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Finite element discretizations of low‐frequency, time‐harmonic magnetic problems lead to sparse, complex symmetric systems of linear equations. The question arises which Krylov subspace methods are appropriate to solve such systems. The quasi minimal residual method combines a constant amount of work and storage per iteration step with a smooth convergence history. These advantages are obtained by building a quasi minimal residual approach on top of a Lanczos process to construct the search space. Solving the complex systems by transforming them to equivalent real ones of double dimension has to be avoided as such real systems have spectra that are less favourable for the convergence of Krylov‐based methods. Numerical experiments are performed on electromagnetic engineering problems to compare the quasi minimal residual method to the bi‐conjugate gradient method and the generalized minimal residual method.

This work aims to present a multilevel optimization strategy based on manifold‐mapping combined with multiquadric interpolation for the coarse model construction.

In the proposed approach the coarse model is obtained by interpolating the fine model using multiquadrics in a small number of points. As the algorithm iterates the response surface model is improved by enriching the set of interpolation points.

This approach allows to accurately solve the TEAM Workshop Problem 25 using as little as 33 finite element simulations. Furthermore, it allows a robust sizing optimization of a cylindrical voice‐coil actuator with seven design variables.

Further analysis is required to gain a better understanding of the role that the initial coarse model accuracy plays in the convergence of the algorithm. The proposed model allows to carry out such analysis by varying the number of points included in the initial response surface model. The effect of the trust‐region stabilization in the presence of manifolds of equivalent solutions is also a topic of further investigations.

Unlike the closely related space‐mapping algorithm, the manifold‐mapping algorithm is guaranteed to converge to a fine model optimal solution. By combining it with multiquadric response surface models, its applicability is extended to problems for which other kinds of coarse model such as lumped parameter approximations for instance are tedious or impossible to construct.

The waste recycling industry increasingly relies on magnetic density separators. These devices generate an upward magnetic force in ferro-fluids allowing to separate the immersed particles according to their mass density. Recently, a new separator design has been proposed that significantly reduces the required amount of permanent magnet material. The purpose of this paper is to alleviate the undesired end-effects in this design by altering the shape of the ferromagnetic covers of the individual poles.

The paper represents the shape of the ferromagnetic pole covers with B-splines and defines a cost functional that measures the non-uniformity of the magnetic field in an area above the poles. The authors apply an iso-geometric shape optimization procedure, which allows us to accurately represent, analyze and optimize the geometry using only a few design variables. The design problem is regularized by imposing constraints that enforce the convexity of the pole cover shapes and is solved by a non-linear optimization procedure. The paper validates the implementation of the algorithm using a simplified variant of the design problem with a known analytical solution. The algorithm is subsequently applied to the problem posed.

The shape optimization attains its target and yields pole cover shapes that give rise to a magnetic field that is uniform over a larger domain.

This increased magnetic field uniformity is obtained at the cost of a pole cover shape that differs per pole. This limitation has negligible impact on the manufacturing of the separator. The new pole cover shapes therefore lead to improved performance of the density separation.

Due to the larger uniformity the generated field, these shapes should enable larger amounts of waste to be processed than the previous design.

This paper treats the shapes optimization of magnetic density separators systematically and presents new shapes for the ferromagnetic poles covers.

The space‐mapping (SM) optimization technique, with its input, implicit or output mapping‐based implementations, provides a basis for computationally efficient engineering optimization. Various algorithms and design optimization problems, related to microwave devices, antennas and electronic circuits, are presented in numerous publications. However, a new application area for SM optimization is currently expanding, i.e. the design of electromechanical actuators. The purpose of this paper is to present an overview of the recent developments.

New algorithm variants and their application to design problems in electromechanics and related fields are briefly summarized.

The paper finds that SM optimization offers a significant speed‐up of the optimization procedures for the design of electromechanical actuators. Its true potential in the area of magnetic systems and actuator design is still rather unexplored.

This overview is complementary to the previous published reviews and shows that the application of SM optimization has also extended to the design of electromechanical devices.

The aim of this paper is to reduce the evaluations number of the fine model within the output space mapping (OSM) technique in order to reduce their computing time.

In this paper, n-level OSM is proposed and expected to be even faster than the conventional OSM. The proposed algorithm takes advantages of the availability of n models of the device to optimize, each of them representing an optimal trade-off between the model error and its computation time. Models with intermediate characteristics between the coarse and fine models are inserted within the proposed algorithm to reduce the number of evaluations of the consuming time model and then the computing time. The advantages of the algorithm are highlighted on the optimization problem of superconducting magnetic energy storage (SMES).

A major computing time gain equals to three is achieved using the n-level OSM algorithm instead of the conventional OSM technique on the optimization problem of SMES.

The originality of this paper is to investigate several models with different granularities within OSM algorithm in order to reduce its computing time without decreasing the performance of the conventional strategy.

