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This paper aims to propose a fast and accurate simulation of large-scale induction heating problems by using nonlinear reduced-order models.

A projection space for model order reduction (MOR) is quickly generated from the first kernels of Volterra’s series to the problem solution. The nonlinear reduced model can be solved with time-harmonic phasor approximation, as the nonlinear quadratic structure of the full problem is preserved by the projection.

The solution of induction heating problems is still computationally expensive, even with a time-harmonic eddy current approximation. Numerical results show that the construction of the nonlinear reduced model has a computational cost which is orders of magnitude smaller than that required for the solution of the full problem.

Only linear magnetic materials are considered in the present formulation.

The proposed MOR approach is suitable for the solution of industrial problems with a computing time which is orders of magnitude smaller than that required for the full unreduced problem, solved by traditional discretization methods such as finite element method.

The most common technique for MOR is the proper orthogonal decomposition. It requires solving the full nonlinear problem several times. The present MOR approach can be built directly at a negligible computational cost instead. From the reduced model, magnetic and temperature fields can be accurately reconstructed in whole time and space domains.

Inverse problems in electromagnetism, namely, the recovery of sources (currents or charges) or system data from measured effects, are usually ill-posed or, in the numerical formulation, ill-conditioned and require suitable regularization to provide meaningful results. To test new regularization methods, there is the need of benchmark problems, which numerical properties and solutions should be well known. Hence, this study aims to define a benchmark problem, suitable to test new regularization approaches and solves with different methods.

To assess reliability and performance of different solving strategies for inverse source problems, a benchmark problem of current synthesis is defined and solved by means of several regularization methods in a comparative way; subsequently, an approach in terms of an artificial neural network (ANN) is considered as a viable alternative to classical regularization schemes. The solution of the underlying forward problem is based on a finite element analysis.

The paper provides a very detailed analysis of the proposed inverse problem in terms of numerical properties of the lead field matrix. The solutions found by different regularization approaches and an ANN method are provided, showing the performance of the applied methods and the numerical issues of the benchmark problem.

The value of the paper is to provide the numerical characteristics and issues of the proposed benchmark problem in a comprehensive way, by means of a wide variety of regularization methods and an ANN approach.

This paper aims to show a complete optimization tool that can be used for the design of coaxial magnetic gears. In the first part, the paper deals with the semi-analytic modelling of these machines and also discusses how to reduce the computational efforts. In the second part, an optimization algorithm is adopted for finding the Pareto optimal geometries.

The machine is subdivided into a set of domains according to their physical and geometrical properties, and the potential distribution is found semi-analytically in them under some simplifying hypothesis. A loss estimation is performed for both ferromagnetic and permanent magnet regions. A stochastic differential evolution (DE) algorithm for multi-objective constrained problems is then applied.

It is shown that the presented design tool gives results in accordance to finite element method (FEM)-based analysis keeping the advantages of robustness and simplicity of the analytical methods. The DE-based strategy performs well on the magnetic gear optimization problem.

The proposed tool appears to be a good starting point when designing coaxial magnetic gears. The optimal Pareto points can be used as initial seeds of FEM-based optimizations, resulting in a cheaper computational method with respect to a full FEM optimization.

This paper takes inspiration from recent works on magnetic gear modelling and completes the design procedure with a suitable efficiency estimation. The paper also shows how to use mature optimization strategies to solve the constrained multi-objective magnetic gear design problem.

The purpose of this paper is to implement the Anderson acceleration for different formulations of eletromagnetic nonlinear problems and analyze the method efficiency and strategies to obtain a fast convergence.

The paper is structured as follows: the general class of fixed point nonlinear problems is shown at first, highlighting the requirements for convergence. The acceleration method is then shown with the associated pseudo-code. Finally, the algorithm is tested on different formulations (finite element, finite element/boundary element) and material properties (nonlinear iron, hysteresis models for laminates). The results in terms of convergence and iterations required are compared to the non-accelerated case.

The Anderson acceleration provides accelerations up to 75 per cent in the test cases that have been analyzed. For the hysteresis test case, a restart technique is proven to be helpful in analogy to the restarted GMRES technique.

