Skip to main content

An Enhancement of the Computational Efficiency of Parametric Component Mode Synthesis Within Limited Parameter Domains Using Conventional Interpolations


This paper presents the usages of conventional interpolation functions for interpolation-based parametric component mode synthesis (IB-PCMS) method within limited parameter domains. One of the representatives of reduced-order models (ROM) is the one using the offline-online strategy, which constructs multiple ROMs at given sampling points in the offline stage and manipulates them to derive a ROM at the new query point in the online stage efficiently via, for example, using the interpolation of the constructed ROMs. For such a process in the online stage, manifold interpolations, congruence transformations, and the mode exclusion steps are required to guarantee the accuracy and the robustness of the ROM, which complexifies computational procedures in the offline stage. For the cases where the design parameters do not change dramatically due to the limited domain of interest, and as a result, if the ROM does not experience any mode veering phenomena, simple interpolations can guarantee accurate solutions. The validities of using conventional interpolations are investigated for a numerical example providing the assessments of the accuracy for representative interpolation functions.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3


  1. A.K. Noor, Recent advances and applications of reduction methods. Appl. Mech. Rev. 47, 125–146 (1994)

    Article  Google Scholar 

  2. D. de Klerk, D.J. Rixen, S.N. Voormeeren, General framework for dynamic substructuring: history, review and classification of techniques. AIAA J. 46, 1169–1181 (2008)

    Article  Google Scholar 

  3. P. Benner, S. Gugercin, K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Rev. 57, 483–531 (2015)

    MathSciNet  Article  Google Scholar 

  4. E. Balmès, Parametric families of reduced finite element models. Theory and applications. Mech. Syst. Signal Process. 10, 381–394 (1996)

    Article  Google Scholar 

  5. D. Amsallem, C. Farhat, Interpolation method for adapting reduced-order models and application to aeroelasticity. AIAA J. 46, 1803–1813 (2008)

    Article  Google Scholar 

  6. D. Amsallem, J. Cortial, K. Carlberg, C. Farhat, A method for interpolating on manifolds structural dynamics reduced-order models. Int. J. Numer. Methods Eng. 80, 1241–1258 (2009)

    Article  Google Scholar 

  7. D. Amsalem, C. Farhat, An online method for interpolating linear parametric reduced-order models. SIAM J. Sci. Comput. 33, 2169–2198 (2011)

    MathSciNet  Article  Google Scholar 

  8. S.-K. Hong, B.I. Epureanu, M.P. Castanier, D.J. Gorsich, Parametric reduced-order models for predicting the vibration response of complex structures with component damage and uncertainties. J. Sound Vib. 330, 1091–1110 (2011)

    Article  Google Scholar 

  9. J. Lee, J. Lee, H. Cho, E. Kim, M. Cho, Reduced-order modeling of nonlinear structural dynamical systems via element-wise stiffness evaluation procedure combined with hyper-reduction. Comput. Mech. 67, 523–540 (2021)

    MathSciNet  Article  Google Scholar 

  10. D.J. Rixen, A dual Craig-Bampton method for dynamic substructuring. J. Comput. Appl. Math. 168, 383–391 (2004)

    MathSciNet  Article  Google Scholar 

  11. K.C. Park, Y.H. Park, Partitioned component mode synthesis via a flexibility approach. AIAA J. 42, 1236–1245 (2004)

    Article  Google Scholar 

  12. C. Papadimitriou, D.-C. Papadioti, Component mode synthesis techniques for finite element model updating. Comput. Struct. 126, 15–28 (2013)

    Article  Google Scholar 

  13. K.J. Bathe, J. Dong, Component mode synthesis with subspace iterations for controlled accuracy of frequency and mode shape solutions. Comput. Struct. 139, 28–32 (2014)

    Article  Google Scholar 

  14. R. Zhao, K. Yu, An efficient transient analysis method for linear time-varying structures based on multi-level substructuring method. Comput. Struct. 146, 76–90 (2015)

    Article  Google Scholar 

  15. J. Lee, M. Cho, An interpolation-based parametric reduced order model combined with component mode synthesis. Comput. Methods. Appl. Mech. Eng. 319, 258–286 (2017)

    MathSciNet  Article  Google Scholar 

  16. J. Lee, M. Cho, Efficient design optimization strategy for structural dynamic systems using a reduced basis method combined with an equivalent static load. Struct. Multidiscip. Optim. 58, 1489–1504 (2018)

    MathSciNet  Article  Google Scholar 

  17. J. Lee, A dynamic substructuring-based parametric reduced-order model considering the interpolation of free-interface substructural modes. J. Mech. Sci. Tech. 32, 5831–5838 (2018)

    Article  Google Scholar 

  18. J. Lee, A parametric reduced-order model using substructural mode selections and interpolation. Comput. Struct. 212, 199–214 (2019)

    Article  Google Scholar 

  19. G.H. Golub, C.F. Van Loan, Matrix Computations, 4th edn. (The Johns Hopkins University Press, Baltimore, 2012)

    MATH  Google Scholar 

  20. M.P. Castanier, Y.-C.C.O. Tan, Characteristic constraint modes for component mode synthesis. AIAA J. 39, 1182–1187 (2001)

    Article  Google Scholar 

  21. E.N. Dvorkin, K.J. Bathe, A continuum mechanics based four-node shell element for general non-linear analysis. Eng. Comput. 1, 77–88 (1984)

    Article  Google Scholar 

Download references


The work was supported by National Research Foundation of Korea, 2022 (NRF_2020R1C1C1011970).

Author information

Authors and Affiliations


Corresponding author

Correspondence to Jaehun Lee.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Lee, J. An Enhancement of the Computational Efficiency of Parametric Component Mode Synthesis Within Limited Parameter Domains Using Conventional Interpolations. Multiscale Sci. Eng. 4, 66–72 (2022).

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:


  • Reduced-order modeling
  • Interpolation
  • Congruence transformation
  • Dynamic substructuring
  • Parametric study