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Three sequential optimization methods, sequential least square method, sequential Kriging method, and sequential linear Bayesian method, are presented for the optimization design of electromagnetic device. Sequential optimization method (SOM) is composed of coarse optimization process and fine optimization process. The main purpose of the former is to reduce the design space; while the target of the latter is to update the optimal design parameters. To illustrate the performance of the proposed methods, an analytic test function and the TEAM Workshop Problem 22 are investigated. Experimental results of test function demonstrate that SOM can obtain satisfactory solutions; and practical application illustrates that the number of finite element sample points is less than 1/10 compared with that by direct optimization method, while the optimal results are even better than that by direct optimization method. Index Terms--Kriging, linear Bayesian estimation (LBE), response surface model, sequential optimization method (SOM).

The multiquadric radial basis function method (MQ RBF or, simply, MQ) developed recently is a truly meshless collocation method with global basis functions. It was introduced for solving many 1- and 2-D partial differential equations (PDEs), including linear and nonlinear problems. However, few works are found for electromagnetic PDEs, especially for 3-D problems. This paper presents an improved MQ collocation method for 3-D electromagnetic problems. Numerical results show a considerable improvement in accuracy over the traditional MQ collocation method, although both methods are direct collocation method with exponential convergence. Index Terms--Meshless method, multiquadric, 3-D problems.

This paper presents the boundary polynomial point interpolation meshless method (BPPIM) and the boundary radial point interpolation meshless method (BRPIM) based on the polynomial basis function (PBF) and radial basis function (RBF), respectively, for transient eddy-current analysis, and their interpolation shape functions satisfy the Kronecker delta function, thus, the essential boundary conditions can be directly imposed on the boundary nodes. An example on analyzing transient eddy current of a square metal column is set to prove the validity of the proposed methods, and a comparison on accuracy between BPPIM and BRPIM is analyzed as well. Index Terms--Boundary meshless method (BMM), polynomial basis function (PBF), radial basis function (RBF), transient eddy current.

The coupled problem of estimating the temperature rise due to the winding and core loss in a vertically oriented magnetic component is considered. The principle contributions in this paper are two-fold: 1) the coupling between the losses and thermal problems for the component is addressed accounting for the effects of nearby barriers and 2) the complication that the convection coefficient is not known accurately is overcome by means of solving a coupled electrothermal--air flow problem in order to characterize heat transfer to the ambient surroundings. It is shown that the coupling between the loss and temperature in the magnetic material has negligible effects on the temperature since the deviation in temperature is not more than 13% at worst if the loss is considered constant for different barrier-to-core distances. The convection coefficients of the core's top and side surfaces are shown not to be significantly influenced by the boundary condition imposed on the barrier. The boundary conditions substantially affect the temperature by introducing an additional path for heat transfer. Additionally, the contribution of radiation is found to be roughly 50% of the total loss regardless of the barrier height and distance and its boundary condition. Index Terms--Convection, heat transfer, loss-temperature coupling, radiation.

This paper discovers and researches problems on numerical oscillations of the solution in element-free Galerkin method (EFGM) when it uses high order polynomial basis, and puts forward the meshless method based on orthogonal basis (MLMBOB), which is composed of essential boundary conditions with Penalty method, then gets the numerical solutions of the partial differential equations. This method holds nearly all qualities of EFGM and removes many drawbacks of it, and it has high accuracy when high order orthogonal basis is used. Therefore, it is fit for many problems in engineering computational electromagnetics. Examples are given to prove the proposed method. Index Terms--Meshless method, moving least square approximations, numerical oscillation, orthogonal basis, penalty method.

We describe the implementation of a knowledge-based system for designing iron core inductors. We identify the underlying issues related to the implementation of such a system. We employ a recursive design methodology based on imitating an expert human designer that is suitable for embedding in the knowledge-based system. A hybrid knowledge base, using both frame-based and rule-bused paradigms, together with assertions and procedural attachment, captures inductor-oriented design expertise. The paper establishes a general framework whereby dedicated knowledge-bused systems for electromagnetic design can be built. It presents results that illustrate the performance of the developed system, particularly in comparison to the standard design procedure found in the literature. Index Terms--Design methodology, electromagnetic devices, inductors, knowledge-bused systems.

