TY - GEN
T1 - Parametric model order reduction by sparse-grid-based interpolation on matrix manifolds for multidimensional parameter spaces
AU - Geuss, Matthias
AU - Butnaru, Daniel
AU - Peherstorfer, Benjamin
AU - Bungartz, Hans Joachim
AU - Lohmann, Boris
N1 - Publisher Copyright:
© 2014 EUCA.
PY - 2014/7/22
Y1 - 2014/7/22
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84911489247&partnerID=8YFLogxK
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U2 - 10.1109/ECC.2014.6862414
DO - 10.1109/ECC.2014.6862414
M3 - Conference contribution
AN - SCOPUS:84911489247
T3 - 2014 European Control Conference, ECC 2014
SP - 2727
EP - 2732
BT - 2014 European Control Conference, ECC 2014
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 13th European Control Conference, ECC 2014
Y2 - 24 June 2014 through 27 June 2014
ER -