The Newton-Raphson method accelerated by using a line search - comparison between energy functional and residual minimization

A line search was combined with the Newton-Raphson method to accelerate the convergence of the iterative calculation in nonlinear magnetic field analysis. As a method for determining a step size for update, the minimization of an energy functional and a square of 2-norm of residual obtained from the finite-element discretization was investigated. It was demonstrated that the energy functional minimization is superior to the residual minimization from the viewpoint of computational cost. The line search is effective even in the magnetic vector potential formulation, which is said to be stable usually. </p

Thin film write head field analysis using a benchmark problem

A benchmark problem has been proposed by the Storage Research Consortium (SRC) in Japan, for evaluating the applicability of computer codes to 3-D nonlinear eddy current analysis of thin film magnetic recording write head. Various codes using the finite element method are compared in terms of the write head field and the computational efficiency. The difficulty in 3-D mesh generation of thin film head is also discussed. The write head fields calculated by various codes using different meshes show fairly good agreement. The calculated write head fields are verified by measurement using a stroboscopic electron beam tomography. It is found that the calculation time strongly depends on unknown variables </p

Matrix Formulation of the Cauer Ladder Network Method for Efficient Eddy-Current Analysis

A matrix formulation of the Cauer ladder network (CLN) method is derived using the finite-element method to clarify the mathematical aspects of the CLN method. The CLN method directly yields orthogonal expansions of electric and magnetic fields that ensure the equivalence of the Cauer network to the eddy-current field. The CLN method is as exact as the Padé approximation via the Lanczos (PVL) process but more efficiently provides the circuit parameters and the orthogonal expansion than the PVL

Model Order Reduction of an Induction Motor Using a Cauer Ladder Network

In this article, a method for motor model order reduction is developed using the Cauer ladder network (CLN). The analyzed domain is decomposed into stator and mover domains, where the multiport CLN of each domain is constructed independently of the other. The two domains are connected through electromagnetic field modes at the boundary. The boundary condition is derived from the coordinate transformation. The reduced model accurately reconstructs the induction motor property affected by slot harmonics

A New Adaptive Mesh Refinement Method in FEA Based on Magnetic Field Conservation at Elements Interfaces and Non- conforming Mesh Refinement Technique

Mesh quality strongly affects the solution accuracy in electromagnetic finite element analysis. Hence, the realization of adequate mesh generation becomes a very important task. Several adaptive meshing methods for automatic adjustments of the mesh density in accordance with the shape and complexity of the analyzed problem, have been proposed. However, the most of them are not enough robust, some are quite laborious and could not be universally used for adaptive meshing of complex analysis models. In this paper, a new adaptive mesh refinement method based on magnetic field conservation at the border between finite elements is proposed. The proposed error estimation method provides easy mesh refinements, generates smaller element within regions with large curvature of the magnetic flux lines. The proposed adaptive mesh refinement method based on non-conforming edge finite elements, which could avoid generation of flat- or ill-shaped elements, was applied to a simple magnetostatic permanent magnet model. To confirm the validity and accuracy, the obtained results were compared with those obtained by means of the Zienkiewich-Zhu (ZZ) error estimator. The results show that the computational error using the proposed method was reduced down to 1.0% compared with that of the ZZ method which yields error of 8.6%, for the same model

Cauer Ladder Network With Multiple Expansion Points for Efficient Model Order Reduction of Eddy-Current Field

The Cauer ladder network (CLN) method provides an efficient representation of eddy-current fields. This paper proposes a reformulation of the CLN method that considers expansion points using the magnetic/current vector potential. To cover a wide range of frequencies, the expansion point may be changed at a later stage of the network. Only a few stages of the ladder network are required for the eddy-current field to be reconstructed accurately around the target frequency using the expansion points

Multi-Port Model Order Reduction Using a Matrix Cauer Ladder Network

To achieve efficient multi-port model order reduction, a multi-port Cauer ladder network (CLN) method is formulated that directly yields resistance and inductance matrices that constitute the network elements in the matrix Cauer form. The eddy-current field driven by multiple power sources is accurately reconstructed using a small number of network elements. The matrix Cauer form achieves faster convergence of the transfer function than a single-port CLN method and almost the same convergence as a block Padé via Lanczos (PVL) method