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Article
Publication date: 3 June 2022

Peter Gangl, Stefan Köthe, Christiane Mellak, Alessio Cesarano and Annette Mütze

This paper aims to deal with the design optimization of a synchronous reluctance machine to be used in an X-ray tube, where the goal is to maximize the torque while keeping low…

644

Abstract

Purpose

This paper aims to deal with the design optimization of a synchronous reluctance machine to be used in an X-ray tube, where the goal is to maximize the torque while keeping low the amount of material used, by means of gradient-based free-form shape optimization.

Design/methodology/approach

The presented approach is based on the mathematical concept of shape derivatives and allows to obtain new motor designs without the need to introduce a geometric parametrization. This paper presents an extension of a standard gradient-based free-form shape optimization algorithm to the case of multiple objective functions by determining updates, which represent a descent of all involved criteria. Moreover, this paper illustrates a way to obtain an approximate Pareto front.

Findings

The presented method allows to obtain optimal designs of arbitrary, non-parametric shape with very low computational cost. This paper validates the results by comparing them to a parametric geometry optimization in JMAG by means of a stochastic optimization algorithm. While the obtained designs are of similar shape, the computational time used by the gradient-based algorithm is in the order of minutes, compared to several hours taken by the stochastic optimization algorithm.

Originality/value

This paper applies the presented gradient-based multi-objective optimization algorithm in the context of free-form shape optimization using the mathematical concept of shape derivatives. The authors obtain a set of Pareto-optimal designs, each of which is a shape that is not represented by a fixed set of parameters. To the best of the authors’ knowledge, this approach to multi-objective free-form shape optimization is novel in the context of electric machines.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering , vol. 41 no. 5
Type: Research Article
ISSN: 0332-1649

Keywords

Available. Open Access. Open Access
Article
Publication date: 18 January 2022

Valentin Hanser, Markus Schöbinger and Karl Hollaus

This work introduces an efficient and accurate technique to solve the eddy current problem in laminated iron cores considering vector hysteresis.

652

Abstract

Purpose

This work introduces an efficient and accurate technique to solve the eddy current problem in laminated iron cores considering vector hysteresis.

Design/methodology/approach

The mixed multiscale finite element method based on the based on the T,Φ-Φ formulation, with the current vector potential T and the magnetic scalar potential Φ allows the laminated core to be modelled as a single homogeneous block. This means that the individual sheets do not have to be resolved, which saves a lot of computing time and reduces the demands on the computer system enormously.

Findings

As a representative numerical example, a single-phase transformer with 4, 20 and 184 sheets is simulated with great success. The eddy current losses of the simulation using the standard finite element method and the simulation using the mixed multiscale finite element method agree very well and the required simulation time is tremendously reduced.

Originality/value

The vector Preisach model is used to account for vector hysteresis and is integrated into the mixed multiscale finite element method for the first time.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering , vol. 41 no. 3
Type: Research Article
ISSN: 0332-1649

Keywords

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Article
Publication date: 4 September 2017

Markus Schöbinger, Karl Hollaus and Joachim Schöberl

This paper aims to improve the efficiency of a numerical method to treat the eddy current problem on a laminated material, where using a mesh that resolves each individual…

106

Abstract

Purpose

This paper aims to improve the efficiency of a numerical method to treat the eddy current problem on a laminated material, where using a mesh that resolves each individual laminate would be too computationally expensive.

Design/methodology/approach

The domain is modeled using a coarse mesh that treats the laminated material as a bulk with averaged properties. The fine-structured behavior is recovered by introducing micro-shape functions in the ansatz space. One such method is analyzed to find further model restrictions.

Findings

By using a special reformulation, it is possible to eliminate the additional degrees of freedom introduced by the multiscale ansatz at the cost of an additional modeling error that decreases with the laminate thickness.

Originality/value

The paper gives a computationally more efficient approximate variant to a known multiscale method.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 36 no. 5
Type: Research Article
ISSN: 0332-1649

Keywords

Available. Open Access. Open Access
Article
Publication date: 16 March 2022

Michael Leumüller, Karl Hollaus and Joachim Schöberl

This paper aims to consider a multiscale electromagnetic wave problem for a housing with a ventilation grill. Using the standard finite element method to discretise the apertures…

426

Abstract

Purpose

This paper aims to consider a multiscale electromagnetic wave problem for a housing with a ventilation grill. Using the standard finite element method to discretise the apertures leads to an unduly large number of unknowns. An efficient approach to simulate the multiple scales is introduced. The aim is to significantly reduce the computational costs.