The development of a computational model for a turbulent electromagnetic stirring (EMS) flow system has considerable flexibility in terms of choosing model parameters and system equations. This paper examines the effect of key model parameters on the turbulent flow that is predicted for an industrial scale EMS system. It is shown that the choice of certain parameters can have a profound influence on the predicted flow. Index Terms--Continuous casting, electromagnetic stirring, material processing, MHD, turbulent flow.

We present a Green's function for a circular loop in a toroidal cavity in a high-permeability material. We show that under certain conditions, Green's function may be expressed in terms of Jacobi's theta functions. We demonstrate an application of such a Green's function in analyzing the performance of pot core transformers. Results compare well with the values obtained by other analytical methods and by the measurement. Index Terms--Coupled circuits method, elliptic functions, Green's function, pot core transformers.

A mathematical model that couples the electrical potential in the arc with the resulting thermal and flow fields has been developed to describe the behaviour of the arc plasma in DC electric arc furnace. The set of conservation equations, along with a potential equation for the electric field, were solved using the PHOENICS software package. Key aspects of the modelling problem, necessary to achieve a stable and meaningful numerical solution for the long DC electric arc, are evaluated. These aspects involve convergence issues as well as the treatment of the nonlinearities. Particular attention was given to the selection and adjustment of several under-relaxation factors.

Upwind-linear edge elements, which can eliminate the non-physical oscillation solution, are presented for 3D moving conductor eddy current problems. This numerical method allows the jump of the normal field component and increases the solution accuracy. The Galekin method is employed in non eddy current domain. This proposed method is used to discretize the formulation that uses the magnetic field intensity H as a variable in the whole solution region. Eddy current problems involving the moving effects are used to validate this technique.

Vector and scalar potential formulations are used together to facilitate accurate calculations of two-dimensional fields and forces in a synchronous motor. The scalar potential method employs a precomputed edge-based source field. The finite element model with a sliding surface in the air gap is implemented to obtain consistent results for the ripple force. Theoretical analysis presented in the paper and numerical results confirm the accuracy of the 'ripple solution' in the sliding surface model.

In this paper the Method of Fundamental Solution, which was originally develope for solving steady state problems, is extended to apply to 3D transient eddy current analysis formulated in terms of the Second Order Vector Potential. In numerical implementation, a time stepping convolution scheme is adopted to eliminate the need for volume discretization and domain calculation. Numerical results of a benchmark problem are provided to demonstrate the validity and accuracy of the technique.

A review of the computational methods that are typically used to model and analyze electromagnetic fields in power engineering applications is provided. The basic methods and applications are briefly reviewed. Emphasis is given to recent research. A comprehensive list of references is provided.

In the present work, the concept of the modified surface impedance boundary conditions (IBC) is extended to three dimensional eddy current problems. Approximate expressions for the modified surface impedances near sharp edges and corners are given. The validity of the expressions are examined by solving test problems using the Method of Fundamental Solutions. The results given by the approximate expressions are compared with the true values of surface impedances obtained from the full region solution (i.e. without the use of IBC) and those agree well with the latter.

This paper deals with the Boundary Element Analysis Method for 3-D transient eddy current problems formulated in terms of the Second Order Vector Potential (SOVP). Indirect boundary integral equations are derived using time-dependent fundamental solution and the fictitious source densities. In numerical implementation, a time stepping convolution approach is adopted to eliminate the need for volume discretization and domain integration. Numerical results of a benchmark problem are provided to demonstrate the validity and accuracy of the technique.

