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Volume 27, Issue 5
Adaptivity in Space and Time for Magnetoquasistatics

Markus Clemens, Jens Lang, Delia Teleaga & Georg Wimmer

DOI: 10.4208/jcm.2009.27.5.015

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

Published online: 2009-10

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  • 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 $\boldsymbol{H}(\rm curl)$-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.

  • Keywords

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

  • AMS Subject Headings

65M60, 65L06, 78M10.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-27-642, author = {Markus Clemens, Jens Lang, Delia Teleaga and Georg Wimmer}, title = {Adaptivity in Space and Time for Magnetoquasistatics}, journal = {Journal of Computational Mathematics}, year = {2009}, volume = {27}, number = {5}, pages = {642--656}, 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 $\boldsymbol{H}(\rm curl)$-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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2009.27.5.015}, url = {http://global-sci.org/intro/article_detail/jcm/8594.html} }
TY - JOUR T1 - Adaptivity in Space and Time for Magnetoquasistatics AU - Markus Clemens, Jens Lang, Delia Teleaga & Georg Wimmer JO - Journal of Computational Mathematics VL - 5 SP - 642 EP - 656 PY - 2009 DA - 2009/10 SN - 27 DO - http://doi.org/10.4208/jcm.2009.27.5.015 UR - https://global-sci.org/intro/article_detail/jcm/8594.html KW - Magnetoquasistatics, Space-time adaptivity, Edge elements, Rosenbrock methods, Hierarchical error estimator, SRC benchmark problem. AB -

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 $\boldsymbol{H}(\rm curl)$-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.

Markus Clemens, Jens Lang, Delia Teleaga and Georg Wimmer. (2009). Adaptivity in Space and Time for Magnetoquasistatics. Journal of Computational Mathematics. 27 (5). 642-656. doi:10.4208/jcm.2009.27.5.015
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