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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

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Article
Publication date: 7 September 2015

Karl Hollaus and Joachim Schöberl

– The purpose of this paper is an accurate computation of eddy currents in laminated media with minimal computer resources.

231

Abstract

Purpose

The purpose of this paper is an accurate computation of eddy currents in laminated media with minimal computer resources.

Design/methodology/approach

Modeling each laminate of the laminated core of electrical devices requires prohibitively many finite elements (FEs). To overcome this restriction a higher order multi-scale FE method with the magnetic vector potential

A

has been developed to cope with 3D problems considering edge effects.

Findings

The multi-scale FE approach facilitates an accurate simulation of the eddy current losses with minimal computer resources. Numerical simulations demonstrate a remarkable accuracy and low computational costs. The effect of regularization on the results is shown.

Practical implications

The eddy current losses are of great interest in the design of electrical devices with laminated cores.

Originality/value

The multi-scale FE approach takes also into account of the edge effects in 3D.

Details

COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, vol. 34 no. 5
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: 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

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