I.R. Ciric

Simple analytical expressions for the magnetic field of current coils

Current coils are decomposed in straight segments of rectangular cross section whose sides are trapezoidal in general. For curved coil portions, the appropriate number of straight segments is considered in terms of the desired accuracy. Simple formulas are derived for the contribution of such a coil segment to the resultant magnetic field by modeling the given volume current density in terms of a distribution of fictitious magnetization inside the segment volume and corresponding surface currents and magnetic charges. The expressions obtained contain only elementary functions, and computed results illustrate their efficiency with respect to existing analytical and numerical integration methods. >

Single integral evaluation for wave scattering by a layered dielectric cylinder

The problem of wave scattering by layered dielectric cylinders is solved through a region-by-region application of a single integral equation formalism. Computational time is dramatically reduced as compared to that required by coupled surface integral equation methods, namely by a factor proportional to the square of the number of layers.

Single source integral equation for wave scattering by multiply-connected dielectric cylinders

The problem of wave scattering by multiply-connected dielectric cylinders is solved through the application of a single source integral equation. The formulation is similar to that of the well known electric field integral equation (which uses coupled sources of electric and magnetic surface currents), but with the particular fields defined such that the scattered field is a function only of an electric surface current which is distributed over all interfaces. Results of two example calculations with this method are compared with those from the electric field integral equation to demonstrate the increased efficiency of the single source integral equation method.

Modelling eddy currents in thin shields

Purpose – The purpose of this paper is to present a simplified rigorous mathematical formulation of the problem of electric currents induced in thin shields with holes yielding more efficient numerical computations with respect to available methods.Design/methodology/approach – A surface integral equation satisfied by the current density was constructed, which is, subsequently, represented at any point by linear combinations of novel vector basis functions only associated with the interior nodes of the discretization mesh, such that the current continuity is everywhere insured. The existence of the holes in the shield is taken into account by associating only one surface vector function with each hole. A method of moments is then applied to compute the scalar coefficients of the vector functions employed.Findings – It was found that the induced current distribution for shields with holes having the complexity of real world structures can be determined with a satisfactory accuracy utilizing a moderate size...

Novel Solution to Eddy-Current Heating of Ferromagnetic Bodies With Nonlinear

An efficient solution is presented for coupled nonlinear eddy currents-thermal diffusion problems. Applying the fixed-point polarization method to the nonlinear eddy-current field problem, with the magnetization dependent on magnetic induction and on temperature, allows the field computation to be performed for each harmonic separately. Since the fictitious permeability can be chosen to be everywhere that of free space, the matrices of the linear systems to be solved at each iteration remain unchanged even when the nonlinear characteristic changes with the temperature. A simple integral equation is used to compute the eddy currents, the inversion of the matrices corresponding to the harmonics being performed only once, before starting the iterative process. The heat conduction-diffusion equation is solved at each time step by the finite-element method. Three illustrative examples are also presented.

{\mbi B}\hbox{–}{\mbi H}

A new procedure for the study of the evolution of the solid phase in a moving solidifying ferromagnetic metal is proposed. The temperature distribution is controlled using eddy currents induced by a coil that covers partially the crucible surface and by cooling the rest of it, with an imposed crucible velocity. Analysis of the thermal field requires the solution of the time-periodic eddy-current problem coupled with the thermal diffusion problem. The nonlinearity of the B-H relation within the ferromagnetic material of the yoke and inside the solidified material cooled below the Curie point, as well as its dependence on temperature, are taken into consideration. Application of the polarization fixed point method allows the construction of an integral equation for eddy currents and always ensures the convergence of the iterative solution. At each time step, the heat diffusion equation is solved through a standard finite element technique, with the thermal conductivity and the specific heat capacity dependent on temperature.

Characteristic Dependent on Temperature

A new surface integral formulation is presented for time-harmonic quasistationary fields in systems of parallel hollow and/or layered solid conductors carrying electric currents and/or immersed in given transverse magnetic fields. The formulation yields an integral equation for a single unknown function over only one of the interfaces of the conductors. The amount of numerical computation needed for the field problem solution is substantially reduced with respect to that required by coupled boundary integral equation techniques, where two unknown functions over all the conductor interfaces are involved. The accuracy of the computed results is determined by using an exact analytical solution. Various test results are compared with those generated from existent boundary integral methods in order to demonstrate the high efficiency of the proposed solution method.

Efficient Analysis of the Solidification of Moving Ferromagnetic Bodies With Eddy-Current Control

An efficient boundary integral equation solution for magnetic field problems is presented, based on a novel magnetic vector potential formulation and using edge elements and tree-cotree spanning. A zero normal component of this vector potential A and the condition for its line integral along any closed path on the boundary are imposed such that the continuity of the normal component of the magnetic flux density is rigorously satisfied. The unknowns employed are the tangential components of /spl nabla//spl times/A and only the tree edge element values. Multiply connected domains are easily dealt with by introducing certain pairs of cotree edges in the set of tree edges, which are used to construct the cuts that transform a multiply connected domain into a simply connected one. The line integrals of A along the cut loops are determined by the respective magnetic fluxes. The stiffness matrix can easily be obtained. Three illustrative examples are given.

Reduced single integral equation for quasistationary fields in solid conductor systems

The quasi-stationary field of a magnetic dipole in free space is modeled by using the field due to a succession of dipoles oriented along any line between the poles of the original. Dipole, the two fields being identical everywhere except for the points on that line. By choosing appropriately the path of the equivalent string of dipoles, the resultant field due to the original dipole can be obtained from the superposition of fields with a simpler structure. In this paper, the proposed modeling method is illustrated for the quasi-stationary ac field of an arbitrarily located and oriented dipole in the presence of a conducting spherical shell, with the analytic expression of the field quantities derived in terms of single series, which are much more convergent than the double series in the expressions available in the literature. The model presented can be applied efficiently for analyzing eddy-current problems and electromagnetic shielding by various spherical, cylindrical, and planar structures in the presence of arbitrary distributions of electric current.

Magnetic vector potential tree edge values for boundary elements

In the electrical impedance imaging algorithms developed so far, the inverse problems involved are treated by using either iterative methods, which generate more accurate results but require large amounts of computation time, or non-iterative methods that are faster but produce less accurate results. In this paper, a new iterative procedure for electrical impedance imaging is presented. At each iteration step, the updated conductivity distribution is used to solve a forward problem and two-layer backpropagation neural networks with nonlinear activation functions are employed for solving an inverse problem. This allows for a smaller computation time with respect to other iterative methods and, at the same time, yields accurate images. Comparison with results obtained by applying an existing impedance tomography algorithm illustrates the efficiency of the proposed iterative method.