The purpose of this paper is to investigate the use of multidisciplinary optimization (MDO) formulations within space‐mapping techniques in order to reduce their computing time.

The aim of this work is to quantify the interest of using MDO formulations within space mapping techniques. A comparison of three MDO formulations is carried out in a short time by using an analytical model of a safety transformer. This comparison reveals the advantage of two formulations in terms of robustness and computing time among the three MDO formulations. Then, the best formulations are investigated within output space mapping, using both analytical and FE models of the transformer.

A major computing time gain equal to 5.5 is achieved using the Individual Disciplinary Feasibility formulation within the output space‐mapping technique in the case of the safety transformer.

The MultiDisciplinary Feasibility formulation is the common formulation used within space‐mapping technique because it is the most conventional way to perform MDO. The originality of this paper is to investigate the Individual Disciplinary Feasibility formulation within output space‐mapping technique in order to allow the parallelization of calculation and to achieve a major reduction of computing time.

Manifold‐mapping (MM) is an efficient surrogate‐based optimization technique aimed at the acceleration of very time‐consuming design problems. In this paper we present two new variants of the original algorithm that make it applicable to a broader range of optimization scenarios.

The first variant is useful when the optimization constraints are expressed by means of functions that are very expensive to compute. The second variant endows the original scheme with a trust‐region strategy and the result is a much more robust algorithm.

Two practical optimization problems from electromagnetics eventually show that the proposed variants perform efficiently.

The original MM algorithm is extended with two new variants. Therefore, the MM approach is applicable to a much larger set of design situations.

This paper aims to give a perspective about the variety of techniques which are available and are being further developed in the area of coupled field formulations, with selective bibliography and practical examples, to help postgraduate students, researchers and designers working in design or analysis of electrical machinery.

This paper reviews the recent trends in coupled field formulations. The use of these formulations for designing and non‐destructive testing of electrical machinery is described, followed by their classifications, solutions and applications. Their advantages and shortcomings are discussed.

The paper gives an overview of research, development and applications of coupled field formulations for electrical machinery based on more than 160 references. All landmark papers are classified. Practical engineering case studies are given which illustrate wide applicability of coupled field formulations.

Problems which continue to pose challenges to researchers are enumerated and the advantages of using the coupled‐field formulation are pointed out.

This paper gives a detailed description of the application of the coupled field formulation method to the analysis of problems that are present in different electrical machines. Examples of analysis of generators and transformers with this formulation are presented. The application examples give guidelines for its use in other analyses.

The coupled‐field formulation is used in the analysis of rotational machines and transformers where reference data are available and comparisons with other methods are performed and the advantages are justified. This paper serves as a guide for the ongoing research on coupled problems in electrical machinery.

Optimisation in electromagnetics, based on finite element models, is often very time‐consuming. In this paper, we present the space‐mapping (SM) technique which aims at speeding up such procedures by exploiting auxiliary models that are less accurate but much cheaper to compute.

The key element in this technique is the SM function. Its purpose is to relate the two models. The SM function, combined with the low accuracy model, makes a surrogate model that can be optimised more efficiently.

By two examples we show that the SM technique is effective. Further we show how the choice of the low accuracy model can influence the acceleration process. On one hand, taking into account more essential features of the problem helps speeding up the whole procedure. On the other hand, extremely simple auxiliary models can already yield a significant acceleration.

Obtaining the low accuracy model is not always straightforward. Some research could be done in this direction. The SM technique can also be applied iteratively, i.e. the auxiliary model is optimised aided by a coarser one. Thus, the generation of hierarchies of models seems to be a promising venue for the SM technique.

Optimisation in electromagnetics, based on finite element models, is often very time‐consuming. The results given show that the SM technique is effective for speeding up such procedures.

The purpose of this paper is to focus on the implementation and management of multi‐objective optimizations, with the help of heuristic algorithms such as space mapping methods.

The authors consider the design of electromechanical actuators by the use of mathematical and computer means. Experiments are then virtual, because they correspond to numerical simulations. Dimensioning is then ensured by an optimization procedure of the space mapping type, whose main characteristic consists in using two models of the same size actuator (instead of a single one for classical optimization methods). Moreover, one considers here that multiple outputs are defined: this defines a multi‐objective optimization. This paper proposes several techniques making it possible to include the definition of multiple objectives to be fulfilled as part of an output space mapping optimization process.

The proposed approaches make it possible to stabilize and accelerate the convergence of multi‐objective optimizations performed by space mapping. This is illustrated by the example of the dimensioning of a resonant linear electromagnetic actuator.

The approach presented in the paper is original because it allows finding of a solution to the multi‐objective problem, without building any Pareto front, and most effectively by improving the convergent behavior of the optimization algorithm.