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Calculation of Magnetic Fields with Finite Elements

In: From Nano to Space

Author

Listed:
  • G. Wimmer

    (University of the Federal Armed Forces Hamburg, Chair for Theory of Electrical Engineering and Computational Electromagnetics, Helmut-Schmidt-University)

  • M. Clemens

    (University of the Federal Armed Forces Hamburg, Chair for Theory of Electrical Engineering and Computational Electromagnetics, Helmut-Schmidt-University)

  • J. Lang

    (Numerical Analysis and Scientific Computing, Darmstadt University of Technology, Department of Mathematics)

Abstract

The discretization of transient and static magnetic field problems with the Whitney Finite Element Method results in differential-algebraic systems of equations of index 1 and nonlinear systems of equations. Hence, a series of nonlinear equations have to be solved. This involves e.g. the solution of the linear(-ized) equations in each time step where the solution process of the iterative preconditioned conjugate gradient method reuses and recycles spectral information of previous linear systems. Additionally, in order to resolve induced eddy current layers sufficiently and regions of ferromagnetic saturation that may appear or vanish depending on the external current excitation a combination of an error controlled spatial adaptivity and an error controlled implicit Runge-Kutta scheme is used to reduce the number of unknowns for the algebraic problems effectively and to avoid unnecessary fine grid resolutions both in space and time. Numerical results are presented for 2D and 3D nonlinear magneto-dynamic problems.

Suggested Citation

  • G. Wimmer & M. Clemens & J. Lang, 2008. "Calculation of Magnetic Fields with Finite Elements," Springer Books, in: Michael H. Breitner & Georg Denk & Peter Rentrop (ed.), From Nano to Space, pages 111-124, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-74238-8_10
    DOI: 10.1007/978-3-540-74238-8_10
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