An interval finite element method for electromagnetic problems with spatially uncertain parameters

During the manufacturing process of dielectric materials used in electromagnetic engineering, the electromagnetic parameters are often spatially uncertain due to the processing technology, environmental temperature, personal operations, etc. Traditionally,the random field model can be used to measure the spatial uncertainties, but its construction requires a large number of samples.On the contrary, the interval field model only needs the upper and lower bounds of the spatially uncertain parameters, which requires much less samples and furthermore is easy to understand and use for engineers. Therefore, in this paper, the interval field model is introduced to describe the spatial uncertainties of dielectric materials, and then an interval finite element method(IFEM) is proposed to calculate the upper and lower bounds of electromagnetic responses. Firstly, the interval field of the dielectric material is represented by the interval K-L expansion and inserted into the scalar Helmholtz wave equations, and thus the interval equilibrium equations are constructed according to the node-based finite element method. Secondly, a perturbation interval finite element method is developed for calculating the upper and lower bounds of electromagnetic responses such as the electric strength and magnetic strength. Finally, the effectiveness of the proposed method is verified by three numerical examples.

Efficient Solution to Electromagnetic Scattering Problems of Bodies of Revolution by Compressive Sensing

Under the theory structure of compressive sensing （CS）, an underdetermined equation is deduced for describing the discrete solution of the electromagnetic integral equation of body of revolution （BOR）, which will result in a small-scale impedance matrix. In the new linear equation system, the small-scale impedance matrix can be regarded as the measurement matrix in CS, while the excited vector is the measurement of unknown currents. Instead of solving dense full rank matrix equations by the iterative method, with suitable sparse representation, for unknown currents on the surface of BOR, the entire current can be accurately obtained by reconstructed algorithms in CS for small-scale undetermined equations. Numerical results show that the proposed method can greatly improve the computgtional efficiency and can decrease memory consumed.

Application of Multi-Grid Method to the Computation of Electromagnetic Scattering Problems

The multi-grid method has been known as an efficient iterative method for the linear systems and nonlinear systems that arise from finite difference approximations for partial differential equations. In this paper, the multigrid method is extended to the application of solving integral equations which appear in electromagnetic scattering problems. The diakoptic theory is used for this purpose. Compared with other methods, the numerical results show that the multigrid method is powerful to solve electromagnetic scattering problems and can be used to compute electromagnetic scattering problems with electrically large bodies and complex structures.

Non-Intrusive Magneto-Optic Detecting System for Investigations of Air Switching Arcs

In current investigations of electric arc plasmas, experiments based on modern testing technology play an important role. To enrich the testing methods and contribute to the understanding and grasping of the inherent mechanism of air switching arcs, in this paper, a nonintrusive detecting system is described that combines the magneto-optic imaging（MOI） technique with the solution to inverse electromagnetic problems. The detecting system works in a sequence of main steps as follows： MOI of the variation of the arc flux density over a plane, magnetic field information extracted from the magneto-optic（MO） images, arc current density distribution and spatial pattern reconstruction by inverting the resulting field data. Correspondingly, in the system, an MOI set-up is designed based on the Faraday effect and the polarization properties of light, and an intelligent inversion algorithm is proposed that involves simulated annealing（SA）.Experiments were carried out for high current（2 kA RMS） discharge cases in a typical low-voltage switchgear. The results show that the MO detection system possesses the advantages of visualization, high resolution and response, and electrical insulation, which provides a novel diagnostics tool for further studies of the arc.

Optimal Design of Electrical Machines Assisted by Hybrid Surrogate Model Based Algorithm

In this paper,for design of large-scale electromagnetic problems,a novel robust global optimization algorithm based on surrogate models is presented.The proposed algorithm can automatically select a proper meta-model technique among multiple alternatives.In this paper,three representative meta-modeling techniques including ordinary Kriging,universal Kriging,and response surface method with multi-quadratic radial basis functions are applied.In each optimization iteration,the above three models are used for parallel calculation.The proposed hybrid surrogate model optimization algorithm synthesizes advantages of these different meta-models.Without verification of a specific meta-model,a suitable one for the engineering problem to be analyzed is automatically selected.Therefore,the proposed algorithm intends to make a better trade-off between numerical efficiency and searching accuracy for solving engineering problems,which are characterized by stronger non-linearity,higher complexity,non-convex feasible region,and expensive performance analysis.

REALISTIC AND CORRECT MODELS OF IMPRESSED SOURCES FOR TIME-HARMONIC ELECTROMAGNETIC BOUNDARY VALUE PROBLEMS INVOLVING METAMATERIALS

The aim of this work is to analyze the role of the impressed sources in determining the well or ill-posedness of time harmonic electromagnetic boundary value problems involving isotropic effective media.It is shown,in particular,that,even if all interfaces are regular,the class of ill-posed problems can be very large in the presence of general square-integrable impressed sources.However,when a simple and realistic constraint is enforced on these sources,requiring that the support of the sources does not include any interface between a traditional medium and a metamaterial,among the problems here considered just those involving an interface between complementary materials remain ill-posed.These considerations have a very significant impact also on the approximability of the solution of well-posed problems since the numerical noise can introduce small fictitious sources even where the sources to be simulated are not present.These effects on finite element simulators are fully analyzed.Finally,we propose an algorithm that allows to obtain much better approximations of the solutions of the most critical wellposed problems.

A moment-based stochastic edge-based smoothed finite element method for electromagnetic forming process

In this paper, a novel stochastic method named as the moment-based stochastic edge-based finite element method(MSES-FEM)is proposed to deal with the uncertain electromagnetic problems. First, electromagnetic and mechanical field are formulated by smoothed Galerkin Weak Form under edge-based smoothed finite element method(ES-FEM) scheme. The moment analysis is then applied to obtain the first four moments of the responses and to observe the effects of each random variable on electromagnetic field responses. The maximum entropy theory is employed to calculate the probability density functions(PDFs) of the responses. A quasi-static electromagnetic problem and a practical electromagnetic forming problem(EMF) are performed. The proposed method successfully solves stochastic electromagnetic forming analysis under the uncertain parameters. Numerical results obtained by the proposed MSES-FEM are quite satisfactory with the ones by the Monte Carlo simulation(MCS).

An Application of the Inverse Solution for Electric Current Distribution From Magnetic Field Measurements in Aluminium Electrolysis Cells

A mathematical theory and the software application based on the full MHD model of the electrolysis cell is used to predict the electric current distribution over the anodes from the measurement of magnetic fields at specifically defined node points assumed to be available from the wireless sensors.The full 3d busbar configuration of two different commercial ceils are used for the model simulations.It is demonstrated that a unique solution for the electric current can be obtained when two sensors per each anode are used to detect the single component of magnetic field.The mathematical software is tested for the sensitivity to the busbar configuration complexity.The ability to monitor continuously the electric current distribution to high accuracy helps to control disturbances and deviations from a normal production process.