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Structure-preserving mesh coupling based on the Buffa-Christiansen complex


Authors: Ossi Niemimäki, Stefan Kurz and Lauri Kettunen
Journal: Math. Comp. 86 (2017), 507-524
MSC (2010): Primary 65N30, 78M10
DOI: https://doi.org/10.1090/mcom/3121
Published electronically: May 17, 2016
MathSciNet review: 3584538
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Abstract: The state of the art for mesh coupling at nonconforming interfaces is presented and reviewed. Mesh coupling is frequently applied to the modeling and simulation of motion in electromagnetic actuators and machines. The paper exploits Whitney elements to present the main ideas. Both interpolation- and projection-based methods are considered. In addition to accuracy and efficiency, we emphasize the question whether the schemes preserve the structure of the de Rham complex, which underlies Maxwell's equations. As a new contribution, a structure-preserving projection method is presented, in which Lagrange multiplier spaces are chosen from the Buffa-Christiansen complex. Its performance is compared with a straightforward interpolation based on Whitney and de Rham maps, and with Galerkin projection.


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Additional Information

Ossi Niemimäki
Affiliation: Tampere University of Technology, DEE - Electromagnetics, P.O. Box 692, 33101 Tampere, Finland
Address at time of publication: Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68, 00014 University of Helsinki, Finland
Email: ossi.niemimaki@helsinki.fi

Stefan Kurz
Affiliation: Tampere University of Technology, DEE - Electromagnetics, P.O. Box 692, 33101 Tampere, Finland
Address at time of publication: Graduate School Computational Engineering, Technische Universität Darmstadt, Dolivostraße 15, 64293 Darmstadt, Germany
Email: kurz@gsc.tu-darmstadt.de

Lauri Kettunen
Affiliation: Tampere University of Technology, DEE - Electromagnetics, P.O. Box 692, 33101 Tampere, Finland
Email: lauri.kettunen@tut.fi

DOI: https://doi.org/10.1090/mcom/3121
Received by editor(s): February 27, 2015
Received by editor(s) in revised form: August 4, 2015
Published electronically: May 17, 2016
Article copyright: © Copyright 2016 American Mathematical Society