Design/methodology/approach

A domain decomposition technique with upscaling is applied to cope with the different scales. The idea is to split the domain of computation into an exterior domain and multiple non-overlapping sub-domains. Each sub-domain represents a single aperture and uses the same finite element mesh. The identical mesh of the sub-domains is efficiently exploited by the hybrid discontinuous Galerkin method and a Schur complement which facilitates the transition from fine meshes in the sub-domains to a coarse mesh in the exterior domain. A coarse skeleton grid is used on the interface between the exterior domain and the individual sub-domains to avoid large dense blocks in the finite element discretisation matrix.

Findings

Applying a Schur complement to the identical discretisation of the sub-domains leads to a method that scales very well with respect to the number of apertures.

Originality/value

The error compared to the standard finite element method is negligible and the computational costs are significantly reduced.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering , vol. 41 no. 3
Type: Research Article
ISSN: 0332-1649

Keywords

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Article
Publication date: 1 June 2005

Joachim Schöberl and Sabine Zaglmayr

The goal of the presented work is the efficient computation of Maxwell boundary and eigenvalue problems using high order H(curl) finite elements.

1274

Abstract

Purpose

The goal of the presented work is the efficient computation of Maxwell boundary and eigenvalue problems using high order H(curl) finite elements.

Design/methodology/approach

Discusses a systematic strategy for the realization of arbitrary order hierarchic H(curl)‐conforming finite elements for triangular and tetrahedral element geometries. The shape functions are classified as lowest order Nédélec, higher‐order edge‐based, face‐based (only in 3D) and element‐based ones.

Findings

Our new shape functions provide not only the global complete sequence property but also local complete sequence properties for each edge‐, face‐, and element‐block. This local property allows an arbitrary variable choice of the polynomial degree for each edge, face, and element. A second advantage of this construction is that simple block‐diagonal preconditioning gets efficient. Our high order shape functions contain gradient shape functions explicitly. In the case of a magnetostatic boundary value problem, the gradient basis functions can be skipped, which reduces the problem size, and improves the condition number.

Originality/value

Successfully applies the new high order elements for a 3D magnetostatic boundary value problem, and a Maxwell eigenvalue problem showing severe edge and corner singularities.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 24 no. 2
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 31 August 2023

James Elgy, Paul D. Ledger, John L. Davidson, Toykan Özdeğer and Anthony J. Peyton

The ability to characterise highly conducting objects, that may also be highly magnetic, by the complex symmetric rank–2 magnetic polarizability tensor (MPT) is important for…

73

Abstract

Purpose

The ability to characterise highly conducting objects, that may also be highly magnetic, by the complex symmetric rank–2 magnetic polarizability tensor (MPT) is important for metal detection applications including discriminating between threat and non-threat objects in security screening, identifying unexploded anti-personnel landmines and ordnance and identifying metals of high commercial value in scrap sorting. Many everyday non-threat items have both a large electrical conductivity and a magnetic behaviour, which, for sufficiently weak fields and the frequencies of interest, can be modelled by a high relative magnetic permeability. This paper aims to discuss the aforementioned idea.

Design/methodology/approach

The numerical simulation of the MPT for everyday non-threat highly conducting magnetic objects over a broad range of frequencies is challenging due to the resulting thin skin depths. The authors address this by employing higher order edge finite element discretisations based on unstructured meshes of tetrahedral elements with the addition of thin layers of prismatic elements. Furthermore, computer aided design (CAD) geometrical models of the non-threat and threat object are often not available and, instead, the authors extract the geometrical features of an object from an imaging procedure.

Findings

The authors obtain accurate numerical MPT characterisations that are in close agreement with experimental measurements for realistic physical objects. The assessment of uncertainty shows the impact of geometrical and material parameter uncertainties on the computational results.

Originality/value

The authors present novel computations and measurements of MPT characterisations of realistic objects made of magnetic materials. A novel assessment of uncertainty in the numerical predictions of MPT characterisations for uncertain geometry and material parameters is included.

Details

Engineering Computations, vol. 40 no. 7/8
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 24 October 2024

James Elgy and Paul David Ledger

Magnetic polarizability tensors (MPTs) provide an economical characterisation of conducting magnetic metallic objects and their spectral signature can aid in the solution of metal…

11

Abstract

Purpose

Magnetic polarizability tensors (MPTs) provide an economical characterisation of conducting magnetic metallic objects and their spectral signature can aid in the solution of metal detection inverse problems, such as scrap metal sorting, searching for unexploded ordnance in areas of former conflict and security screening at event venues and transport hubs. In this work, the authors aim to discuss methods for efficiently building large dictionaries for classification approaches.

Design/methodology/approach

Previous work has established explicit formulae for MPT coefficients, underpinned by a rigorous mathematical theory. To assist with the efficient computation of MPTs at differing parameters and objects of interest, this work applies new observations about the way the MPT coefficients can be computed. Furthermore, the authors discuss discretisation strategies for hp-finite elements on meshes of unstructured tetrahedra combined with prismatic boundary layer elements for resolving thin skin depths and using an adaptive proper orthogonal decomposition (POD) reduced-order modelling methodology to accelerate computations for varying parameters.

