Parametric model order reduction by sparse-grid-based interpolation on matrix manifolds for multidimensional parameter spaces

Matthias Geuss, Daniel Butnaru, Benjamin Peherstorfer, Hans Joachim Bungartz, Boris Lohmann

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Current methods of parametric model order reduction based on the interpolation of system matrices are extended in this paper to an efficient method to tackle multidimensional parameter spaces. In order to overcome the curse of dimensionality the technique of sparse grids with multiple outputs is applied. The procedure is divided into an offline and online phase. In the offline phase the weighting matrices to the corresponding basis functions are computed with respect to generalized coordinates and appropriate matrix manifolds. The number of levels for the sparse grid can be set manually or determined by a tolerance criterion. The calculation of the interpolated system takes place during the online phase by evaluating the interpolant. The performance of the proposed method is demonstrated by two numerical examples.

Original languageEnglish (US)
Title of host publication2014 European Control Conference, ECC 2014
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages2727-2732
Number of pages6
ISBN (Electronic)9783952426913
DOIs
StatePublished - Jan 1 2014
Event13th European Control Conference, ECC 2014 - Strasbourg, France
Duration: Jun 24 2014Jun 27 2014

Other

Other13th European Control Conference, ECC 2014
CountryFrance
CityStrasbourg
Period6/24/146/27/14

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Interpolation

ASJC Scopus subject areas

  • Control and Systems Engineering

Cite this

Geuss, M., Butnaru, D., Peherstorfer, B., Bungartz, H. J., & Lohmann, B. (2014). Parametric model order reduction by sparse-grid-based interpolation on matrix manifolds for multidimensional parameter spaces. In 2014 European Control Conference, ECC 2014 (pp. 2727-2732). [6862414] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ECC.2014.6862414

Parametric model order reduction by sparse-grid-based interpolation on matrix manifolds for multidimensional parameter spaces. / Geuss, Matthias; Butnaru, Daniel; Peherstorfer, Benjamin; Bungartz, Hans Joachim; Lohmann, Boris.

2014 European Control Conference, ECC 2014. Institute of Electrical and Electronics Engineers Inc., 2014. p. 2727-2732 6862414.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Geuss, M, Butnaru, D, Peherstorfer, B, Bungartz, HJ & Lohmann, B 2014, Parametric model order reduction by sparse-grid-based interpolation on matrix manifolds for multidimensional parameter spaces. in 2014 European Control Conference, ECC 2014., 6862414, Institute of Electrical and Electronics Engineers Inc., pp. 2727-2732, 13th European Control Conference, ECC 2014, Strasbourg, France, 6/24/14. https://doi.org/10.1109/ECC.2014.6862414
Geuss M, Butnaru D, Peherstorfer B, Bungartz HJ, Lohmann B. Parametric model order reduction by sparse-grid-based interpolation on matrix manifolds for multidimensional parameter spaces. In 2014 European Control Conference, ECC 2014. Institute of Electrical and Electronics Engineers Inc. 2014. p. 2727-2732. 6862414 https://doi.org/10.1109/ECC.2014.6862414
Geuss, Matthias ; Butnaru, Daniel ; Peherstorfer, Benjamin ; Bungartz, Hans Joachim ; Lohmann, Boris. / Parametric model order reduction by sparse-grid-based interpolation on matrix manifolds for multidimensional parameter spaces. 2014 European Control Conference, ECC 2014. Institute of Electrical and Electronics Engineers Inc., 2014. pp. 2727-2732
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