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Non‐divergent and irrotational projection operators are proposed and implemented in a FORTRAN program for the direct vector solution of Laplacian electric and magnetic fields, using finite element approximations. It is shown that this approach, in addition to giving continuous electric and magnetic fields, yields far more accurate results compared to the regular potential formulations. Some properties of the matrices are derived.

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.

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.

As commercial and military aircraft continue to be subject to direct lightning flashes, there is a great need to characterize correctly the electrical currents and electric potential fluctuations on an aircraft to determine alternative design approaches to minimizing the severity of the lightning-aircraft dynamics. Moreover, with the increased severity of thunderstorms due to global warming, the need arises even more to predict and quantify electrical characteristics of the lightning-aircraft electrodynamics, which is normally not measurable, using a reliable electric model of the aircraft. Such a model is advanced here. The paper aims to discuss these issues.

The case considered in this paper is that of an aircraft directly attached to an earth flash lightning channel. The paper develops a new approach to modelling the aircraft using electric dipoles. The model has the power to represent sharp edges such as wings, tail ends and radome for any aircraft with different dimensions by using a number of different sized dipoles. The distributed transmission line model (TLM) of the lightning return stroke incorporating the distributed aircraft model is used to determine aircraft electrical elements and finally the electric current induced on the aircraft body due to lightning's interaction with the aircraft. The model is validated by the waveform method and experimental results.

The dipole model proposed is a very powerful tool for minute representation of the different shapes of aircraft frame and to determine the best geometrical shape and fuselage material to reduce electric stress. This charge simulation method costs less computer storage and faster computing time.

The paper for the first time presents a computer-based simulation tool that allows scientists and engineers to study the dynamics of voltage and current along the aircraft surface when the aircraft is attached to a cloud to ground lightning channel.

Presents a review on implementing finite element methods on supercomputers, workstations and PCs and gives main trends in hardware and software developments. An appendix included at the end of the paper presents a bibliography on the subjects retrospectively to 1985 and approximately 1,100 references are listed.

This paper aims to show that simple geometry‐based hp‐algorithms using an explicit a posteriori error estimator are efficient in wave propagation computation of complex structures containing geometric singularities.

Four different hp‐algorithms are compared with common h‐ and p‐adaptation in electrostatic and time‐harmonic problems regarding efficiency in number of degrees of freedom and runtime. An explicit a posteriori error estimator in energy norm is used for adaptive algorithms.

Residual‐based error estimation is sufficient to control the adaptation process. A geometry‐based hp‐algorithm produces the smallest number of degrees of freedom and results in shortest runtime. Predicted error algorithms may choose inappropriate kind of refinement method depending on p‐enrichment threshold value. Achieving exponential error convergence is sensitive to the element‐wise decision on h‐refinement or p‐enrichment.

Initial mesh size must be sufficiently small to confine influence of phase lag error.

Information on implementation of hp‐algorithm and use of explicit error estimator in electromagnetic wave propagation is provided.

The paper is a resource for developing efficient finite element software for high‐frequency electromagnetic field computation providing guaranteed error bound.

This paper details how the equations describing the magnetic field inside the motor and the equations of its electric circuit can be integrated in one only system, which can be solved using the Finite Element Method (FEM). When a model of a circuit is used, the solution of the magnetic field equation is the input to calculate the currents of the machine windings. As the magnetic field depends on these currents, it is necessary to follow an iterative process until initial and final currents match. With the technique proposed in this paper, because both magnetic field equations and electric circuit equations are integrated in the system, just in one step, the currents and induced voltages can be obtained with high accuracy and considerable time saving.

Centres on the decomposition of the total electromagnetic torque of electrical machines for two components. The proposed idea of decomposition relies on the physical meaning of currents that appear in electromagnetic field region. The first torque component acts on external and conduction currents, the second on the material medium particles currents. Proves the main equations with the help of differential Maxwell’s equations. An example has been shown of the calculation of electromagnetic torque components for a synchronous salient‐pole generator.

Stochastic methods offer a certain robustness quality to optimization process. In this paper, the genetic algorithm, based on the computer simulation of the natural evolution, is used for the shape optimization of an electromagnetic actuator. The framework is modeled by a 2D finite element method allowing the computation of the magnetic force. The aim is to obtain a desired force profile considering the armature movement.

The purpose of this paper is to investigate the accuracy of different force calculation methods and their impact on mechanical deformations. For this purpose, a micrometer scaled actuator is considered, which consists of a micro‐coil and of a permanent magnet (PM) embedded in a deformable elastomeric layer.

For the magnetic field evaluation a hybrid numerical approach (finite element method/boundary element method (FEM/BEM) coupling and a FEM/BEM/Biot‐Savart approach) is used, whereas FEM is implemented for the mechanical deformation analysis. Furthermore, for the magneto‐mechanical coupling several force calculation methods, namely the Maxwell stress tensor, the virtual work approach and the equivalent magnetic sources methods, are considered and compared to each other and to laboratory measurements.

The numerically evaluated magnetic forces and the measured ones are in good accordance with each other with respect to the normal force acting on the PM. Nevertheless, depending on the used method the tangential force components differ from each other, which leads to slightly different mechanical deformations.

Since the force calculations are compared to measurement data, it is possible to give a suggestion about their applicability. The mechanical behavior of the actuator due to the acting forces is solely calculated and therefore only an assumption concerning the deformation can be given.

A new kind of micrometer scaled actuator is numerically investigated by using two different hybrid approaches for the magnetic field evaluation. Based on those, the results of several force calculation methods are compared to measurement data. Furthermore, a subsequent structural analysis is performed, which shows slightly different mechanical deformations depending on the used force calculation method.