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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 compare stochastic gradient method used for neural network training with global optimizer without use of gradient information, in particular differential evolution.

This contribute shows the application of heuristic optimization algorithms to the training phase of artificial neural network whose aim is to predict renewable power production as function of environmental variables such as solar irradiance and temperature. The training problem is cast as the minimization of a cost function whose degrees of freedom are the parameters of the neural network. A differential evolution algorithm is substituted to the more usual gradient-based minimization procedure, and the comparison of their performances is presented.

The two procedures based on stochastic gradient and differential evolution reach the same results being the gradient based moderately quicker in convergence but with a lower value of reliability, as a significant number of runs do not reach convergence.

The approach has been applied to two forecasting problems and, even if results are encouraging, the need for extend the approach to other problems is needed.

The new approach could open the training of neural network to more stable and general methods, exploiting the potentialities of parallel computing.

To the best of the authors’ knowledge, the research presented is fully original for the part regarding the neural network training with differential evolution.

The purpose of this paper is to present an electro‐thermo‐structural analysis based on the cell method (CM).

CM is useful for solving coupled problems when the same geometrical discretization can be adopted for different phenomena. In this case, the same geometrical structures and operators can be used, leading to a simplification of the numerical model.

In order to asses the performance of the proposed coupling scheme, results have been compared with values measured on a carbon‐fiber specimen heated by an electric current and with an applied the mechanical load.

A new dynamic coupling scheme based on the CM has been proposed and assessed with respect to measurements. A good agreement between model results and measurements has been shown, at least until second order effects appears, like the breaking of some fibers of the specimen or high‐temperature effects on epoxy resin.

The implementation of a vector Preisach model for the modelling of anisotropic hysteretic soft magnetic materials is outlined. Some comparisons with measurements on alternate and rotational magnetic field excitations are shown. The hysteresis model is inserted inside a two‐dimensional finite element solver formulated in terms of magnetic vector potential and nonlinear solution is handled by means of the fixed point method with H‐scheme. Results obtained on a two‐dimensional geometry are described and discussed.

The paper aims to describe the coupling of magnetostatic finite formulation of electromagnetic field with two integral methods.

The first hybrid scheme is based on Green's function applied to magnetization source while the other one is based on a magnetic scalar potential boundary element method. A comparison of the two techniques is performed on a benchmark case with analytical solution, on a 2D multiply‐connected problem and on an industrial case where measurements are available.

The proposed hybrid approaches have proved to be effective techniques to solve open boundary non‐linear magnetostatic problems. Similar convergence speed with respect to the number of unknowns is found for both schemes

The paper shows the effectiveness of hybrid schemes applied to the finite formulation, assessing their performances on various test cases.

The aim of this paper is to highlight the educational value of algebraic numerical methods with respect to traditional numerical techniques based on differential formulation.

Algebraic formulations of electromagnetic fields are gaining a new interest in the research community. One common characteristic of these methods is that they impose field equations, for instance charge or mass conservation, directly in algebraic form as a sum of partial contributes, without using differential operators like the divergence one. This feature leads directly to a system of linear equations without requiring any intermediate differential formulation as in finite element method. In addition, these systems of linear equations can be efficiently expressed as a product of matrices related to problem topology and material characteristics.

Owing to these features, a MATLAB implementation of these theoretical frameworks is particularly efficient and simple and can be used by electrical engineering students which, even if with a basic mathematical background, have a good practice with network theory and its computer implementation. Following this way of thinking, a MATLAB based environment has been created and here it is presented and discussed.

The implementation of the algebraic formulation can be done by using very basic mathematical tools, therefore the algebraic method becomes also a good way to introduce the numerical field analysis to undergraduate students.

The paper presents the optimization of the power flows inside a microgrid with renewable sources and two kinds of storage. The considered microgrid consists in commercial buildings with maximum daily peak value of 50 kW, photovoltaic arrays with total capacity of 175 kW, a 50 kW/50 kWh high speed flywheel storage and a 50 kW/50 kWh set of Li-ion accumulators.

The power flows in the microgrid are optimized the day ahead at one hour discretization in order to minimize the electric bill. Several scheduling strategies are proposed for solving the corresponding optimization problem including standard deterministic methods, stochastic algorithms and hybrid heuristics.

All scheduling strategies investigated in the paper are compared with regard to their accuracy and computational time.

Beyond the comparison of different algorithms devoted to the power flow optimization problem, our approach also addresses the integration of battery ageing in the scheduling strategy.