J. Comp. Math., 27 (2009), pp. 642-656.


Adaptivity in Space and Time for Magnetoquasistatics

Markus Clemens 1, Jens Lang, 2, Delia Teleaga 3, Georg Wimmer 4

1 Helmut-Schmidt-Universitat Hamburg, Holstenhofweg 85, 22043 Hamburg, Germany
2 Technische Universitat Darmstadt, Schlossgartenstrae 7, 64289 Darmstadt, Germany
3 Technische Universitat Darmstadt, Schlossgartenstrae 7, 64289 Darmstadt, Germany
4 Helmut-Schmidt-Universitat Hamburg, Holstenhofweg 85, 22043 Hamburg, Germany

Received 2007-11-30 Revised 2008-6-26 Accepted 2009-2-5 Online 2009-4-27
doi:10.4208/jcm.2009.27.5.015

Abstract

This paper addresses fully space-time adaptive magnetic field computations. We describe an adaptive Whitney finite element method for solving the magnetoquasistatic formulation of Maxwell's equations on unstructured 3D tetrahedral grids. Spatial mesh refinement and coarsening are based on hierarchical error estimators especially designed for combining tetrahedral H(curl)-conforming edge elements in space with linearly implicit Rosenbrock methods in time. An embedding technique is applied to get efficiency in time through variable time steps. Finally, we present numerical results for the magnetic recording write head benchmark problem proposed by the Storage Research Consortium in Japan.

Key words: Magnetoquasistatics, Space-time adaptivity, Edge elements, Rosenbrock methods, Hierarchical error estimator, SRC benchmark problem.

AMS subject classifications: 65M60, 65L06, 78M10.


Email: m.clemens@hsu-hh.de, lang@mathematik.tu-darmstadt.de, dteleaga@mathematik.tu-darmstadt.de, g.wimmer@hsu-hh.de
 

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