Three-Dimensional Eddy Current Analysis by Hybrid Finite Element and Boundary Element Method

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We have been developing the Hybrid Finite Element and Boundary Element Method for three-dimensional electromagnetic field analysis includes eddy current calculation. Among various electromagnetic quantities, the magnetic vector potential A and the electric scalar potential phi are widely used for the eddy current analysis. This approach is known as the A-phi method. We adopts the quantities A-phi in both the boundary element method and the finite element method. For some problems, it is very complicated to complicated to combine boundary conditions of the boundary element method with those of the usual finite element method. To avoid this difficulty, we have developed a novel boundary element formulation using magnetic potential.Although the A-phi method is theoretically satisfactory, we need four variables for each node in three-dimensional analysis. In order to reduce the number of unknown variables, we proposed the adoption of the magnetic field intensity H and the magnetic scalar potential psi in the hybrid method.We applied the proposed method to the real electric apparatus ; linear induction motor, magnetic levitation system, hyperthermia and superconducting magnet system.We also developed a novel optimal design method for electromagnetic fields. The optimal design method is based on a combination of the hybrid finite element and boundary element method for electromagnetic field calculation and the mathematical programming method for solving corresponding optimization problem. Application of the optimal design method to practical examples ; superconducting magnet system with magnetic shielding for Magnetic Resonance Imaging and hybrid magnet for magnetic levitation system, gave satisfying results.