The acceleration that has been suggested in this paper is rarely adopted for the electromagnetic case (it is normally adopted in the electronic simulation case). The procedure is general and works with different magneto-quasi static formulations as shown in the paper. The obtained accelerations allow to reduce the number of iterations required up to 75 per cent in the benchmark cases. The method is also a good candidate in the hysteresis case, where normally the fixed point schemes are preferred to the Newton ones.

The purpose of this paper is to show that the performance of differential evolution (DE) can be substantially improved by a combination of techniques. These enhancements are applicable to both single and multiobjective problems. Their combined use allows the optimization of complex 3D electromagnetic devices.

DE is improved by a combination of techniques which are applied in a cascade way and their single and combined effect is tested on well‐known benchmarks and domain‐specific applications.

It is shown that the combined use of enhancement techniques provides substantial improvements in the speed of convergence for both single and multiobjective problems.

The increased speed of convergence may come at the price of a somewhat decreased robustness. However, such behavior is justified by the CPU time constraints under which the optimization has to be performed.

The proposed approach appears to be an efficient general purpose stochastic optimizer for electromagnetic design problems.

This paper explorers the combined use of many of the most recent and successful algorithmic improvements to DE and applies them to both single and multiobjective problems.

The purpose of this paper is to optimize the performance of direct methanol fuel cells for portable applications by combining a non‐linear, fully coupled circuit model and a stochastic optimization procedure.

A novel non‐linear equivalent circuit that accounts for electrochemical reactions and charge generation inside catalyst layers, electronic and protonic conduction, methanol crossover through the membrane, mass transport of reactants inside diffusion layers is presented. The discharge dynamic of the fuel cell, depending on the initial methanol concentration and on the load profile, is modelled by using the mass conservation equation. The equivalent circuit is interfaced to a stochastic optimization procedure in order to maximize the battery duration while minimizing fuel crossover.

In the proposed circuit scheme, unlike semi‐empirical models, lumped circuit parameters are derived directly from mass transport and electric equations in order to fully describe the dynamic performance of the fuel cell. Physical and geometrical parameters are optimized in order to improve the system runtime. It is shown that a combined use of fuel cells and lithium batteries can improve the runtime of portable electronic devices compared to traditional supply systems based on lithium batteries only.

The one‐dimensional model of the micro fuel cell does not take into account possible transverse mass and electric charge flows in the fuel cell layers; most of the geometric and physics model parameters cannot be estimated from direct in situ or ex situ measurements.

Direct methanol fuel cells are nowadays a promising technology for replacing or complementing lithium batteries due to their high energy density. Most limiting features of direct methanol fuel cells are the fuel crossover and its slow oxidation kinetics. By using the proposed approach, fuel cell parameters can be optimized in order to enhance the discharge runtime and to reduce the methanol crossover.

The equivalent circuit model with optimized lumped non‐linear parameters can be used when designing power management units for portable electronic devices.

The purpose of this paper is to show the main features of the redox flow battery technology, present the current state-of-the-art of both industrial and research systems and to highlight the main research challenges.

The study is based on an extensive survey of recent literature as well as on the authors' own experience in the modelling of RFB systems.

RFBs present unique features which make them suitable for distributed storage and thus particularly interesting in the context of smart grids. Current research aims at resolving some outstanding issues which still limit the widespread use of RFBs.

A more widespread use of energy storage technologies, and RFBs in particular, will allow a much higher penetration of renewable energy sources.

The paper presents one of the few comprehensive studies on RFBs including both technological and modelling aspects.

To the purpose of this paper is to show the main features of the Direct Multisearch method and how it can be enhanced and hybridized without compromising its mathematical properties.

The study is based on a mathematical analysis of the properties of the method which is then validated with analytical benchmarks and tested on a problem related to magnetic-assisted surgery.

The presented multi-objective optimizer, based on an extension of the well-known Pattern Search (PS) method, due to its deterministic nature, enjoys provable convergence properties. Furthermore, the method is successfully extended by hybridizing it with some stochastic approaches in order to improve its performance. Numerical examples show the effectiveness of the developed approach which can be used as a general and robust tool for multi-objective optimization. In a specific application, related to magnetic-assisted surgery, the proposed algorithm achieved 100 percent detection accuracy under realistic test conditions.

Due to the provable convergence characteristics of the algorithm, the presented technique can be applied to problems where minima must be identified with very high accuracy.

The paper presents enhanced and hybridized versions of the PS algorithm.