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We present a level set method for numerical shape optimization of electromagnetic systems. The level set method does not only lead to efficient computational schemes, but also is able to handle topological changes such as merging, splitting and even disappearing of connected components. The velocity field on boundaries is obtained by a shape derivative of continuum sensitivity analysis using the material derivative concept and an adjoint variable technique. Two numerical results of dielectric optimization between electrodes showed that the level set method is feasible and effective in solving shape optimization problems of electromagnetic systems. Index Terms--Continuum sensitivity, finite-element analysis (FEA), level set method, shape optimization.

In this paper, we present an efficient modeling scheme based on a level set approach for electromagnetic systems including moving parts. The combination of finite elements and the level-set technique allows us to trace the interface variation on a fixed mesh of finite element. It does not require remeshing for the evolving geometry. The material data of moving objects is easily set using the Heaviside function obtained from the level set equation. For the driving force of dynamics equation, the total force on dielectric object is obtained by integrating the body force density of electric charge method. The numerical results of the test model show usefulness of the proposed scheme. Index Terms--Dynamics, finite element modeling, level set method, moving object.

In this paper, an implementation of virtual work principle in virtual air gap is proposed for the calculation of contact and body forces. To calculate the proper values of the magnetic field at virtual air-gap, we exploit the generalized magnetic source methods. It is shown that appropriately sized virtual elements can be allocated in the virtual air-gap by one-dimensionally extending the virtual gap while keeping the previously calculated field intensity. Both an element's and total forces can be obtained by virtual distortion of the concerned virtual elements. The proposed method provides a good accuracy even when the two contacting objects have the different permeability. As a validation, numerical examples are presented for the force distribution and total force. Index Terms--Body force distribution, force calculation, virtual air gap, virtual element, virtual work principle.

This paper proposes a coupling method involving the finite element (FE) equation of a discretized region and an analytical equation along with the field singularity of line currents in two-dimensional space. The singular field in the interior region is represented by Green's function of the line source, and the exterior region of air, conductor, or ferromagnetic material is represented by using the finite element method (FEM). An analytical expression for a magnetic field that contains unknown coefficients is coupled with the FE formulation for a coupled system equation with a matrix form. A numerical experiment relating to a line current near a ferromagnetic material shows the validity of this coupling method. Index Terms--Analytical solution, coupling schemes finite element method (FEM), Fourier series expansion, singular line current.

In this paper, a numerical scheme for obtaining ferrofluid shape formation is presented using the revisited Kelvin's force formula. The formula adopts the newly appreciated field intensity from the original Kelvin's concept and the virtual air gap scheme. For the hydrostatic equilibrium subject to magneto-static field, both electromagnetic and gravitational body forces should be considered. The free surface profile of ferrofluid can be obtained through numerical iterations based on the fact that the pressures on the free surface should be the same. Test models are presented as validations of the proposed scheme. Index Terms--Ferrofluid, hydrostatics, Kelvin's formula, magnetic body force, virtual air gap.

It is required to calculate the electromagnetic forces at the distributed parts of electric machines for the prediction of performance. In this paper, the body force distribution of electric machines such as surface permanent magnet and interior permanent magnet is presented and discussed for the first time using the recently developed body force calculation methods which are based on the virtual air gap scheme. The torque contribution of the body force is investigated according to radial and circumferential directions. Index Terms--Electromagnetic body force, interior permanent-magnet motor, surface permanent-magnet motor, virtual air gap.

A topology optimization technique is applied to the design of dielectric-loaded waveguide filters. Dielectric material distribution inside the waveguide is optimized to achieve desired frequency response. A gradient-based optimizer is used for topology optimization, along with adjoint variable method to calculate sensitivity. The results of numerical examples show feasibility of the proposed method. Index Terms--Dielectric resonator, sensitivity analysis, topology optimization, waveguide filter.

A complete finite-element analysis method for corona discharge process, which is governed and coupled by charge transport equation and electric field equation, was presented. The charge transport equation of first order was transformed into second order by utilizing the artificial diffusion scheme. The two second-order equations were analyzed by the finite-element formulation which is well-developed for second-order equations. The Fowler-Nordheim injection boundary condition was adopted for charge transport equation. After verifying the numerical results by comparing to the analytic solutions using parallel plane electrodes with one carrier system, we extended the result to blade-plane electrodes in 2-D xy geometry with three carriers system. Radius of the sharp tip was taken to be 50 [micro]m. When this sharp geometry was solved by utilizing the space discretizing methods, the very sharp tip was found to cause a singularity in electric field and space charge distribution around the tip. To avoid these numerical difficulties in the finite-element method, finer meshes, a higher-order shape function, and artificial diffusion scheme were employed. Index Terms--Artificial diffusion, corona discharge, Fowler-Nordheim field emission, hydrodynamic diffusion-drift model, space charge propagation.

