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The electromagnetic fields have a great influence on the behaviour of all the living systems. The as low as reasonably achievable (ALARA) principle imposes, in case of long exposures to low (i.e. power systems) or high frequency (i.e. microwave systems or cell phones) fields, some limitations to the radiated fields by the industrial equipment. On the other hand, some benefits can be taken from the effects of the electromagnetic fields on the living being: the hyperthermal technique is well known for the treatment of the cancer. Either we want to be protected from the fields, or we want to take benefit of the positive effects of these fields, all the effects thermal as well as genetic have to be well known. Like in any industrial application, the electromagnetic field computation allows a better knowledge of the phenomena, and an optimised design. Hence, there is a very important challenge for the techniques of computation of electromagnetic fields. The major difficulties that appear are: (1) related to the material properties – the “material” (the human body) has very unusual properties (magnetic permeability, electric permittivity, electric conductivity), these properties are not well known and depend on the activity of the person, and this material is an active material at the cell scale; (2) related to the coupling phenomena – the problem is actually a coupled problem: the thermal effect is one of the major effects and it is affected by the blood circulation; (3) related to the geometry – the geometry is complex and one has to take into account the environment. The problems that we have to face with are – the identification of the properties of the “material”, the coupled problem solution and the representation of the simulated phenomena.

This paper presents new trends in parallel methods used to solve finite element matrix systems: standard iterative and direct solving methods first, and then domain decomposition methods. For example, the current status and properties of two prevailing programming environments (PVM and MPI) are finally given and compared when implemented together with a finite element time domain formulation.

This paper aims to present a novel hybrid time integration approach for efficient numerical simulations of multiscale problems involving interactions of electromagnetic fields with fine structures.

The entire computational domain is discretized with a coarse grid and a locally refined subgrid containing the tiny objects. On the coarse grid, the time integration of Maxwell’s equations is realized by the conventional finite-difference technique, while on the subgrid, the unconditionally stable Krylov-subspace-exponential method is adopted to breakthrough the Courant–Friedrichs–Lewy stability condition.

It is shown that in contrast with the conventional finite-difference time-domain method, the proposed approach significantly reduces the memory costs and computation time while providing comparative results.

An efficient hybrid time integration approach for numerical simulations of multiscale electromagnetic problems is presented.

Inverting electroheat problems involves synthesizing the electromagnetic arrangement of coils and geometries to realize a desired heat distribution. To this end two finite element problems need to be solved, first for the magnetic fields and the joule heat that the associated eddy currents generate and then, based on these heat sources, the second problem for heat distribution. This two-part problem needs to be iterated on to obtain the desired thermal distribution by optimization. Being a time consuming process, the purpose of this paper is to parallelize the process using the graphics processing unit (GPU) and the real-coded genetic algorithm, each for both speed and accuracy.

This coupled problem represents a heavy computational load with long wait-times for results. The GPU has recently been demonstrated to enhance the efficiency and accuracy of the finite element computations and cut down solution times. It has also been used to speedup the naturally parallel genetic algorithm. The authors use the GPU to perform coupled electroheat finite element optimization by the genetic algorithm to achieve computational efficiencies far better than those reported for a single finite element problem. In the genetic algorithm, coding objective functions in real numbers rather than binary arithmetic gives added speed and accuracy.

The feasibility of the method proposed to reduce computational time and increase accuracy is established through the simple problem of shaping a current carrying conductor so as to yield a constant temperature along a line. The authors obtained a speedup (CPU time to GPU time ratio) saturating to about 28 at a population size of 500 because of increasing communications between threads. But this far better than what is possible on a workstation.

By using the intrinsically parallel genetic algorithm on a GPU, large complex coupled problems may be solved very quickly. The method demonstrated here without accounting for radiation and convection, may be trivially extended to more completely modeled electroheat systems. Since the primary purpose here is to establish methodology and feasibility, the thermal problem is simplified by neglecting convection and radiation. While that introduces some error, the computational procedure is still validated.