This paper describes the application of the Method of Fundamental Solutions (MFS) to 3D eddy current problems. The most salient feature of the method is that by locating the source points on an auxiliary boundary the singular kernels encountered in most BEM are avoided. Therefore good results can be obtained. A(super *) - PSI formulation is used in the 3D MFS. Furthermore, by eliminating the dependent coefficients from the equations, the unknowns are reduced by one on each node as compared to the conventional BEM. In so doing, a minimum order formulation is obtained. Two examples of the application of the approach are given in this paper. Results are compared with analytical solutions as well as the conventional BEM solutions.

In this paper, a novel and normalized Z-transform-based finite-difference time-domain (ZTFDTD) method is presented for simulating the interaction of the electromagnetic (EM) wave with unmagnetized plasma. The 2-D ZTFDTD formulations for unmagnetized plasma are derived. Using a simplified 2-D model for a perfectly conducting cylinder covered with unmagnetized plasma, the stealth effect of unmagnetized plasma is studied in different thicknesses of plasma, electron densities of plasma, EM wave frequencies, and plasma collision frequencies. Numerical results indicate that plasma stealth is effective in theory and reasonable selection for the plasma parameters can greatly enhance its effectiveness. Index Terms--Finite-difference time-domain (FDTD), plasma stealth, radar cross section (RCS), Z-transform.

This paper presents the multiquadrics collocation method (MQCM) for transient eddy current problems. Both the implicit scheme and Crank--Nicolson time matching scheme are used here for time discretization. An example on analyzing transient eddy current of a square metal column is illustrated to prove the accuracy and affectivity of the proposed method. Index Terms--Initial-boundary problem, meshless method, multiquadrics, transient eddy current.

This paper presents a boundary meshless method (BMLM) for transient eddy current problems. With difference to the traditional boundary element method (BEM), the BMLM combines a point interpolation method (PIM) for construction of spatial interpolation functions with a boundary integral formulation for the governing equations, thus the spatial interpolation functions satisfy the Kronecker delta function and the essential boundary condition can be directly imposed without any other procedure. Theoretical analysis in details is given and a transient eddy current example is also presented to prove the proposed theory. Index Terms--Boundary meshless method, initial-boundary problem, numerical analysis, transient eddy current.

This paper presents a wavelet-based multiresolution analysis method for solving the inverse problem in eddy current testing (ECT). Using the probe impedance signals as the measurement data, the reconstruction of conductivity profiles can be performed by a minimization scheme. The method allows to identify the regions where the perturbation may be localized and to retrieve the unknown parameters only in those regions. Some numerical simulation results show the feasibility of the technique. Index Terms--Eddy current testing, inverse problems, multiresolution analysis, probe impedance change.

The micro superconducting magnetic energy storage system is becoming a powerful tool for application in power systems. Nowadays, devices include active shielding systems instead of passive ferromagnetic shields. This calls for sophisticated analysis and design techniques able to provide satisfactory performance in terms of stored energy efficiency, reduced stray field, and/or minimal superconductor's volume. In this paper, the features of an active shielding system using multiple parallel solenoid configurations for superconducting magnets are analyzed and the results of their corresponding stray fields are compared. Two optimization strategies are briefly presented. The results using the proposed optimization strategies for magnet systems of energy capacity of 1 MJ, 5 MJ, and 10 MJ are given, respectively. Index Terms--Actively shielding, multiple parallel solenoids, optimized design, superconducting magnetic energy storage (SMES) system.

This paper presents the multiresolution algorithm for integral and boundary element formulations of electric and magnetic field problems. Incorporating the merits of entire domain and subsectional basis functions, a sparse matrix can be directly obtained. Thus, memory storage is reduced and, by using diagonal preconditioning, the solution of the equations can be accelerated. Index Terms--Electric and magnetic field computations, integral equation and boundary element methods, multiresolution, wavelet transforms.

