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Balanced Truncation Model Reduction of Large-Scale Dense Systems on Parallel Computers

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  • PETER BENNER
  • ENRIQUE S. QUINTANA-ORTí
  • GREGORIO QUINTANA-ORTí

Abstract

Model reduction is an area of fundamental importance in many modeling and control applications. In this paper we analyze the use of parallel computing in model reduction methods based on balanced truncation of large-scale dense systems. The methods require the computation of the Gramians of a linear-time invariant system. Using a sign function-based solver for computing full-rank factors of the Gramians yields some favorable computational aspects in the subsequent computation of the reduced-order model, particularly for non-minimal systems. As sign function-based computations only require efficient implementations of basic linear algebra operations readily available, e.g., in the BLAS, LAPACK, and ScaLAPACK, good performance of the resulting algorithms on parallel computers is to be expected. Our experimental results on a PC cluster show the performance and scalability of the parallel implementation.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:nmcmxx:v:6:y:2000:i:4:p:383-405
    DOI: 10.1076/mcmd.6.4.383.3658
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    Cited by:

    1. 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.
    2. Ion Necoara & Tudor-Corneliu Ionescu, 2022. "Optimal H 2 Moment Matching-Based Model Reduction for Linear Systems through (Non)convex Optimization," Mathematics, MDPI, vol. 10(10), pages 1-19, May.

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