TY - JOUR
T1 - Adaptivity in Space and Time for Magnetoquasistatics
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 - <p style="text-align: justify;">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&#39;s equations on unstructured 3D tetrahedral grids. Spatial mesh refinement and coarsening are based on hierarchical error estimators especially designed for combining tetrahedral $\boldsymbol{H}(\rm&nbsp;curl)$-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.</p>