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To model magneto‐harmonic devices including solid conductors with holes when the skin depth is very small.

The 3D finite element magnetic scalar potential formulation combined with the surface impedance condition approximation is used. It allows the modelling of thin skin depth effect at low cost.

The paper shows how to use surface impedance condition for solid conductors with holes, when using the magnetic scalar potential. Specific equations must be added to respect Ampere's theorem. The paper establishes these equations and the coupling with the finite element formulation. The final system of equations is symmetric.

The formulation allows to treat linear material in the magneto‐harmonic assumption.

The use of surface impedance condition with the 3D finite element magnetic scalar potential formulation is well known. The originality is to take into account holes (multiply connected conductors).

The paper presents a new variant of the H-Φ field formulation for solving 3-D magnetostatic and frequency domain eddy current problems. The suggested formulation uses the vector and scalar tetrahedral elements within conducting and non-conducting domains, respectively. The presented numerical method is capable of solving multiply connected regions and eliminates the need for computing the source current density and the source magnetic field before the actual magnetostatic and eddy current simulations. The obtained magnetostatic results are verified by comparison against the corresponding results of the standard stationary current distribution analysis combined with the Biot-Savart integration. The accuracy of the eddy current results is demonstrated by comparison against the classical A-A-f approach in frequency domain.

The theory and implementation of the new H-Φ magnetostatic and eddy current solver is presented in detail. The method delivers reliable results without the need to compute the source current density and source magnetic field before the actual simulation.

The proposed H-Φ produce radically smaller and considerably better conditioned equation systems than the alternative A-A approach, which usually requires the unphysical regularization in terms of a low electric conductivity value within the nonconductive domain.

The presented numerical method is capable of solving multiply connected regions and eliminates the need for computing the source current density and the source magnetic field before the actual magnetostatic and eddy current simulations.

The purpose of this paper is to solve generic magnetostatic problems by BEM, by studying how to use a boundary integral equation (BIE) with the double layer charge as unknown derived from the scalar potential.

Since the double layer charge produces only the potential gap without disturbing the normal magnetic flux density, the field is accurately formulated even by one BIE with one unknown. Once the double layer charge is determined, Biot‐Savart's law gives easily the magnetic flux density.

The BIE using double layer charge is capable of treating robustly geometrical singularities at edges and corners. It is also capable of solving the problems with extremely high magnetic permeability.

The proposed BIE contains only the double layer charge while the conventional equations derived from the scalar potential contain the single and double layer charges as unknowns. In the multiply connected problems, the excitation potential in the material is derived from the magnetomotive force to represent the circulating fields due to multiply connected exciting currents.

This paper deals with the three‐dimensional modeling of massive conductors carrying a total imposed current and involving multiply connected regions. Both stationary motion and time harmonic eddy current problems are considered. The aim of the modeling is to determine the current distribution and the eddy current’s effects inside the conductor, as well as to calculate the Lorentz force acting on a conducting region. The choice of a suitable formulation based on solving the current vector potential T and the magnetic scalar potential φ is argued, then various methods for the restoration of the Ampere law in the multiply connected regions are presented. Two methods for calculating an auxiliary vector potential T₀ are applied in order to calculate the force acting on the armature of a railgun and the repulsion between the electrodes of a vacuum circuit breaker, then the results are compared.

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.

This paper aims to present the Cauchy problem for the Laplace’s equation for profiles of gas turbine blades with one and three cooling channels. The distribution of heat transfer coefficient and temperature on the outer boundary of the blade are known. On this basis, the temperature on inner surfaces of the blade (the walls of cooling channels) is determined.

Such posed inverse problem was solved using the finite element method in the domain of the discrete Fourier transform (DFT).

Calculations indicate that the regularization in the domain of the DFT enables obtaining a stable solution to the inverse problem. In the example under consideration, problems with reconstruction constant temperature, assumed on the outer boundary of the blade, in the vicinity of the trailing and leading edges occurred.

The application of DFT in connection with regularization is an original achievement presented in this study.

This paper proposes an automatic procedure to characterize discrete source fields.

A technique is developed to characterize curl‐conform fields to be used as source fields or non‐local basis functions in finite element formulations. A reduced characterization of such fields using curl‐conform finite elements is defined. An automatic construction of these curl‐conform spaces is proposed.

A reduced characterization of such fields is shown to be convenient for the coupling with complementary reaction fields and for simply and explicitly defining non‐local quantities, such as currents in h‐conform magnetodynamic formulations. The reduced form rests on the choice of supports for the fields limited to reduced cut spaces associated with cuts making the definition domain simply connected.

Develops a procedure to simplify the construction of curl‐conform source fields.

The paper aims to theoretically study the mathematical model of a steady flow of a heat-conductive incompressible viscous fluid through a spatially periodic plane profile cascade.

Reduction of the infinite periodical problem to one period. Leray-Schauder fixed point principle was used.

This study proves the existence of a weak solution for arbitrarily large given data (i.e. the inflow velocity and the acting specific body force).

The author proposed a special boundary condition on the outflow of the domain not only for the velocity and pressure but also for the temperature.

To the author’s knowledge, the problem has not been studied earlier. More detailed overview is given in the paper in the first part.

In this paper, a hybrid formulation for solving time harmonic eddy current problems in terms of magnetic field h is considered. In particular, we discuss some properties of the implicit boundary condition on the discrete level and the computation of the integral operator exploited in this context. An iterative technique is confirmed to be efficient in solving the arising, partly dense, complex linear system of equations. Furthermore, some test results, including timings for linear solvers are presented.

Benchmark problem 7 of the TEAM workshop consists of an asymmetrical conductor with a hole. 17 computer codes are applied, and 25 solutions are compared with each other and with experimental results for eddy current densities and flux densities. Most of the codes were found to give satisfactory solutions.