A Robust Algorithm for Parametric Model Order Reduction Based on Implicit Moment Matching

  • Peter Benner
  • Lihong FengEmail author
Part of the MS&A - Modeling, Simulation and Applications book series (MS&A, volume 9)


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.


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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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Max Planck Institute for Dynamics of Complex Technical SystemsMagdeburgGermany

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