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Article
Publication date: 1 June 2001

M. Kaltenbacher, S. Reitzinger, M. Schinnerl, J. Schöberl and H. Landes

The focus of this paper is on the efficient numerical computation of 3D electromagnetic field problems by using the finite element (FE) and multigrid (MG) methods. The magnetic…

547

Abstract

The focus of this paper is on the efficient numerical computation of 3D electromagnetic field problems by using the finite element (FE) and multigrid (MG) methods. The magnetic vector potential is used as the field variable and the discretization is performed by Lagrange (nodal) as well as Ne´de´lec (edge) finite elements. The resulting system of equations is solved by applying a preconditioned conjugate gradient (PCG) method with an adapted algebraic multigrid (AMG) as well as an appropriate geometric MG preconditioner.

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COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 20 no. 2
Type: Research Article
ISSN: 0332-1649

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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.

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

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Available. Open Access. Open Access
Article
Publication date: 25 July 2019

Klaus Roppert, Florian Toth and Manfred Kaltenbacher

The purpose of this paper is to examine a solution strategy for coupled nonlinear magnetic-thermal problems and apply it to the heating process of a thin moving steel sheet…

1115

Abstract

Purpose

The purpose of this paper is to examine a solution strategy for coupled nonlinear magnetic-thermal problems and apply it to the heating process of a thin moving steel sheet. Performing efficient numerical simulations of induction heating processes becomes ever more important because of faster production development cycles, where the quasi steady-state solution of the problem plays a pivotal role.

Design/methodology/approach

To avoid time-consuming transient simulations, the eddy current problem is transformed into frequency domain and a harmonic balancing scheme is used to take into account the nonlinear BH-curve. The thermal problem is solved in steady-state domain, which is carried out by including a convective term to model the stationary heat transport due to the sheet velocity.

Findings

The presented solution strategy is compared to a classical nonlinear transient reference solution of the eddy current problem and shows good convergence, even for a small number of considered harmonics.

Originality/value

Numerical simulations of induction heating processes are necessary to fully understand certain phenomena, e.g. local overheating of areas in thin structures. With the presented approach it is possible to perform large 3D simulations without excessive computational resources by exploiting certain properties of the multiharmonic solution of the eddy current problem. Together with the use of nonconforming interfaces, the overall computational complexity of the problem can be decreased significantly.

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

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Article
Publication date: 7 March 2016

Slawomir Koziel and Adrian Bekasiewicz

Strategies for accelerated multi-objective optimization of compact microwave and RF structures are investigated, including the possibility of exploiting surrogate modeling…

151

Abstract

Purpose

Strategies for accelerated multi-objective optimization of compact microwave and RF structures are investigated, including the possibility of exploiting surrogate modeling techniques for electromagnetic (EM)-driven design speedup for such components. The paper aims to discuss these issues.

Design/methodology/approach

Two algorithmic frameworks are described that are based on fast response surface approximation models, structure decomposition, and Pareto front refinement. Numerical case studies are provided demonstrating feasibility of solving real-world problems involving multi-objective optimization of miniaturized microwave passives and expensive EM-simulation models of such structures.

Findings

It is possible, through appropriate combination of the surrogate modeling techniques and response correction methods, to identify the set of alternative designs representing the best possible trade-offs between conflicting design objectives in a realistic time frame corresponding to a few dozen of high-fidelity EM simulations of the respective structures.

Research limitations/implications

The present study sets a direction for further studied on expedited optimization of computationally expensive simulation models for miniaturized microwave components.

Originality/value

The proposed algorithmic framework proved useful for fast design of microwave structures, which is extremely challenging when using conventional methods. To the authors’ knowledge, this is one of the first attempts to surrogate-assisted multi-objective optimization of compact components at the EM-simulation level.

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Article
Publication date: 1 September 2003

M. Rausch, M. Gebhardt, M. Kaltenbacher and H. Landes

In this paper, an efficient magnetomechanical calculation scheme based on the finite element method is presented. This scheme is used for the precise forecast of the dynamical…

707

Abstract

In this paper, an efficient magnetomechanical calculation scheme based on the finite element method is presented. This scheme is used for the precise forecast of the dynamical behavior of a clinical magnetic resonance imaging scanner. The validity of the computer simulations has been verified by means of appropriate measurements. Application examples include the optimization of the superconducting magnet regarding the eddy currents and vibrations in its cryostat.