Three different Kelvin force expressions were expanded by incorporating the virtual air-gap scheme to calculate the total force and the distributions of force density. Conventionally, the Kelvin force density can be expressed by using two different fields such as an external applied field and total field acting on a dipole. Until now, the Kelvin force density with total field (KV) has been used for calculating the total force and force density. Since there is no single well-accepted manipulating technique, it has been difficult to directly compute the Kelvin force by adopting the external field approach; however, using the virtual air-gap scheme, the direct calculation of both Kelvin force density with external applied field (KVE), and with total field (KVT) as the local distributions of body force density was able to be evaluated. We tested three numerical analysis models to verify our proposed method. First, the nonlinear magnetic material was considered and compared the total force with different gap distances to contact position. Second, the distributions of force density were compared to each other. An irregularity aroused in the distributions of force density by the KVE and KVT. Finally, to remove the irregularity, one possible approach, forming sliced-tube regions aligned with the field direction, was suggested and examined. Index Terms--External field, force field, Kelvin force density, total field, virtual air-gap scheme.

Predicting the motion of superparamagnetic iron oxide nanoparticles (SPION) in biological systems is one of the most relevant parameters for the biomedical application of SPION. Recently, magnetic nanoparticles such as SPION have been utilized as the MR image contrast agent, targeted drug delivery, magnetic separation, biosensor, etc. Because the size of SPION is in the nanometer scale, it is difficult to test their dynamics under an external magnetic field experimentally. Moreover, when the SPION moves in a viscous fluid such as blood, the situation can be more complicated. To overcome these difficulties, we proposed a fast-solving technique combined with the finite-element method for analyzing the dynamic characteristics of SPION in a viscous fluid under an external magnetic field. Using this numerical modeling, the effective system dimension, external magnetic field, particle size, and trajectory of SPION can be estimated. To verify the proposed method, three magnetic systems with permanent magnet and micro capillary were tested. Index Terms--Superparamagnetic iron oxide nanoparticles (SPION), targeted drug delivery, trajectory, viscous fluid.

In this paper, the virtual air-gap formulae for electromagnetic forces are derived from the generalized forms of equivalent source methods, such as magnetic charge and magnetizing current. The virtual air-gap approach is based on the idea that insertion of infinitesimally thin air gap causes no real variation of electromagnetic field system. For total force calculation of a magnetic body in contact with other ones of ferromagnetic or permanent magnets, the virtual air-gap formulae can employ the conventional force methods, such as Maxwell stress, magnetic charge, and magnetizing current. The virtual air-gap approach is validated by numerical test results. Index Terms--Force calculation, generalized magnetic charge method, generalized magnetizing current method, virtual air gap.

For the mechanical structure design of electric machines, each force component on parts of an electric machine need to be separated. In this paper, a separation scheme of each torque component is presented. It is based on the magnetic force density analysis of the general formulation of equivalent magnetic charge method and Lorentz force density. The force density analysis can be applied to all parts of the system region including the inside of material and the interface of different materials. An interior permanent magnet motor and a surface permanent magnet motor are adopted for numerical test in this paper. Their numerical results show validity and usefulness of the presented method. Index Terms--Force density, general equivalent magnetic charge method, permanent magnet motor, torque component.

To analyze the mechanical dynamic characteristics of electromechanical system, we present a new and fast method using the reduced modeling technique for the levitated conductor. As of now, to solve this electromechanical system, the finite element method (FEM) or the boundary element method (BEM) employing the finite difference time-stepping scheme is used. These approaches, however, need too much solving time because the system matrix equation should be solved at each time step. Additionally, when the operation condition is changed or it needs more incremental steps, the system should be solved from the beginning again. To reduce the solving time, we use the circuit parameters of self- and mutual inductances which are evaluated using the FEM and the conductor segmentation. The formulated ordinary differential equations are solved using the fourth-order Runge--Kutta method. To show validity and usefulness of this proposed method, the TEAM Workshop Problem 28 model is tested, and the results of the experiment and time-stepping FEM are compared to this new method. Index Terms--Eddy current levitation, electromagnetic motional system, extracted circuit parameter, finite element method (FEM), Runge--Kutta method.

The conventional force calculation methods can be applied only for the total force of the objects surrounded by air or vacuum. In this paper, a new general form of equivalent magnetic charge method is proposed for calculating force density and total forces of materials in contact including ferromagnetic and permanent magnet. It provides surface force density on the interface of different materials. The validity of this method is shown by direct observation of the formulas and numerical tests. Index Terms--Force density, magnetic charge method, total force.