Abstract
Parametric model order reduction (PMOR) has received a tremendous amount of attention in recent years. Among the first approaches considered, mainly in system and control theory as well as computational electromagnetics and nanoelectronics, are methods based on multi-moment matching. Despite numerous other successful methods, including the reduced-basis method (RBM), other methods based on (rational, matrix, manifold) interpolation, or Kriging techniques, multi-moment matching methods remain a reliable, robust, and flexible method for model reduction of linear parametric systems. Here we propose a numerically stable algorithm for PMOR based on multi-moment matching. Given any number of parameters and any number of moments of the parametric system, the algorithm generates a projection matrix for model reduction by implicit moment matching. The implementation of the method based on a repeated modified Gram-Schmidt-like process renders the method numerically stable. The proposed method is simple yet efficient. Numerical experiments show that the proposed algorithm is very accurate.
Keywords
- Orthonormal Basis
- Proper Orthogonal Decomposition
- Model Order Reduction
- Krylov Subspace
- Power Series Expansion
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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- 1.
1 See http://modelreduction.org.
- 2.
2 Here we use a nonzero expansion point for the Laplace variable s, s 0 = 0.001, a zero expansion point for k, k 0 = 0, to ensure that the matrix \(\tilde E\) is nonsingular. For all the simulation results in Sect. 6.5.1, the same expansion points are taken for all the tested MOR methods: the non-parametric moment-matching MOR, the explicit multi-moment matching and the proposed Algorithm 6.1.
- 3.
3 http://morwiki.mpi-magdeburg.mpg.de/morwiki/index.php/Scanning_Electrochemical_Microscopy.
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Benner, P., Feng, L. (2014). A Robust Algorithm for Parametric Model Order Reduction Based on Implicit Moment Matching. In: Quarteroni, A., Rozza, G. (eds) Reduced Order Methods for Modeling and Computational Reduction. MS&A - Modeling, Simulation and Applications, vol 9. Springer, Cham. https://doi.org/10.1007/978-3-319-02090-7_6
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