An adaptive scheme for a class of interpolatory model reduction methods for frequency response problems

Authors

  • Ulrich Hetmaniuk,

    1. Department of Applied Mathematics, University of Washington, Seattle, WA, USA
    Search for more papers by this author
  • Radek Tezaur,

    1. Department of Aeronautics and Astronautics, Stanford University, Stanford, CA, USA
    Search for more papers by this author
  • Charbel Farhat

    Corresponding author
    1. Department of Mechanical Engineering, Stanford University, Stanford, CA, USA
    2. Institute for Computational and Mathematical Engineering, Stanford University, Stanford, CA, USA
    • Department of Aeronautics and Astronautics, Stanford University, Stanford, CA, USA
    Search for more papers by this author

Correspondence to: Charbel Farhat, Department of Aeronautics and Astronautics, Stanford University, Stanford, CA 94305, USA.

E-mail: cfarhat@stanford.edu

SUMMARY

Frequency sweep problems arise in many structural dynamic, acoustic, and structural acoustic applications. In each case, they incur the evaluation of a frequency response function for a typically large number of frequencies. Because each function evaluation requires the solution of an often large-scale system of equations, frequency sweep problems are computationally intensive. Interpolatory model order reduction is a powerful tool for reducing their cost. However, the performance of this tool depends on the location and number of the interpolation frequency points. It also depends on the number of consecutive frequency derivatives of the response function that are matched at each frequency point. So far, these two choices have been made in the literature in a heuristic manner. In contrast, this paper proposes an automatic adaptive strategy based on monitoring the Euclidean norm of the relative residual associated with the function to be evaluated over the frequency band of interest. More specifically, the number of interpolation points and the number of matched frequency derivatives are adaptively increased until the global Euclidean norm of the relative residual is reduced below a user-specified tolerance. The robustness, accuracy, and computational efficiency of this adaptive strategy are highlighted with the solution of several frequency sweep problems associated with large-scale structural dynamic, acoustic, and structural acoustic finite element models. Copyright © 2012 John Wiley & Sons, Ltd.

Ancillary