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• Prof. Dr. Peter Benner
  Technische Universität Chemnitz,
  Fakultät für Mathematik, 09107 Chemnitz, Germany
  Tel: +49 (0)371-531-38367
  E-mail: benner@mathematik.tu-chemnitz.de
• Prof. Dr. Jan Gerrit Korvink
  Albert-Ludwigs-Universität Freiburg,
  Lehrstuhl für Simulation,
  Institut für Mikrosystemtechnik, 79110 Freiburg, Germany
  Tel: +49 (0)761-203-7436
  E-mail: korvink@imtek.uni-freiburg.de

• Dr. Ulrike Baur
  Technische Universität Chemnitz,
  Fakultät für Mathematik, 09107 Chemnitz, Germany
  Tel: +49 (0)371-531-36547
  E-mail: ubaur@mathematik.tu-chemnitz.de

• Dr. Lihong Feng
  Albert-Ludwigs-Universität Freiburg
  IMTEK - Institut für Mikrosystemtechnik, 79110 Freiburg
  Tel: +49 (0)761-203-7380
  E-mail: lihong.feng@imtek.uni-freiburg.de

• Mohammad Sahadet Hossain
  Technische Universität Chemnitz,
  Fakultät für Mathematik, 09107 Chemnitz, Germany
  Tel: +49 (0)371-531-36612
  E-mail: mohammad-sahadet.hossain@s2005.tu-chemnitz.de

Project description:

In current design processes for microsystems, numerical simulation plays only a minor role. This is due to the absence of suitable tools to study outer influences on complex microsystems in several energy domains efficiently or even in real-time. The usual model reduction allows a remarkable acceleration of time- or frequency-dependent evaluations. However, the reduced-order systems have the disadvantage that they allow only a small amount of alternatives in model variations. That is, each modification of the physical model such as a geometrical variation or boundary conditions requires a new model reduction. To overcome these difficulties it is required to generate systems of reduced order which contain additional parameters.
Thus, the aim of this project is the development of parameter-preserving model reduction methods and the integration of the algorithm into the design process for microsystems. We will follow two different approaches. The first one is based on Krylov subspace methods and the other one depends on balanced truncation. Both approaches are coupled with rational interpolation. To validate the new methods we will use three especially chosen parametric microsystem models. The different approaches will be compared and evaluated using these as benchmark problems.

Poster:

Parametric Model Order Reduction;
Evaluation Max Planck Institute for Dynamics of Complex Technical Systems Magdeburg;
Magdeburg, March 14, 2012.

Related publications:

U. Baur, P. Benner, A. Greiner, J.G. Korvink, J. Lienemann and C. Moosmann
Parameter preserving model reduction for MEMS applications,
Mathematical and Computational Modelling of Dynamical Systems, vol. 17, nr. 4, pp. 297-317, 2011.

U. Baur, C. A. Beattie, P. Benner and S. Gugercin
Interpolatory Projection Methods for Parameterized Model Reduction,
SIAM J. Sci. Comput., vol. 31, nr. 5, pp. 2489-2518. 2011.

L. Feng, P. Benner and J. G. Korvink
Parametric Model Order Reduction Accelerated by Recycling Algorithm,
Proc. of 48th IEEE Conference on Decision and 28th Chinese Control Conf., Shanghai, pp. 4328-4333, 2009.

U. Baur and P. Benner
Model Reduction for Parametric Systems Using Balanced Truncation and Interpolation (in German),
at-Automatisierungstechnik, vol. 57, nr. 8, pp. 411-420, 2009.
DOI: 10.1524/auto.2009.0787

L. Feng und P. Benner
Model Order Reduction for Systems with Non-Rational Transfer Function Arising in Computational Electromagnetics,
Mathematics in Industry, Scientific Computing in Electrical Engineering (SCEE 2008), Springer.

