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Article
Publication date: 2 October 2019

Makoto Kumagai, Shimpei Kakita and Yoshifumi Okamoto

This paper aims to present the affinity of BiCGStab and BiCGStab2 with successive over-relaxation (SOR) preconditioner supported by Eisenstat’s technique for a linear system…

Abstract

Purpose

This paper aims to present the affinity of BiCGStab and BiCGStab2 with successive over-relaxation (SOR) preconditioner supported by Eisenstat’s technique for a linear system derived from the time-periodic finite element method (TP-FEM). To solve the time domain electromagnetic field problem with long transient state, TP-FEM is very useful from the perspective of rapidly achieving a steady state. Because TP-FEM solves all of the state variables at once, the linear system derived from TP-FEM becomes the large scale and nonsymmetric, whereas the detailed performance of some preconditioned Krylov subspace method is not reported.

Design/methodology/approach

In this paper, BiCGStab and BiCGStab2 are used as the linear solver for a large-sparse nonsymmetric linear system derived from TP-FEM. In addition, incomplete LU (ILU) factorization is applied as a preconditioner to compare SOR supported by Eisenstat’s technique. As examples, the pot-type reactor and three-phase transformer is analyzed.

Findings

In the problem of the pot-type reactor, when SOR preconditioner supported by Eisenstat’s technique is applied to BiCGStab and BiCGStab2, the elapsed time can be reduced dramatically. However, in the problem of the three-phase transformer, the iterative process of the linear solvers with SOR preconditioner is not terminated, whereas the iterative process of linear solvers with ILU preconditioner is terminated. The preconditioner that can be supported by Eisenstat’s technique is not necessarily appropriate for the problem to derive from TP-FEM.

Originality/value

In this paper, the affinity of preconditioned linear solver supported by Eisenstat’s technique for the nonsymmetric linear system derived from TP-FEM is demonstrated.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering , vol. 38 no. 5
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 19 July 2022

Yasuhito Takahashi, Koji Fujiwara and Takeshi Iwashita

This study aims to enhance the parallel performance of a parallel-in-space-and-time (PinST) finite-element method (FEM) using time step overlapping. The effectiveness of the…

Abstract

Purpose

This study aims to enhance the parallel performance of a parallel-in-space-and-time (PinST) finite-element method (FEM) using time step overlapping. The effectiveness of the developed method is clarified in a magnet eddy-current loss analysis of a practical interior permanent magnet synchronous motor (IPMSM) using a massively parallel computing environment.

Design/methodology/approach

The developed PinST FEM is a combination of the domain decomposition method as a parallel-in-space (PinS) method and a parallel time-periodic explicit error correction (PTP-EEC) method, which is one of the parallel-in-time (PinT) approaches. The parallel performance of the PinST FEM is further improved by overlapping the time steps with different processes in the PTP-EEC method.

Findings

By applying the overlapping PTP-EEC method, the convergence of the transient solution to its steady state can be accelerated drastically. Consequently, the good parallel performance of the PinST FEM is achieved in magnetic field analyses of the practical IPMSM using a massively parallel computing environment, in which over 10,000 processes are used.

Originality/value

In this study, the PinST FEM based on time step overlapping is newly developed and its effectiveness is demonstrated in a massively parallel computing environment, in which using either the PinS or PinT method alone cannot achieve sufficient parallel performance. This finding implies a new direction of parallel computing approaches for electromagnetic field computation.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering , vol. 42 no. 2
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 25 July 2019

Yasuhito Takahashi, Koji Fujiwara, Takeshi Iwashita and Hiroshi Nakashima

This paper aims to propose a parallel-in-space-time finite-element method (FEM) for transient motor starting analyses. Although the domain decomposition method (DDM) is suitable…

Abstract

Purpose

This paper aims to propose a parallel-in-space-time finite-element method (FEM) for transient motor starting analyses. Although the domain decomposition method (DDM) is suitable for solving large-scale problems and the parallel-in-time (PinT) integration method such as Parareal and time domain parallel FEM (TDPFEM) is effective for problems with a large number of time steps, their parallel performances get saturated as the number of processes increases. To overcome the difficulty, the hybrid approach in which both the DDM and PinT integration methods are used is investigated in a highly parallel computing environment.

Design/methodology/approach

First, the parallel performances of the DDM, Parareal and TDPFEM were compared because the scalability of these methods in highly parallel computation has not been deeply discussed. Then, the combination of the DDM and Parareal was investigated as a parallel-in-space-time FEM. The effectiveness of the developed method was demonstrated in transient starting analyses of induction motors.

Findings

The combination of Parareal with the DDM can improve the parallel performance in the case where the parallel performance of the DDM, TDPFEM or Parareal is saturated in highly parallel computation. In the case where the number of unknowns is large and the number of available processes is limited, the use of DDM is the most effective from the standpoint of computational cost.

Originality/value

This paper newly develops the parallel-in-space-time FEM and demonstrates its effectiveness in nonlinear magnetoquasistatic field analyses of electric machines. This finding is significantly important because a new direction of parallel computing techniques and great potential for its further development are clarified.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering , vol. 38 no. 5
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 1 February 2000

I.M. Smith

A system for doing finite element computations in parallel is described. It is general purpose in the sense that it can be used across a wide range of finite element applications…

Abstract

A system for doing finite element computations in parallel is described. It is general purpose in the sense that it can be used across a wide range of finite element applications and in the sense that it is not restricted to any particular parallel hardware. Its performance on computers ranging from clusters of PCs to massively parallel high performance machines is illustrated.

Details

Engineering Computations, vol. 17 no. 1
Type: Research Article
ISSN: 0264-4401

Keywords

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