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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Structure-preserving mesh coupling based on the Buffa-Christiansen complex
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by Ossi Niemimäki, Stefan Kurz and Lauri Kettunen PDF
Math. Comp. 86 (2017), 507-524 Request permission

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
  • MR Author ID: 768977
  • Email: kurz@gsc.tu-darmstadt.de
  • Lauri Kettunen
  • Affiliation: Tampere University of Technology, DEE - Electromagnetics, P.O. Box 692, 33101 Tampere, Finland
  • MR Author ID: 630615
  • Email: lauri.kettunen@tut.fi
  • Received by editor(s): February 27, 2015
  • Received by editor(s) in revised form: August 4, 2015
  • Published electronically: May 17, 2016
  • © Copyright 2016 American Mathematical Society
  • Journal: Math. Comp. 86 (2017), 507-524
  • MSC (2010): Primary 65N30, 78M10
  • DOI: https://doi.org/10.1090/mcom/3121
  • MathSciNet review: 3584538