U. Baur and P. Benner
Parametrische Modellreduktion mit dünnen Gittern,
In B. Lohmann and A. Kugi (eds.), Tagungsband GMA-FA 1.30 'Modellierung, Identifikation und Simulation in der Automatisierungstechnik',
workshop in Anif, Austria, pp. 262-271, 2008. [ISBN: 978-3-9502451-1-0],

L. Feng and P. Benner
A robust algorithm for parametric model order reduction based on implicit moment matching,
Proceedings in Applied Mathematics and Mechanics, vol. 7, nr. 1, pp. 1021501-1021502, 2008.

L. Feng und P. Benner
Parametrische Modellreduktion durch impliziten Momentenabgleich,
in B. Lohmann and A. Kugi (eds.), Tagungsband GMA-FA 1.30 'Modellbildung, Identifizierung und Simulation in der Automatisierungstechnik',
workshop in Anif, pp. 34-47, 2007. [ISBN: 978-3-9502451-1-0]

C. Moosmann
ParaMOR - Model Order Reduction for parameterized MEMS applications
PhD thesis, IMTEK, University of Freiburg, Germany, 2006.

C. Moosmann and J. Korvink
Automatic parametric MOR for MEMS design
GMA-Fachausschuss 1.30, Modellbildung, Identifikation und Simulation in der Automatisierungstechnik,
Workshop am Bostalsee (Saarland), Germany, 2006.

E. B. Rudnyi, C. Moosmann, A. Greiner, T. Bechtold, J. G. Korvink
Parameter Preserving Model Reduction for MEMS System-level Simulation and Design,
MATHMOD 2006, February 8 - 10, Vienna University of Technology,
Austria, 2006.

Related talks:

U. Baur
Model Reduction for Parametric Systems Using Balanced Truncation and Interpolation
MoRePaS 09 - Model Reduction of Parametrized Systems;
Münster, Germany, September 16, 2009.

P. Benner
System-Theoretic and Interpolatory Methods for Parametric Model Reduction
MoRePaS 09 - Model Reduction of Parametrized Systems;
Münster, Germany, September 16, 2009.

U. Baur
Interpolatorische Verfahren zur Modellreduktion parametrischer Systeme
Regelungstechnisches Seminar at TU Munich;
Munich, Germany, July 2, 2009.

P. Benner
System-Theoretic and Interpolatory Methods for Parametric Model Reduction
Colloquium of the Department of Computational & Applied Mathematics;
Rice University, Houston, March 9, 2009.

U. Baur
Parameter-preserving model reduction by an interpolatory balanced truncation approach
SIAM Conference on Computational Science and Engineering (CSE09);
Miami, USA, March 3, 009.

U. Baur
Parametric model reduction with a balanced truncation/interpolatory approach using sparse grids
Seminar der Simulation, University Freiburg;
Freiburg, Germany, January 14, 2009.

P. Benner
Von Mikro zu Nano: Mathematik für die Computer von morgen
Dies Academicus 'Mathematik - Alles, was zählt' at the TU Chemnitz, November 12, 2008,
and 'Formel M - Mathematik für Innovation und Energieforschung', Duisburg, October 26 to 28, 2008.

U. Baur
Parametric model reduction with sparse grids,
GMA Fachausschuss 1.30;
Salzburg/Anif, Austria, September 26, 2008.

L. Feng
Model Order Reduction for Systems with Non-Rational Transfer Function Arising in Computational Electromagnetics
Scientific Computing in Electrical Engineering (SCEE 08);
Helsinki University of Technology, Finland, Sept. 28-Oct. 3, 2008.

L. Feng
Robust Algorithm for Parametric Model Order Reduction
Symposium on Recent Advances in Model Order Reduction;
TU Eindhoven, The Netherlands, November 2007.

P. Benner and L. Feng
Parametric  model reduction by implicit moment matching
GMA Fachausschuss 1.30;
Salzburg/Anif, Austria, September 27, 2007.

L. Feng
A Robust Algorithm for Parametric Model Order Reduction
6th International Congress on Industrial and Applied Mathematics (ICIAM 07);
Zurich, Switzerland, July 2007.