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Stability-preserving parametric model reduction by matrix interpolation

Author

Listed:
  • Rudy Eid
  • Rosa Castañé-Selga
  • Heiko Panzer
  • Thomas Wolf
  • Boris Lohmann

Abstract

In this article, a method to preserve stability in parametric model reduction by matrix interpolation is presented. Based on the matrix measure approach, sufficient conditions on the original system matrices are derived. Once they are fulfilled, the stability of each of the reduced models is guaranteed as well as that of the parametric model resulting from interpolation. In addition, it is shown that these sufficient conditions are met by port-Hamiltonian systems and by a relevant set of second-order systems obtained by the finite element method. The new approach is illustrated by two numerical examples.

Suggested Citation

  • Rudy Eid & Rosa Castañé-Selga & Heiko Panzer & Thomas Wolf & Boris Lohmann, 2010. "Stability-preserving parametric model reduction by matrix interpolation," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 17(4), pages 319-335, November.
    • Handle: RePEc:taf:nmcmxx:v:17:y:2010:i:4:p:319-335
    DOI: 10.1080/13873954.2011.547671
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    References listed on IDEAS

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    1. Peter Benner & Enrique S. Quintana-Ortí & Gregorio Quintana-Ortí, 2000. "Balanced Truncation Model Reduction of Large-Scale Dense Systems on Parallel Computers," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 6(4), pages 383-405, December.
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    Cited by:

    1. Nadine Jung & Anthony T. Patera & Bernard Haasdonk & Boris Lohmann, 2011. "Model order reduction and error estimation with an application to the parameter-dependent eddy current equation," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 17(6), pages 561-582, April.

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