Takeshi Mifune

Optimization of Inductors Using Evolutionary Algorithms and Its Experimental Validation

This paper presents parameter and topology optimization of inductor shapes using evolutionary algorithms. The goal of the optimization is to reduce the size of inductors satisfying the specifications on inductance values under weak and strong bias-current conditions. The inductance values are computed from the finite-element (FE) method taking magnetic saturation into account. The result of the parameter optimization, which leads to significant reduction in the volume, is realized for test, and the dependence of inductance on bias currents is experimentally measured, which is shown to agree well with the computed values. Moreover, novel methods are introduced for topology optimization to obtain inductor shapes with homogeneous ferrite cores suitable for mass production.

Similarities Between Implicit Correction Multigrid Method and A-phi Formulation in Electromagnetic Field Analysis

This paper proposes an implicit error correction method that corresponds to the explicit error correction methods, such as Hiptmairs hybrid smoother and the conventional multigrid method. The A-phi method can be seen as the implicit error correction method corresponding to the hybrid smoother. Numerical tests confirm that the A-phi method produces a similar correction effect on the error belonging to the kernel of the discrete curl operator as that of the hybrid smoother. Furthermore, this paper introduces an implicit correction multigrid method, which is the implicit error correction version of the conventional multigrid method. In this method, linear systems on all levels in a multigrid method are combined into a large linear system. This linear system is solved by an iterative solver, and any preconditioning techniques can be used. Numerical tests show that the proposed method involves coarse grid correction effects and achieves a convergence rate independent of the grid-size, thus confirming the effectiveness of the implicit error correction method.

A fast solver for FEM analyses using the parallelized algebraic multigrid method

The algebraic multigrid (AMG) method is an effi- cient solver for linear systems arising in finite element analyses. The AMG method is applicable at a matrix level, different from the geometric multigrid solvers. This paper proposes a combination of the parallel processing technique and the AMG method as a fast solver for electromagnetic field analyses. While the AMG method consists of a setup phase and a solution phase, parallel processing of the former phase is difficult. We present the use of long-range interpolation instead of the conventional direct interpolation for improvement of the parallel efficiency of the AMG setup phase. A magnetostatic analysis and an eddy-current analysis show the solver performance. The numerical results show that parallelized AMG is a fast solver and has sufficient scalability, as compared with the conventional solver.

Macroscopic magnetization modeling of silicon steel sheets using an assembly of six-domain particles

A simplified domain structure model having six domains is proposed for mesoscopic magnetization under cubic anisotropy. The six-domain model represents 90° and 180° domain-wall motions by the volume-ratio variations of domains. The magnetization process of grain-oriented and non-oriented silicon steel sheets is represented by the assembly of six-domain models. Simulated magnetization curves agree well with measured properties, and the effect of compressive stress is successfully reconstructed.

Parallel Hierarchical Matrices with Adaptive Cross Approximation on Symmetric Multiprocessing Clusters

We discuss a scheme for hierarchical matrices with adaptive cross approximation on symmetric multiprocessing clusters. We propose a set of parallel algorithms that are applicable to hierarchical matrices. The proposed algorithms are implemented using the flat-MPI and hybrid MPI+OpenMP programming models. The performance of these implementations is evaluated using an electric field analysis computed on two symmetric multiprocessing cluster systems. Although the flat-MPI version gives better parallel scalability when constructing hierarchical matrices, the speed-up reaches a limit in the hierarchical matrix-vector multiplication. We succeeded in developing a hybrid MPI+OpenMP version to improve the parallel scalability. In numerical experiments, the hybrid version exhibits a better parallel speed-up for the hierarchical matrix-vector multiplication up to 256 cores.

A Vector Play Model for Finite-Element Eddy-Current Analysis Using the Newton-Raphson Method

The differentiation of the vector hysteretic function represented by a vector play model is discussed for efficient nonlinear electromagnetic field computation using the Newton-Raphson method. The combination of the nonlinear finite-element method and the vector play model achieves accurate representation of the AC anisotropic magnetic property of nonoriented silicon steel sheet under rotational magnetic flux conditions. The proposed method is successfully applied to the eddy-current analysis of iron-cored inductors excited by a current or voltage source.

Convergence Acceleration of Iterative Solvers for the Finite Element Analysis Using the Implicit and Explicit Error Correction Methods

Our previous paper proposed two frameworks for iterative linear solvers: the implicit and explicit error correction methods. In this paper, we discuss the convergence property of these methods. A formula we derive explains the reasonability of the auxiliary matrix that Kameari suggested for thin elements. Additionally, an enhanced auxiliary matrix is devised for thin elements, in which the material property changes discontinuously.

Equivalent circuit modeling of dynamic hysteretic property of silicon steel under pulse width modulation excitation

This paper describes the development of an efficient and accurate dynamic hysteresis model that combines the Cauer circuit representations with the play model. The physical meaning of the standard Cauer circuit is discussed and is used to derive a mathematical representation of hysteretic inductors. The iron-loss and hysteresis loops of silicon steel that were obtained using the proposed model agree with experimental data measured under sinusoidal and pulse width modulation excitations.

3-D Optimization of Ferrite Inductor Considering Hysteresis Loss

This paper presents three-dimensional shape optimization of inductors for the dc-dc converters, in which the nonconforming voxel-based finite element method (FEM) is employed to realize fast FE mesh generation during the optimization. The operating point of the inductor under the bias current condition, which is estimated from the circuit analysis, is obtained by nonlinear FE analysis. Then, the FE equation linearized around the operating point is solved being coupled with the circuit equation to obtain the magnetic fields in the inductor. The hysteresis loss is computed from the Steinmetz formula. Validity of the field computation is tested by comparing the numerical results with measured data. The multiobjective optimization of the inductor shapes is performed to minimize the winding resistance and hysteresis loss. It is shown that the present method can effectively find the Pareto solutions which can lead to improvement in the efficiency of the dc-dc converter.

Algebraic multigrid preconditioning for 3-D magnetic finite-element analyses using nodal elements and edge elements

Most computation costs in magnetic finite-element analyses are consumed solving large-scale linear systems of equations; therefore, the development of fast linear solvers would be effective to reduce the computation time. This research is aimed to develop an efficient algebraic multigrid (AMG) preconditioner for three-dimensional (3-D) magnetic finite-element analyses utilizing nodal and edge elements. A new AMG preconditioner for eddy-current analyses is proposed, which separately treats nodal elements and edge elements in the construction of the coarse grids. Numerical results demonstrated the performances of AMG solvers in magnetostatic analyses and eddy-current analyses. The proposed AMG preconditioner achieves a better convergence than a conventional one in eddy-current analyses