Dynamic Multi-Point Rational Interpolation for Frequency-Selective Model Order Reduction

2006 ◽  
Author(s):  
Mehboob Alam ◽  
Arthur Nieuwoudt ◽  
Yehia Massoud
Keyword(s):  
Model Order Reduction ◽  
Order Reduction ◽  
Rational Interpolation ◽  
Model Order ◽  
Frequency Selective

scholarly journals Non-intrusive double-greedy parametric model reduction by interpolation of frequency-domain rational surrogates

2021 ◽  
Author(s):  
Fabio Nobile ◽  
Davide Pradovera
Keyword(s):  
Parameter Space ◽  
Model Order Reduction ◽  
Optimization Problem ◽  
Order Reduction ◽  
Rational Interpolation ◽  
Sparse Grids ◽  
Parametric Model ◽  
High Dimensional ◽  
Model Order ◽  
Interpolation Strategy

We propose a model order reduction approach for non-intrusive surrogate modeling of parametric dynamical systems. The reduced model over the whole parameter space is built by combining surrogates in frequency only, built at few selected values of the parameters. This, in particular, requires matching the respective poles by solving an optimization problem. If the frequency surrogates are constructed by a suitable rational interpolation strategy, frequency and parameters can both be sampled in an adaptive fashion. This, in general, yields frequency surrogates with different numbers of poles, a situation addressed by our proposed algorithm. Moreover, we explain how our method can be applied even in high-dimensional settings, by employing locally-refined sparse grids in parameter space to weaken the curse of dimensionality. Numerical examples are used to showcase the effectiveness of the method, and to highlight some of its limitations in dealing with unbalanced pole matching, as well as with a large number of parameters.

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