Masaaki Shimasaki

Numerical solution of Plateau’s problem by a finite element method

This paper concerns the application of a finite element method to the numerical solution of a nonrestricted form of the Plateau problem, as well as to a free boundary prob- lem of Plateau type. The solutions obtained here are examined for several examples and are considered to be sufficiently accurate. It is also observed that the hysteresis effect, which is a feature of a nonlinear problem, appears in this problem. 1. Introduction. Methods for the numerical solution of the Plateau problem have so far been examined by D. Greenspan (3), (4), using the combination technique of difference and variational methods, and by P. Concus (5), using a finite difference method. These two methods can be applied only to the so-called restricted form of the Plateau problem described by Forsythe and Wasow (2, Section 18.9), that is, to the problems where the boundary condition is represented by a single-valued function. Thus, they cannot be applied to the problem where the boundary condition is repre- sented by a multi-valued function, such as Courants example described later. This paper shows that such multi-valued boundary-value problems can be solved numerically by a finite element method. In this case, two solution methods, one for a free boundary problem and the other in a cyclindrical coordinate system, are presented.

Isotropic vector hysteresis represented by superposition of stop hysteron models

The present paper first shows that the scalar stop hysteron model has the property of equal vertical chords for back-and-forth input variations of the same amplitude. This property leads to an identification method of the scalar model. Secondly, identification methods are developed for the 3-D and 2-D isotropic vector models that are constructed by the superposition of scalar stop hysteron models. Numerical simulations show that these methods identify the scalar and vector models satisfactorily.

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.

Eddy-current analysis using vector hysteresis models with play and stop hysterons

Vector hysteresis models are applied to an eddy-current analysis. The vector hysteresis models are composed by play hysterons and stop hysterons. The eddy-current analysis shows that both play and stop hysteron models can effectively describe isotropic vector hysteretic behavior. The stop hysteron model is more efficient in analyses using the magnetic vector potential than the play model because the stop model can give the magnetic field from the magnetic flux density without an iteration process.

Algebraic multicolor ordering for parallelized ICCG solver in finite-element analyses

Proposes a new black-box-type parallel processing method for the incomplete Cholesky conjugate gradient (ICCG) solver. The new method is based on a multicolor ordering concept and an automatic reordering process in the solver. Parallel performance is evaluated in the context of three-dimensional finite edge-element eddy-current analysis. The proposed method attains high parallelism with a small increase in CG iterations and achieves high parallel performance.

Stop model with input-dependent shape function and its identification methods

We propose an input-dependent shape function for the stop model to remove its property of equal vertical chords regardless of dc bias. We compare several identification methods for the stop model and show that the input-dependent shape function improves the ability to represent the stop model effectively. A least-squares identification method using both symmetric and asymmetric B-H loops achieves the most precise representation of hysteretic characteristics for a silicon steel sheet. However, if only symmetric loops are available for identification, a newly proposed identification method gives more accurate representation than other methods including the least-squares method.

Comparison Criteria for Parallel Orderings in ILU Preconditioning

This paper introduces block red-black ordering in a general three-dimensional form for parallel incomplete LU (ILU) preconditioning. This parallel ordering method is designed to attain fast convergence with reduced synchronization among processors in parallelized forward and backward substitutions. In this method, the grid-nodes are divided into blocks and red-black ordering is applied to them. Since blocks with identical colors never have a data-dependency, the blocks in each color can be processed in parallel. Moreover, in order to compare parallel orderings, we propose a new tool for investigating orderings on convergence. The analytic index for convergence, which is based on the remainder matrix, is easily computed and has a unique value for a fixed ordering. Nodes are classified into seven groups, and the effect of each group on convergence is estimated. Numerical tests using a three-dimensional problem confirm the validity of both proposed parallel ordering and analytic convergence comparison methods.

An analysis of Pascal programs in compiler writing

A method and results of static and dynamic analysis of Pascal programs are described. In order to investigate characteristics of large systems programs developed by the stepwise refinement programming approach and written in Pascal, several Pascal compilers written in Pascal were analysed from both static and dynamic points of view. As a main conclusion, procedures play an important role in the stepwise refinement approach and implementors of a compiler and designers of high level language machines for Pascal‐like languages should pay careful attention to this point. The set data structure is one of the characteristics of the Pascal language and statistics of set operations are also described.

Representation Theorems for stop and play models with input-dependent shape functions

Stop and play models with input-dependent shape functions are equivalent to the nonlinear Preisach model proposed by Mayergoyz. This equivalence engenders the necessary and sufficient conditions for a hysteretic nonlinearity to be represented by stop and play models that have input-dependent shape functions. A representation theorem for the stop model having an input-independent shape function is also given. The latter theorem is used to improve the representation accuracy of the stop model for a silicon steel sheet.

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.