In eddy-current testing (ECT), a thin-opening crack is frequently encountered. In this paper, such a crack is modeled by using an ideal crack, in which the eddy-current field perturbation due to the crack is described as the effect produced by an equivalent current dipole layer located on its surface. The dipole density can be found by solving an electric field integral equation. By following a moment method scheme, numerical predictions are made for steam generator tube ECT benchmark models Step 2 and Step 3, where a conductor plate and a tube wall, respectively, are detected. The probe impedance changes are evaluated and are compared with experiments, and good agreements are found. By using rapid algorithms to compute the dyadic Green's function, the total required CPU time is only several seconds for each problem. Index Terms--Crack, eddy-current testing, integral equation, numerical simulation.

The properties of edge element methods are further investigated through two types of mathematical models. H - [Phi] formulation is proposed for 3D moving conductor eddy current problems. Second-order nodal-based finite elements are used in non-eddy current region for easily dealing with interface conditions. Asymmetrical equation is calculated by improved BICG solver. Index terms - Moving conductor problems, H - [Phi] model, Second-order FEM.

A simple image method is described to predict the attenuation caused by a semi-infinite permeable layer on the static magnetic field produced by a 3-D conductor array. It is shown that the permeable layer gives rise to a array of current element images, of progressively smaller magnitude and increasing distance from the layer. The convergence of the method is examined. The method is applied to the problem of evaluating bottom electrode bus designs for a DC electric arc furnace. Index Terms - Image method, magnetostatic fields, permeable plate, magnetic shielding.

In this paper we analyze current flow in a long conductor which contains a step change in the conductivity. The cross section of the conductor is circular. An analytical method is used. The field variables are expressed in terms of Bessel and exponential functions. Expressions are derived for the current density and the incremental resistance introduced by the discontinuity. Numerical results are presented to show the dependence of the incremental resistance on the conductivity change. Qualitative expressions are provided for the incremental resistance. Index Terms - Analytical, Bessel functions, discontinuous conductivity, eddy currents.

This paper presents a wavelet-Galerkin method to solve dynamic electromagnetic field problems. It differs from some former methods which discretize the whole space domain using wavelet functions, however it discretizes the space domain with finite element, because of its flexibility to the boundary. At the same time, it introduces the scaling function as trial functions for time domain, which are space orthogonal along the real line but has poor ability to adapt complex boundaries. Thus, it corporates both's merits. The results are better without suffering too much calculation time.

A novel numerical method, which uses linear edge elements in eddy current region and nodal finite elements in non eddy current regions, is presented for solving 3D eddy current problems. The mathematical models are divided into two parts according to their properties. the theory of linear edge elements is developed. The test results show the validity of the algorithm.

This paper deals with a hybrid FEM-SERIES formulation and solution for axisymmetricai linear and nonlinear magnetostatic problems with an open region. In the interior region, a conventional FEM is formulated, while a SERIES formulation is proposed in the exterior region. Several examples are given for illustration and the numerical results are compared with those obtained by finite element solutions.

This paper establishes a means by which the volume and position of nonmagnetic spherical solidified bodies suspended in a magnetic fluid can be ascertained. This information is obtained by monitoring the change in flux as a function of the sphere's position and radius. The calculated and experimental results are in good agreement.

This paper describes the application of the Method of Fundamental Solutions to steady state three-dimensional eddy current problems based on the second order vector potential formulation. Numerical results of two test problems using the technique are provided and compared with the available BEM and analytical solutions.

Finite element method is used for obtaining unique magnetization distribution M and the corresponding internal magnetic field H inside magnetic materials subjected to an applied field. The finite element method has obtained M directly by finding the minimum of a given mathematical function [W.sub.M](M) that is interpreted as the sum of the internal free energy of polarization and internal and external magnetic energies.

An analytical approach using simplified expressions is described for estimating the tangential component of the magnetic field at the surface of pot core transformers. The tangential field is used for estimating core loss, which is important for designing the transformers used at high frequency.

Three design methods, widely used for high frequency inductors and transformers, are critically compared using, as a basis, the example of low profile, small footprint, low loss 500 kHz devices. In comparison to the results obtained from more detailed Finite Element models, it is shown that the standard methods provide surprisingly good estimates of the copper and core losses. Index Terms--efficiency, high frequency devices, inductors and transformers, magnetic devices.