Numerical study of a time-domain finite element method for nonlinear magnetic problems in three dimensions

Su Yan, Jian Ming Jin, Chao Fu Wang, Joseph Kotulski

Research output: Contribution to journalArticle

Abstract

—In this work, numerical analysis of nonlinear ferromagnetic problems is presented using the three-dimensional time-domain-nite element method (TDFEM). Formulated with the second- order nonlinear partial differential equation (PDE) combined with the inverse Jiles-Atherton (J-A) vector hysteresis model, the nonlinear problems are solved in the time domain with the Newton- Raphson method. To solve the ordinary differential equation (ODE) representing the magnetic hysteresis accurately and effciently, several ODE solvers are specically designed and investigated. To improve the computational effciency of the Newton-Raphson method, the multi-dimensional secant methods, aka Broyden's methods, are incorporated in the nonlinear TDFEM solver. A nonuniform time-stepping scheme is also developed using the weighted residual approach to remove the requirement of a uniform time-step size during the simulation. The capability and the performance of the proposed methods are demonstrated by various numerical examples.

Original languageEnglish (US)
Article numberA006
Pages (from-to)69-91
Number of pages23
JournalProgress in Electromagnetics Research
Volume153
DOIs
StatePublished - Jan 1 2015

ASJC Scopus subject areas

  • Radiation
  • Condensed Matter Physics
  • Electrical and Electronic Engineering

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