Fast nonlinear finite element analysis using Newton-Raphson method implemented by Krylov subspace method with relaxed convergence criterion

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.

Citation

Okamoto, Y., Kameari, A., Fujiwara, K., Tsuburaya, T. and Sato, S. (2015), "Fast nonlinear finite element analysis using Newton-Raphson method implemented by Krylov subspace method with relaxed convergence criterion", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 34 No. 5, pp. 1537-1552. https://doi.org/10.1108/COMPEL-02-2015-0075