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COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 22 no. 3
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 18 April 2017

Slawomir Koziel and Adrian Bekasiewicz

This paper aims to investigate deterministic strategies for low-cost multi-objective design optimization of compact microwave structures, specifically, impedance matching…

100

Abstract

Purpose

This paper aims to investigate deterministic strategies for low-cost multi-objective design optimization of compact microwave structures, specifically, impedance matching transformers. The considered methods involve surrogate modeling techniques and variable-fidelity electromagnetic (EM) simulations. In contrary to majority of conventional approaches, they do not rely on population-based metaheuristics, which permit lowering the design cost and improve reliability.

Design/methodology/approach

There are two algorithmic frameworks presented, both fully deterministic. The first algorithm involves creating a path covering the Pareto front and arranged as a sequence of patches relocated in the course of optimization. Response correction techniques are used to find the Pareto front representation at the high-fidelity EM simulation level. The second algorithm exploits Pareto front exploration where subsequent Pareto-optimal designs are obtained by moving along the front by means of solving appropriately defined local constrained optimization problems. Numerical case studies are provided demonstrating feasibility of solving real-world problems involving expensive EM-simulation models of impedance transformer structures.

Findings

It is possible, by means of combining surrogate modeling techniques and constrained local optimization, to identify the set of alternative designs representing Pareto-optimal solutions, in a realistic time frame corresponding to a few dozen of high-fidelity EM simulations of the respective structures. Multi-objective optimization for the considered class of structures can be realized using deterministic approaches without defaulting to evolutionary methods.

Research limitations/implications

The present study can be considered a step toward further studies on expedited optimization of computationally expensive simulation models for miniaturized microwave components.

Originality/value

The proposed algorithmic solutions proved useful for expedited multi-objective design optimization of miniaturized microwave structures. The problem is extremely challenging when using conventional methods, in particular evolutionary algorithms. To the authors’ knowledge, this is one of the first attempts to investigate deterministic surrogate-assisted multi-objective optimization of compact components at the EM-simulation level.

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Article
Publication date: 1 July 2014

Timo Hülsmann, Andreas Bartel, Sebastian Schöps and Herbert De Gersem

The purpose of this paper is to develop a fast and accurate analytic model function for the single-valued H-B curve of ferromagnetic materials, where hysteresis can be disregarded…

226

Abstract

Purpose

The purpose of this paper is to develop a fast and accurate analytic model function for the single-valued H-B curve of ferromagnetic materials, where hysteresis can be disregarded (normal magnetization curve). Nonlinear magnetoquasistatic simulations demand smooth monotone material models to ensure physical correctness and good convergence in Newton's method.

Design/methodology/approach

The Brauer model has these beneficial properties, but is not sufficiently accurate for low and high fields in the normal magnetization curve. The paper extends the Brauer model to better fit material behavior in the Rayleigh region (low fields) and in full saturation. Procedures for obtaining optimal parameters from given measurement points are proposed and tested for two technical materials. The approach is compared with cubic spline and monotonicity preserving spline interpolation with respect to error and computational effort.

Findings

The extended Brauer model is more accurate and even maintains the computational advantages of the classical Brauer model. The methods for obtaining optimal parameters yield good results if the measurement points have a distinctive Rayleigh region.

Originality/value

The model function for ferromagnetic materials enhances the precision of the classical Brauer model without notable additional simulation cost.

Details

COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, vol. 33 no. 4
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 3 October 2016

Slawomir Koziel and Adrian Bekasiewicz

Development of techniques for expedited design optimization of complex and numerically expensive electromagnetic (EM) simulation models of antenna structures validated both…

199

Abstract

Purpose

Development of techniques for expedited design optimization of complex and numerically expensive electromagnetic (EM) simulation models of antenna structures validated both numerically and experimentally. The paper aims to discuss these issues.