Findings

The success of the proposed methodologies is demonstrated using a series of examples. A significant reduction in computational effort is observed across all examples. The authors identify and recommend a simple discretisation strategy and improved accuracy is obtained using adaptive POD.

Originality/value

The authors present novel computations, timings and error certificates of MPT characterisations of realistic objects made of magnetic materials. A novel postprocessing implementation is introduced and an adaptive POD algorithm is demonstrated.

Details

Engineering Computations, vol. 41 no. 10
Type: Research Article
ISSN: 0264-4401

Keywords

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Article
Publication date: 1 December 2004

M. Clemens, S. Feigh, M. Wilke and T. Weiland

The simulation of magnetic fields with geometric discretization schemes using magnetic vector potentials involves the solution of very large discrete consistently singular…

380

Abstract

The simulation of magnetic fields with geometric discretization schemes using magnetic vector potentials involves the solution of very large discrete consistently singular curl‐curl systems of equations. Geometric and algebraic multigrid schemes for their solution require intergrid transfer operators of restriction and prolongation that achieve the discrete conservation of integral quantities serving as state‐variables of geometric discretization methods. For non‐conservative restriction operations, a consistency error correction operator related to an algebraic filtering is proposed. Numerical results show the effects of the consistency correction for a non‐nested geometric multigrid method.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 23 no. 4
Type: Research Article
ISSN: 0332-1649

Keywords

Available. Open Access. Open Access
Article
Publication date: 8 August 2019

Karl Hollaus

The simulation of eddy currents in laminated iron cores by the finite element method (FEM) is of great interest in the design of electrical devices. Modeling each laminate by…

1148

Abstract

Purpose

The simulation of eddy currents in laminated iron cores by the finite element method (FEM) is of great interest in the design of electrical devices. Modeling each laminate by finite elements leads to extremely large nonlinear systems of equations impossible to solve with present computer resources reasonably. The purpose of this study is to show that the multiscale finite element method (MSFEM) overcomes this difficulty.

Design/methodology/approach

A new MSFEM approach for eddy currents of laminated nonlinear iron cores in three dimensions based on the magnetic vector potential is presented. How to construct the MSFEM approach in principal is shown. The MSFEM with the Biot–Savart field in the frequency domain, a higher-order approach, the time stepping method and with the harmonic balance method are introduced and studied.

Findings

Various simulations demonstrate the feasibility, efficiency and versatility of the new MSFEM.

Originality/value

The novel MSFEM solves true three-dimensional eddy current problems in laminated iron cores taking into account of the edge effect.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering , vol. 38 no. 5
Type: Research Article
ISSN: 0332-1649

Keywords

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Article
Publication date: 9 September 2013

Andreas Hauck, Michael Ertl, Joachim Schöberl and Manfred Kaltenbacher

The purpose of this paper is to propose a solution strategy for both accurate and efficient simulation of nonlinear magnetostatic problems in thin structures using higher order…

168

Abstract

Purpose

The purpose of this paper is to propose a solution strategy for both accurate and efficient simulation of nonlinear magnetostatic problems in thin structures using higher order finite element methods. Special interest is put in the investigation of the step-lap joints of transformer cores, with a focus on the spatial resolution of the field quantities.

Design/methodology/approach

The usage of hierarchical finite elements of higher order makes it possible to adapt the local accuracy in different spatial directions in thin steel sheets. Due to explicit representation of gradients in the basis functions, a simple Schwarz-type block preconditioner with a conjugate gradient solver can efficiently solve the arising algebraic system. By adapting the block size automatically according to the aspect ratio, deterioration of convergence in case of thin elements can be prevented. The resulting Newton scheme is accelerated utilizing the hierarchical splitting in a two-level scheme, where an initial guess is computed on a coarse sub-space.

Findings

Compared to an isotropic choice of polynomial order for the basis functions, significant runtime and memory can be saved in the simulation of thin structures without losing accuracy. The iterative solution scheme proves to be robust with respect to the polynomial order, even for aspect ratios of 1:1000 and anisotropies in two directions. An additional saving in runtime and Newton iterations can be achieved by solving the nonlinear problem initially on the lowest order basis functions only and projecting the solution to the complete space as starting value, analogous to a full multigrid scheme.

Originality/value

Within the presented solution strategy, especially the anisotropic block preconditioner and the accelerated Newton scheme based on the two-level splitting constitute a novel contribution. They provide building blocks, which can be utilized for other types of magnetic field problems like transient nonlinear problems or hysteresis modeling as well.

Details

COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, vol. 32 no. 5
Type: Research Article
ISSN: 0332-1649

Keywords

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