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

Yoshifumi Okamoto; Akihisa Kamear; Koji Fujiwara; Tomonori Tsuburaya; Shuji Sato

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

Yoshifumi Okamoto ^[1] ; Akihisa Kamear ^[4] ; Koji Fujiwara ^[2] ; Tomonori Tsuburaya ^[3] ; Shuji Sato ^[3]
1. [1] Hosei University
  
  Hosei University
  
  Japón
2. [2] Doshisha University
  
  Doshisha University
  
  Kamigyō-ku, Japón
3. [3] Utsunomiya University
  
  Utsunomiya University
  
  Japón
4. [4] Science Solutions International Lab. Inc
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Localización: Compel: International journal for computation and mathematics in electrical and electronic engineering, ISSN 0332-1649, Vol. 34, Nº 5 (Special Issue: IGTE 2014), 2015, págs. 1537-1552
Idioma: inglés
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Resumen
- 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.