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In clinical treatments of a class of tumors, e.g. skin tumors, the drug uptake of tumor tissue is helped by means of a pulsed electric field, which permeabilizes the cell membranes. This technique, which is called electroporation, exploits the conductivity of the tissues: however, the tumor tissue could be characterized by inhomogeneous areas, eventually causing a non-uniform distribution of current. In this paper, the authors propose a field model to predict the effect of tissue inhomogeneity, which can affect the current density distribution. In particular, finite-element simulations, considering non-linear conductivity against field relationship, are developed. Measurements on a set of samples subject to controlled inhomogeneity make it possible to assess the numerical model in view of identifying the equivalent resistance between pairs of electrodes.

In recent years, superficial chest wall recurrence from breast cancer can be effectively treated by means of electrochemotherapy, with the majority of patients achieving response to treatment. Nevertheless, tumor spread along superficial lymphatic vessels makes this peculiar type of tumor recurrence prone to involve large skin areas and difficult to treat. In these cases, electroporation with standard, small size needle electrodes can be time-consuming and produce an inhomogeneous coverage of the target area, ultimately resulting in patient under treatment.

The text is an introduction to the selected papers from the HES-2023 conference, which focuses on the application of electromagnetic fields for materials processing. The conference was postponed by a year due to the pandemic and the war in Ukraine. The main developments in electroheat involve a multi-physics approach to modeling and simulation, with a focus on coupling different physical domains. The use of AI-based methods, such as digital twins and machine learning, in electrothermal systems is a current topic of research. The conference also covered topics such as induction heating, induction hardening, and inverse problems in induction heating. Overall, 52 papers were presented at the conference, and the 10 selected papers cover the main topics discussed. [Extracted from the article]

This paper presents a methodology to study nonlinear electromagnetic phenomena inside ferromagnetic pieces where eddy currents are driven by an external supply source in the medium frequency range. The proposed methodology takes, as reference, a nonlinear time-harmonic solution of the iron part and then identifies, by means of an optimization procedure, the magnetic permeability values of an equivalent layered linear material which would give the same value of Joule losses of the nonlinear case. This approach has been applied to a test configuration obtaining good results. Index Terms--Induction heating, nonlinear time-harmonic eddy currents, optimization.

The paper presents a two-stage approach to solve a class of nonlinear 3-D eddy current problems with high saturation, typical of induction heating processes. The proposed method separates the problem of heavy nonlinearity from the complexity of the geometry, by resorting to a 1-D fast nonlinear solver which is coupled with a linear 3-D solver. Under certain hypotheses on the geometry, the approach is shown to be effective and accurate. Comparison with a commercial 3-D nonlinear code are provided. Index Terms--Induction heating, magnetoquasistatic, nonlinear ac model.

A finite formulation is presented for the solution of coupled problems of steady-state electric and transient thermal conductions in 3-D regions. The model is based on the cell method approach and takes advantage of the very agile algebraic formulations that it can provide for field theories. Dual barycentric cell complexes are used for both space and time domains, the latter inducing a Crank-Nicolson time integration scheme. An example of application is given, consisting in the simulation of a treatment for the thermal ablation of fiver cancer. Comparisons are given with a commercial finite-element method program. Index Terms--Cell method (CM), coupled problems, finite formulation, hyperthermic treatments.

An application of the Cell Method to a coupled nonlinear problem is presented. The two coupled physical aspects consist of the magnetic quasistatic and thermal transient problems. Their investigation is concerned in a wide range of applications such as the analysis of devices for the induction heating treatment of conductive workpieces. Assuming a cylindrical geometry, that is usual in such devices, the numerical model exploits a two-dimensional axis-symmetrical formulation to perform the simultaneous analyses of the transient thermal and ac eddy currents problems. As a consequence of the large temperature rise, typical in these treatments, both coupled problems are considered nonlinear. The formulation is validated comparing the numerical results against those adopted with commercial codes based on the finite element method and against the experimental data measured on a test device, too. Index Terms--Cell method, coupled problems, eddy currents, finite formulations, induction-heating.

The paper presents a formulation for two-dimensional anisotropic eddy current problems developed both in the time and the frequency domains. It is based on the cell method, that makes use of integral electromagnetic quantities related to each other through algebraic constitutive and structure equations. This formulation directly assembles both the so-called stiffness and mass matrices by means of an inspection approach with no need to use topological incidence matrices, thus providing an agile construction of the fundamental system and requiring to compute only the primal cell complex, not the dual one. The formulation is compared with an equivalent finite element method method based on the Galerkin and Crank--Nicolson schemes, both being used for simulating an experimental induction-heating apparatus. Index Terms--Cell method, eddy currents, finite formulation, fundamental matrices.

The Cell Method (CM) is an approach to the numerical solution of field physical problems that has been recently applied to the electromagnetic computation. It is gaining more and more interest as it allows easy formulations based on integral (finite) quantities, with no need to resort to local quantities related by differential equations to be suitably regularized in numerical form. The paper deals with an application of the CM to the solution of electrostatic problems. Two formulations are presented: The first is suitable for isotropic electrostatic media, and the second is specifically suited for the anisotropic ones. The main items of the method and the structure of the two algorithms are described, and some results obtained for reference cases are reported. A comparison is also shown with the results from a first-order finite element method (FEM) algorithm. Index Terms--Cell Method, electrostatics, numerical techniques, static fields.

An inverse problem concerning the industrial process of steel bars hardening and tempering is considered. The associated optimization problem is formulated in terms of membership functions and, for the sake of comparison, also in terms of quadratic residuals; both geometric and electromagnetic design variables have been considered. The numerical solution is achieved by coupling a finite difference procedure for the calculation of the electromagnetic and thermal fields to a deterministic strategy of minimization based On modified Fletcher and Reeves method. Index terms: Induction Heating, Optimization Methods, Finite Difference method.

In this paper an optimization procedure for the optimal design of a transverse-flux induction heating system is presented. Hooke and Jeeves direct search technique is used for the optimization procedure. The finite element method is used for the electromagnetic field calculation and the integral parameter determination. The results obtained by this procedure are compared with those available in literature.