On the Resistance between the Two Disc Electrodes Applied to an Infinite Plate Conductor

The problem of disc electrodes is discussed on the basis of a Fredholm integral equation of the second kind. To compute the resistance between the two electrodes, numerical analysis is carried out utilizing the Laguerre-Gauss quadrature formula. The result is compared with that obtained from Riemann's solution which contains a physical contradiction. A formula of infinite integral involving a Bessel function is also given

On a Generalized Problem of Disc Electrodes II

A formal solution of a set of quadruple integral equations is given. The integral equations are reduced to a pair of simultaneous integral equations of Fredholm type which may be solved by a method similar to that used for a single equation. As an example, the problem of a circular plate condenser with guard rings is considered. It is shown that all the well-known disc electrode problems may be treated as special cases

On a Generalized Problem of Disc Electrodes I

A problem of disc electrodes is discussed on the basis of dual integral equations both for an electrostatic problem and for a steady current field problem in the unified manner. It is shown that two well-known problems, 1) the plate condenser problem and 2) the disc electrode problem for steady current may be treated as special cases

Two Types of Isotropic Vector Play Models and Their Rotational Hysteresis Losses

This paper presents a comparison of two types of isotropic vector play models and their generalized models. The first vector model is represented by a superposition of scalar play models. The other type is given by a geometrical vectorization of play hysteron. The rotational hysteresis losses of both models are discussed. A method is proposed to adjust the simulated rotational hysteresis loss to a measured loss

A micromagnetic study of domain structure modeling

To develop a mesoscopic model for magnetic-domain behavior, a domain structure model (DSM) was examined and compared with a micromagnetic simulation. The domain structure of this model is given by several domains with uniform magnetization vectors and domain walls. The directions of magnetization vectors and the locations of domain walls are determined so as to minimize the magnetic total energy of the magnetic material. The DSM was modified to improve its representation capability for domain behavior. The domain wall energy is multiplied by a vanishing factor to represent the disappearance of magnetic domain. The sequential quadratic programming procedure is divided into two steps to improve an energy minimization process. A comparison with micromagnetic simulation shows that the modified DSM improves the representation accuracy of the magnetization process

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 Hiptmair's 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

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

Two types of isotropic vector play models and their rotational hysteresis losses

This paper presents a comparison of two types of isotropic vector play models and their generalized models. The first vector model is represented by a superposition of scalar play models. The other type is given by a geometrical vectorization of play hysteron. The rotational hysteresis losses of both models are discussed. A method is proposed to adjust the simulated rotational hysteresis loss to a measured loss