Design/methodology/approach

The optimization task is performed using a technique that combines gradient search with adjoint sensitivities, trust region framework, as well as EM simulation models with various levels of fidelity (coarse, medium and fine). Adaptive procedure for switching between the models of increasing accuracy in the course of the optimization process is implemented. Numerical and experimental case studies are provided to validate correctness of the design approach.

Findings

Appropriate combination of suitable design optimization algorithm embedded in a trust region framework, as well as model selection techniques, allows for considerable reduction of the antenna optimization cost compared to conventional methods.

Research limitations/implications

The study demonstrates feasibility of EM-simulation-driven design optimization of antennas at low computational cost. The presented techniques reach beyond the common design approaches based on direct optimization of EM models using conventional gradient-based or derivative-free methods, particularly in terms of reliability and reduction of the computational costs of the design processes.

Originality/value

Simulation-driven design optimization of contemporary antenna structures is very challenging when high-fidelity EM simulations are utilized for performance utilization of structure at hand. The proposed variable-fidelity optimization technique with adjoint sensitivity and trust regions permits rapid optimization of numerically demanding antenna designs (here, dielectric resonator antenna and compact monopole), which cannot be achieved when conventional methods are of use. The design cost of proposed strategy is up to 60 percent lower than direct optimization exploiting adjoint sensitivities. Experimental validation of the results is also provided.

Details

Engineering Computations, vol. 33 no. 7
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 1 June 2001

Markus Clemens, Markus Wilke and Thomas Weiland

Transient eddy current formulations based on the Finite Integration Technique (FIT) for the magneto‐quasistatic regime are extended to include motional induction effects of moving…

345

Abstract

Transient eddy current formulations based on the Finite Integration Technique (FIT) for the magneto‐quasistatic regime are extended to include motional induction effects of moving conductors with simple geometries by different approaches. A new regularization of the formulation using discrete grad‐div augmentation of the curlcurl formulation is presented and tested. To improve the implicit time integration process, several schemes for an error controlled variable time step selection are presented and for the repetitive solution of the arising large sparse systems of equations a sparse direct solver is compared to iterative methods such as a preconditioned conjugate gradient method and a new algebraic multigrid solver, which is aware of the curlcurl nullspace.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 20 no. 2
Type: Research Article
ISSN: 0332-1649

Keywords

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Article
Publication date: 15 November 2011

Markus Clemens, Sebastian Scho¨ps, Herbert De Gersem and Andreas Bartel

The space discretization of eddy‐current problems in the magnetic vector potential formulation leads to a system of differential‐algebraic equations. They are typically time…

277

Abstract

Purpose

The space discretization of eddy‐current problems in the magnetic vector potential formulation leads to a system of differential‐algebraic equations. They are typically time discretized by an implicit method. This requires the solution of large linear systems in the Newton iterations. The authors seek to speed up this procedure. In most relevant applications, several materials are non‐conducting and behave linearly, e.g. air and insulation materials. The corresponding matrix system parts remain constant but are repeatedly solved during Newton iterations and time‐stepping routines. The paper aims to exploit invariant matrix parts to accelerate the system solution.

Design/methodology/approach

Following the principle “reduce, reuse, recycle”, the paper proposes a Schur complement method to precompute a factorization of the linear parts. In 3D models this decomposition requires a regularization in non‐conductive regions. Therefore, the grad‐div regularization is revisited and tailored such that it takes anisotropies into account.

Findings

The reduced problem exhibits a decreased effective condition number. Thus, fewer preconditioned conjugate gradient iterations are necessary. Numerical examples show a decrease of the overall simulation time, if the step size is small enough. 3D simulations with large time step sizes might not benefit from this approach, because the better condition does not compensate for the computational costs of the direct solvers used for the Schur complement. The combination of the Schur approach with other more sophisticated preconditioners or multigrid solvers is subject to current research.

Originality/value

The Schur complement method is adapted for the eddy‐current problem. Therefore, a new partitioning approach into linear/non‐linear and static/dynamic domains is proposed. Furthermore, a new variant of the grad‐div gauging is introduced that allows for anisotropies and enables the Schur complement method in 3D.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 30 no. 6
Type: Research Article
ISSN: 0332-1649

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