Model order reduction for magneto-quasistatic equations

  • We consider model reduction of Maxwell's equations arising in magneto-quasistatic field problems. A finite element discretization of such equations leads to large-scale differential-algebraic equations of special structure. For model reduction of linear systems, we employ a balanced truncation approach, whereas nonlinear systems are reduced using a proper orthogonal decomposition method combined with a discrete empirical interpolation technique. We will exploit the special structure of the underlying problem to improve the performance of the model reduction algorithms. Furthermore, we discuss an efficient evaluation of the Jacobi matrix required in nonlinear time integration of the reduced models.

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Author:Johanna Kerler-Back, Tatjana StykelGND
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Series (Serial Number):Preprints des Instituts für Mathematik der Universität Augsburg (2015-14)
Publishing Institution:Universität Augsburg
Release Date:2015/10/23
Tag:Maxwell's equations; magneto-quasistatic problems; model order reduction; balanced truncation; proper orthogonal decomposition; discrete empirical interpolation method
GND-Keyword:Maxwellsche Gleichungen; Ordnungsreduktion; Orthogonale Zerlegung; Interpolation; Mathematisches Modell; Differential-algebraisches Gleichungssystem
Erschienen in: IFAC-PapersOnLine, Proceedings of the 8th Vienna International Conference on Mathematical Modelling (MATHMOD 2015, Vienna, Austria, February 18-20, 2015), 48(1), 2015, pp. 240-241
Institutes:Mathematisch-Naturwissenschaftlich-Technische Fakultät
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Numerische Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Licence (German):License LogoDeutsches Urheberrecht mit Print on Demand