Fast Nonlinear Finite Element Analysis Using Newton-Raphson Method Implemented by Krylov Subspace Method with Relaxed Convergence Criterion
Fast Nonlinear Finite Element Analysis Using Newton-Raphson Method Implemented by Krylov Subspace Method with Relaxed Convergence Criterion
复制标题
放宽收敛准则 Krylov 子空间法实现牛顿-拉夫逊法快速非线性有限元分析
DOI：
10.1108/compel-02-2015-0075
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
and Shuji Sato
中科院分区：
文献类型：
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作者：
Yoshifumi Okamoto;Akihisa Kameari;Koji Fujiwara;Tomonori Tsuburaya;and Shuji Sato
目的——本文的目的是实现快速非线性有限元分析（FEA）。设计/方法/途径——通过利用克雷洛夫子空间方法的放宽收敛准则实现的牛顿-拉夫森方法来实现非线性磁场分析。研究结果——本文从数学上分析了如果放宽线性化方程的收敛准则，可以实现非线性收敛的原因。研究限制/启示——所提出的方法对于减少非线性磁场分析中的运行时间至关重要。实际意义——该方法不仅可以扩展到静态场，还可以扩展到与电路方程强耦合的时域有限元分析。社会意义——由于使用该方法可以实现电机性能评估的加速，从而提高制造的工作效率。原创性/价值——可以看出，如果放宽线性化方程的收敛准则，可以实现非线性收敛。利用实际的非线性磁场问题验证了所提出的方法。
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.