Some 2-D Multiscale Finite-Element Formulations for the Eddy Current Problem in Iron Laminates

Hollaus, Karl; Schöberl, Joachim

doi:10.1109/tmag.2017.2777395

Cited by 36 publications

(32 citation statements)

References 19 publications

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“…Thanks to space splitting, the computational savings are enormous and the accuracy is excellent. The 2-D/1-D MSFEM can obviously be extended to solve nonlinear problems, to this end, compared with [2] and [7].…”

Section: Discussionmentioning

confidence: 99%

“…are carried out analytically. For averaging of the coefficients, which are involved in (7), see [2].…”

Section: ) Weak Form Of the 2-d/1-d Msfemmentioning

confidence: 99%

“…Brute force 3-D standard FEM (SFEM) models are still too expensive [1] for routine simulations. To avoid them, the problem is solved using the ideas of the MSFEM [2] and the 2-D/1-D methods [3], [4], which are very efficient for this specific purpose. A significant shortcoming of these methods based on the magnetic vector potential (MVP) A is the inability to consider air gaps and the EE [5], [6].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Air Gap and Edge Effect in the 2-D/1-D Method With the Magnetic Vector Potential ${A}$ Using MSFEM

Hollaus

Schobinger

2020

IEEE Trans. Magn.

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Eddy currents (ECs) are simulated in a single laminate, representing the whole core of an electrical machine. Despite this drastic reduction in the complexity of the problem, a 3-D finite-element model turns out to be still too expensive for simulations. To overcome this difficulty, 2-D/1-D methods are used. This article presents a solution to consider both air gap and edge effect (EE) based on the multiscale finite-element method (MSFEM) using the magnetic vector potential (MVP) A. Linear material properties are assumed; therefore, this article is carried out in the frequency domain. The new 2-D/1-D MSFEM is discussed, and various simulation results are presented. Index Terms-2-D/1-D method, eddy-current (EC) problems, edge effect (EE), iron core, lamination, magnetic vector potential (MVP) A, multiscale finite-element method (MSFEM).

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Section: Discussionmentioning

confidence: 99%

“…are carried out analytically. For averaging of the coefficients, which are involved in (7), see [2].…”

Section: ) Weak Form Of the 2-d/1-d Msfemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Air Gap and Edge Effect in the 2-D/1-D Method With the Magnetic Vector Potential ${A}$ Using MSFEM

Hollaus

Schobinger

2020

IEEE Trans. Magn.

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“…Although the multiscale finite element method (MSFEM) can be exploited to simulate eddy currents in laminated iron more efficiently the complexity of the problems are still too large to solve them conveniently. The computational costs are a multiple of the costs of anisotropic models in brute force methods according to the components used in the multiscale formulation, compare with [2].…”

Section: Introductionmentioning

confidence: 99%

MOR for the MSFEM of the Eddy Current Problem in Linear Laminated Media

Hollaus¹,

Schöberl²,

Schobinger³

2020

SNE

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The multiscale finite element method has proven to be a powerful method in the simulation of eddy currents in laminated cores. However, the resulting equation systems of the problems relevant in electrical engineering are still too large to be solved conveniently. The use of model order reduction methods to overcome this shortcoming is obvious. The feasibility to exploit the specific approach of the multiscale finite element method in terms of a structural model order reduction method has been studied in this work. A small numerical example shows satisfactory results.

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“…This contribution presents a novel approach to this idea utilizing a multiscale finite element method (MS-FEM, [3]). The main principle is to express the behavior of the solution along the z axis via a polynomial ansatz which directly couples into the two dimen-sional problem, thereby eliminating the need to repeatedly solve two dependent problems.…”

Section: Introductionmentioning

confidence: 99%

MSFEM for the Linear 2D1D-Problem of Eddy Currents in Thin Iron Sheets

Schobinger¹,

Schöberl²,

Hollaus³

2020

SNE

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A 2D/1D method to simulate the eddy currents in a single thin iron sheet is presented. It utilizes ideas of the multiscale method by decomposing the solution with respect to its dependence on the coordinate directions. Instead of the three dimensional domain, the eddy current problem is solved only on the two dimensional cross section of the sheet, with the behavior of the solution along the thickness being simulated via an expansion into polynomial shape functions. This greatly reduces the number and the coupling density of the degrees of freedom. A numerical example shows a satisfying accuracy for both the A and the T formulation.

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Some 2-D Multiscale Finite-Element Formulations for the Eddy Current Problem in Iron Laminates

Cited by 36 publications

References 19 publications

Air Gap and Edge Effect in the 2-D/1-D Method With the Magnetic Vector Potential ${A}$ Using MSFEM

Air Gap and Edge Effect in the 2-D/1-D Method With the Magnetic Vector Potential ${A}$ Using MSFEM

MOR for the MSFEM of the Eddy Current Problem in Linear Laminated Media

MSFEM for the Linear 2D1D-Problem of Eddy Currents in Thin Iron Sheets

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