed. The proposed error estimation method provides easy mesh refinements, and generates smaller element within regions with large curvature of the magnetic flux lines. The proposed adaptive mesh refinement method based on non-conforming edge finite elements, which could avoid generation of flat or ill-shaped elements, was applied to a simple magnetostatic permanent magnet model. To confirm the validity and accuracy, the obtained results were compared with those obtained by means of the Zienkiewicz-Zhu (ZZ) error estimator. The results show that the computational error using the proposed method was reduced down to 1% compared with that of the ZZ method, which yields error of 8.6%, for the same model

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“…Another concept consists of introducing additional degrees of freedom on the interface in the form of Lagrange multipliers, representing the flux of the primary unknown, which means that the strong continuity of the primary unknown is replaced by a weak one, also called Mortar methods. Towards 3D electromagnetics, special care has to be taken to achieve appropriate Lagrange multipliers, described, e.g., in [4] for magnetostatics as well as [5] and [6] for the eddy current case in electric machines. A promising approach, based on biorthogonality relations from [7], is presented in [8] and [9], where the Lagrange multiplier is eliminated by a discrete projection operator.…”

Section: Introductionmentioning

confidence: 99%