The methodology established has direct applications in electrical machine design, metallurgical mixing processes, and hyperthermia treatment in oncology. In these three practical application areas, the authors need to compute the exciting coil (or antenna) arrangement (current magnitude and phase) and device geometry that would accomplish a desired heat distribution to achieve mixing, reduce machine heat or burn cancerous tissue. This process presented does it more accurately and speedily.

Particularly the above-mentioned application in oncology will alleviate human suffering through use in hyperthermia treatment planning in cancer treatment. The method presented provides scope for new commercial software development and employment.

Previous finite element shape optimization of coupled electroheat problems by this group used gradient methods whose difficulties are explained. Others have used analytical and circuit models in place of finite elements. This paper applies the massive parallelization possible with GPUs to the inherently parallel genetic algorithm, and extends it from single field system problems to coupled problems, and thereby realizes practicable solution times for such a computationally complex problem. Further, by using GPU computations rather than CPU, accuracy is enhanced. And then by using real number rather than binary coding for object functions, further accuracy and speed gains are realized.

Improved numerical calculation techniques for low‐frequency current density distributions within high‐resolution anatomy models caused by ambient electric or magnetic fields or direct contact to potential drops using the finite integration technique (FIT).

The methodology of calculating low‐frequency electromagnetic fields within high‐resolution anatomy models using the FIT is extended by a local grid refinement scheme using a non‐matching‐grid formulation domain. Furthermore, distributed computing techniques are presented. Several numerical examples are analyzed using these techniques.

Numerical simulations of low‐frequency current density distributions may now be performed with a higher accuracy due to an increased local grid resolution in the areas of interest in the human body voxel models when using the presented techniques.

The local subgridding approach is introduced to reduce the number of unknowns in the very large‐scale linear algebraic systems of equations that have to be solved and thus to reduce the required computational time and memory resources. The use of distributed computation techniques such as, e.g. the use of a parallel solver package as PETSc follows the same goals.

The purpose of this paper is to combine the Jiles-Atherton (J-A) hysteresis model with the field separation approach to realize the accurate simulation of dynamic magnetostrictive characteristics of silicon steel sheet.

First, the energy loss of silicon steel sheet is divided into hysteresis loss Why, classical eddy current loss Wed and anomalous loss Wan according to the statistical theory of losses. The Why is calculated by static J-A hysteresis model, Wed and Wan are calculated by the analytical formulae. Then, based on the field separation approach, the dynamic magnetic field is derived. Finally, a new dynamic magnetostrictive model is proposed by means of the quadratic domain rotation model.

Comparison of simulation and experimental results verifies that the proposed model has high accuracy and strong universality.

The proposed method improves the existing method’s problem of relying on too much experimental data, and the method ensures the calculation accuracy, parameter identification accuracy and engineering practicability. Consequently, the presented work greatly facilitates further explorations and studies on simulation of dynamic magnetostrictive characteristics of silicon steel sheet.

The purpose of this paper is to propose a chaotic optimization method for identifying the parameters of the Jiles–Atherton (J-A) hysteresis model.

The J-A model has five parameters which are assigned with physical meaning and whose determination is demanding. To determine these parameters, the fitness function, which represents the difference between the measured and the modeled hysteresis loop, is formed. Optimal parameter values are the values that minimize the fitness function.

The parameters of J-A model for three magnetic materials are determined. The model with the optimal parameters is validated using measured data and comparison with particle swarm optimization algorithm, genetic algorithm, pattern search and simulated annealing algorithm. The results show that the proposed method provides better agreement between measured and modeled hysteresis loop than other methods used for comparison. The proposed method is also suitable for simultaneous optimization of multiple hysteresis loops.

Chaotic optimization method is implemented for the first time for J-A model parameter identification. Numerical comparisons with results obtained with other optimization algorithms demonstrate that this method is a suitable alternative in parameters identification of J-A hysteresis model. Furthermore, this method is easy to implement and set up.

