Tomonori Tsuburaya, Yoshifumi Okamoto and Shuji Sato
The purpose of this paper is to improve the performance of block-multicolor (BMC) ordering for the parallelized incomplete-Cholesky-preconditioned conjugate gradient (ICCG…
Abstract
Purpose
The purpose of this paper is to improve the performance of block-multicolor (BMC) ordering for the parallelized incomplete-Cholesky-preconditioned conjugate gradient (ICCG) method. Then, the BMC ordering based on level structure arising in reverse Cuthill-McKee RCM ordering is newly proposed. The name of proposed method is abbreviated as “RBMC”. This paper shows the validity of proposed method by comparison with greedy-based multicolor (MC) and conventional BMC on the real symmetric linear system derived from the voltage-driven finite element method in time domain.
Design/methodology/approach
In RBMC, the blocking and coloring is performed level by level. The number of synchronizations in forward and backward substitution is reduced so that all blocks can be colored with two colors. However, the load-balance in forward and backward substitution might deteriorate because the irregular block matrices are distributed around diagonal. To uniformize load-balance in forward and backward substitution, the RBMC combined with the concept of block red-black ordering has been developed.
Findings
The modified RBMC was the most effective for reduction of the elapsed time among four orderings (MC, BMC, RBMC, modified RBMC) owing to improvement of convergence characteristic and load-balance.
Originality/value
The proposed method had two advantages: although the number of unknowns per block must be previously determined in BMC, its parameter is automatically determined in proposed method, the number of synchronization in forward and backward substitution can be reduced.
Details
Keywords
Yoshifumi Okamoto, Akihisa Kameari, Koji Fujiwara, Tomonori Tsuburaya and Shuji Sato
– The purpose of this paper is the realization of Fast nonlinear finite element analysis (FEA).
Abstract
Purpose
The purpose of this paper is the realization of Fast nonlinear finite element analysis (FEA).
Design/methodology/approach
Nonlinear magnetic field analysis is achieved by using Newton-Raphson method implemented by relaxed convergence criterion of Krylov subspace method.
Findings
This paper mathematically analyzes the reason why nonlinear convergence can be achieved if the convergence criterion for linearized equation is relaxed.
Research limitations/implications
The proposed method is essential to reduce the elapsed time in nonlinear magnetic field analysis of quasi-stationary field.
Practical implications
The proposed method is able to be extended to not only static field but also time domain FEA strongly coupled with circuit equation.
Social implications
Because the speedup of performance evaluation of electrical machines would be achieved using proposed method, the work efficiency in manufacturing would be accelerated.
Originality/value
It can be seen that the nonlinear convergence can be achieved if the convergence criterion for linearized equation is relaxed. The verification of proposed method is demonstrated using practical nonlinear magnetic field problem.
Details
Keywords
Yoshifumi Okamoto, Yusuke Tominaga, Shinji Wakao and Shuji Sato
The purpose of this paper is to improve the multistep algorithm using evolutionary algorithm (EA) for the topology optimization of magnetostatic shielding, and the paper reveals…
Abstract
Purpose
The purpose of this paper is to improve the multistep algorithm using evolutionary algorithm (EA) for the topology optimization of magnetostatic shielding, and the paper reveals the effectiveness of methodology by comparison with conventional optimization method. Furthermore, the design target is to obtain the novel shape of magnetostatic shielding.
Design/methodology/approach
The EAs based on random search allow engineers to define general-purpose objects with various constraint conditions; however, many iterations are required in the FEA for the evaluation of the objective function, and it is difficult to realize a practical solution without island and void distribution. Then, the authors proposed the multistep algorithm with design space restriction, and improved the multistep algorithm in order to get better solution than the previous one.
Findings
The variant model of optimized topology derived from improved multistep algorithm is defined to clarify the effectiveness of the optimized topology. The upper curvature of the inner shielding contributed to the reduction of magnetic flux density in the target domain.
Research limitations/implications
Because the converged topology has many pixel element unevenness, the special smoother to remove the unevenness will play an important role for the realization of practical magnetostatic shielding.
Practical implications
The optimized topology will give us useful detailed structure of magnetostatic shielding.
Originality/value
First, while the conventional algorithm could not find the reasonable shape, the improved multistep optimization can capture the reasonable shape. Second, An additional search is attached to the multistep optimization procedure. It is shown that the performance of improved multistep algorithm is better than that of conventional algorithm.