Application of multi-stage diagonally-implicit runge-kutta algorithm to transient magnetic field computation using finite element method

H. L. Li, Siu Lau Ho, Weinong Fu

Research output: Journal article publicationJournal articleAcademic researchpeer-review

4 Citations (Scopus)


A multi-stage diagonally-implicit Runge-Kutta (DIRK) algorithm is applied to discretize the time variable in transient magnetic field computation using finite element method (FEM). A formulation, which has the same format as the backward Euler (BE) algorithm for both linear and nonlinear problems, is deduced for simple and ready numerical implementation. The DIRK algorithm is compared with the BE algorithm which is an effective and popular algorithm in FEM. The merits and disadvantages of these two algorithms are highlighted. An ingeniously combined algorithm exploiting the merits of both BE and DIRK is presented and a numerical experiment shows that it can significantly improve the accuracy with no additional computing burden. For nonlinear problems, a DIRK nonlinear iteration strategy is presented and it can be shown that the total computing time of one integration time step can be shortened by about 36% without any accuracy loss in the solutions.
Original languageEnglish
Article number6136652
Pages (from-to)279-282
Number of pages4
JournalIEEE Transactions on Magnetics
Issue number2
Publication statusPublished - 1 Feb 2012


  • Computing time
  • DIRK algorithm
  • finite element method
  • nonlinear iteration
  • transient magnetic field

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Electronic, Optical and Magnetic Materials

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