The paper aims to improve convergence characteristics of the Newton–Raphson (NR) method applied to time-periodic finite element method using various line searches, as time-periodic finite element method causes deterioration of convergence characteristic of nonlinear analysis based on NR method. The study also aims to accelerate and improve accuracy of electromagnetic field analysis for improvement of the performance of electrical machine.
The paper proposes new type line searches that set approximate step size for NR method. The line search evaluated step size using higher-order interpolation of functional derivative. In addition, two criteria for applying these line search were proposed. First method set one scalar value for every NR iteration that is named constant step size. Second method define different step size in each time step of time-periodic finite element method to update solution vector that is named different step size.
The paper provides efficient line searches to improve convergence characteristics for NR method. Nonlinear magnetic field analysis of two transformer models is demonstrated. The proposed methods achieve the following results: higher-order functional NR is efficient in improving convergence characteristics, and the proposed methods succeeded about twice faster in both models.
The paper fulfills improvement of convergence characteristics of the NR method applied to time-periodic finite element method using proposed line searches and accelerate electromagnetic field analysis.
Kakita, S. and Okamoto, Y. (2019), "Enhancement of convergence characteristics of Newton-Raphson method with line search for nonlinear eddy current analysis based on time-periodic FEM", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 38 No. 5, pp. 1627-1640. https://doi.org/10.1108/COMPEL-12-2018-0491
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