Improperly fitted parameters for the Jiles–Atherton (JA) hysteresis model can lead to non-physical hysteresis loops when ferromagnetic materials are simulated. This can be remedied by including a proper physical constraint in the parameter-fitting optimization algorithm. This paper aims to implement the constraint in the meta-heuristic simulated annealing (SA) optimization and Nelder–Mead simplex (NMS) algorithms to find JA model parameters that yield a physical hysteresis loop. The quasi-static B(H)-characteristics of a non-oriented (NO) silicon steel sheet are simulated, using existing measurements from a single sheet tester. Hysteresis loops received from the JA model under modified logistic function and piecewise cubic spline fitted to the average M(H) curve are compared against the measured minor and major hysteresis loops.

A physical constraint takes into account the anhysteretic susceptibility at the origin. This helps in the optimization decision-making, whether to accept or reject randomly generated parameters at a given iteration step. A combination of global and local heuristic optimization methods is used to determine the parameters of the JA hysteresis model. First, the SA method is applied and after that the NMS method is used in the process.

The implementation of a physical constraint improves the robustness of the parameter fitting and leads to more physical hysteresis loops. Modeling the anhysteretic magnetization by a spline fitted to the average of a measured major hysteresis loop provides a significantly better fit with the data than using analytical functions for the purpose. The results show that a modified logistic function can be considered a suitable anhysteretic (analytical) function for the NO silicon steel used in this paper. At high magnitude excitations, the average M(H) curve yields the proper fitting with the measured hysteresis loop. However, the parameters valid for the major hysteresis loop do not produce proper fitting for minor hysteresis loops.

The physical constraint is added in the SA and NMS optimization algorithms. The optimization algorithms are taken from the GNU Scientific Library, which is available from the GNU project. The methods described in this paper can be applied to estimate the physical parameters of the JA hysteresis model, particularly for the unidirectional alternating B(H) characteristics of NO silicon steel.

The purpose of this paper is to introduce a chaotic harmony search (CHS) approach based on the chaotic Zaslavskii map to parameters identification of Jiles-Atherton vector hysteresis model.

In laminated magnetic cores when the magnetic flux rotates in the lamination plane, one observes an increase in the magnetic losses. The magnetization in these regions is very complex needing a vector model to analyze and predict its behavior. The vector Jiles-Atherton hysteresis model can be employed in rotational flux modeling. The vector Jiles-Atherton model needs a set of five parameters for each space direction taken into account. In this context, a significant amount of research has already been undertaken to investigate the application of metaheuristics in solving difficult engineering optimization problems. Harmony search (HS) is a derivative-free real parameter optimization metaheuristic algorithm, and it draws inspiration from the musical improvisation process of searching for a perfect state of harmony. In this paper, a CHS approach based on the chaotic Zaslavskii map is proposed and evaluated.

The proposed CHS presents an efficient strategy to improve the search performance in preventing premature convergence to local minima when compared with the classical HS algorithm. Numerical comparisons with results using classical HS, genetic algorithms (GAs), particle swarm optimization (PSO), and evolution strategies (ES) demonstrated that the performance of the CHS is promising in parameters identification of Jiles-Atherton vector hysteresis model.

This paper presents an efficient CHS approach applied to parameters identification of Jiles-Atherton vector hysteresis model.

The purpose of this paper is to implement a simple, fast and accurate heuristic method for parameter determination of Jiles‐Atherton (JA) hysteresis model for representing magnetization in electrical steel sheets. The performance of the method is validated using measured data and comparison with previous methods.

JA model requires five parameters to represent the hysteretic behavior of ferromagnetic materials. In order to determine these parameters, measured hysteresis loop is used here to calculate a fitness function which is defined by comparing the measured and simulated magnetization loops. This fitness function is minimized by optimization algorithms.

In total, four different measured hysteresis loops are studied in this paper. Each optimization algorithm is executed 50 times to investigate the convergence, speed, and accuracy of six methods. All methods begin with the same randomly generated initial parameters. Physical boundaries are used for parameters to avoid unaccepted results. Thorough examination of results shows that the proposed method is more appropriate than previously implemented methods for the parameter determination of Jiles‐Atherton model in all studied cases. The required parameters for each optimization method are also presented.

Shuffled frog leaping algorithm (SFLA) is implemented for the first time for JA model parameter determination. The results show that SFLA is faster and more accurate in comparison with other methods. Furthermore, this algorithm is easy to implement and tune.