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Fast and Novel Computational Methods for Multi-scale and Multi-physics: FETI and POD-ROM

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Abstract

In this paper, the finite element tearing and interconnecting (FETI) method and proper orthogonal decomposition-based reduced order model (POD-ROM) are suggested as fast and novel computational approaches for multi-scale and multi-physics analysis. FETI is one of non-overlapping domain decomposition methods, facilitating the parallel computation. POD-ROM reduces the number of degrees of freedom (DoFs) to several representative POD modes which completely describe the behavior of the full order model. The computational time for the analyses using large number of DoFs can be decreased by using the previously mentioned methods. The present FETI-local and POD-ROM are found to reduce computational time significantly in each example.

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References

  1. C. Farhat, F.X. Roux, A method of finite element tearing and interconnecting and its parallel solution algorithm. Int. J. Numer. Methods Eng. 32(6), 1205–1227 (1991)

    Article  MathSciNet  Google Scholar 

  2. K.C. Park, C.A. Felippa, U.A. Gumaste, A localized version of the method of lagrange multipliers and its applications. Comput. Mech. 24, 476–490 (2000)

    Article  Google Scholar 

  3. H.S. Joo, H.S. Cho, S.I. Kim, S.-J. Shin, J.Y. Kwak, Parallel computation fort three-dimensional shell analysis of curved configuration based on domain decomposition method. J. Comput. Sci. 24(24), 24–33 (2018)

    Article  Google Scholar 

  4. J.Y. Kwak, T.Y. Chun, S.-J. Shin, O.A. Bauchau, Domain decomposition approach to flexible multibody dynamics simulation. Comput. Mech. 53, 147–158 (2014)

    Article  MathSciNet  Google Scholar 

  5. J. Li, C. Farhat, P. Avery, R. Tezaur, A dual-primal FETI method for solving a class of fluid-structure interaction problems in the frequency domain. Int. J. Numer. Methods Eng. 89, 418–437 (2012)

    Article  MathSciNet  Google Scholar 

  6. C. Farhat, L. Crivelli, A transient FETI methodology for large-scale parallel implicit computations in structural mechanics. Int. J. Numer. Methods Eng. 37, 1945–1975 (1994)

    Article  MathSciNet  Google Scholar 

  7. J. Tiovanen, P. Avery, C. Farhat, A multilevel FETI-DP method and its performance for problems with billions of degrees of freedom. Int. J. Numer. Methods Eng. 116, 661–682 (2018)

    Article  MathSciNet  Google Scholar 

  8. C.W. Rowley, T. Colonius, R.M. Murray, Model reduction for compressible flows using POD and Galerkin projection. Physica D 189, 115–129 (2004)

    Article  MathSciNet  Google Scholar 

  9. J. Baiges, R. Cordina, S. Idelsohn, Explicit reduced-order models for the stabilized finite element approximation of the incompressible Navier–Stokes equations. Numer. Methods Fluids 72(12), 1219–1243 (2013)

    Article  MathSciNet  Google Scholar 

  10. M.W. Lee, H.M. Park, An efficient method of solving the Navier–Stokes equations for flow control. Int. J. Numer. Methods Eng. 41, 1133–1151 (1998)

    Article  MathSciNet  Google Scholar 

  11. B. Galleti, C.H. Bruneau, L. Zannetti, A. Iollo, Low-order modelling of laminar flow regimes past a confined square cylinder. J. Fluid Mech. 503, 161–170 (2004)

    Article  MathSciNet  Google Scholar 

  12. J. Burkardt, M. Gunzburger, H.C. Lee, POD and CVT-based reduced-order modeling of Navier–Stokes flows. Comput. Methods Appl. Mech. Eng. 196, 337–355 (2006)

    Article  MathSciNet  Google Scholar 

  13. B.F. Feeny, On the physical interpretation of proper orthogonal modes in vibrations. J. Sound Vib. 211, 607–616 (1997)

    Article  Google Scholar 

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

    Article  Google Scholar 

  15. H. Cho, S.-J. Shin, H. Kim, M. Cho, Enhanced model-order reduction approach via online adaptation for parametrized nonlinear structural problems. Comput. Mech. 65, 331–353 (2020)

    Article  MathSciNet  Google Scholar 

  16. C. Farhat, P. Avery, R. Tezaur, J. Li, FETI-DPH: a dual-primal domain decomposition method for acoustic scattering. J. Comput. Acoust. 13(3), 499–524 (2005)

    Article  MathSciNet  Google Scholar 

  17. S. Lee, H. Cho, H. Kim, S. Shin, Time-domain non-linear aeroelastic analysis via a projection-based reduced-order model. Aeronaut. J. (2020). https://doi.org/10.1017/aer.2020.59

    Article  Google Scholar 

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Acknowledgements

This work was supported by the Advanced Research Center Program (NRF-2013R1A5A1073861) through a grant from the National Research Foundation of Korea (NRF), which was funded by the Korean government (MSIP) and contracted through the Advanced Space Propulsion Research Center at Seoul National University. Also, it was supported by the EDISON Program through the National Research Foundation of Korea funded by the Ministry of Science, and ICT (Grant no. NRF-2020M3C1A6043396).

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Authors and Affiliations

  1. Seoul National University, Seoul, 08826, Republic of Korea

    Si-Hun Lee, Yongse Kim, DuHyun Gong & HyunShig Joo

  2. Jeonbuk National University, Jeonju, 54896, Republic of Korea

    Haeseong Cho

  3. Sejong University, Seoul, 05006, Republic of Korea

    Haedong Kim

  4. Institute of Advanced Aerospace Technology, Seoul National University, Seoul, 08826, Republic of Korea

    SangJoon Shin

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  1. Si-Hun Lee
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  2. Yongse Kim
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Correspondence to SangJoon Shin.

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Lee, SH., Kim, Y., Gong, D. et al. Fast and Novel Computational Methods for Multi-scale and Multi-physics: FETI and POD-ROM. Multiscale Sci. Eng. 2, 189–197 (2020). https://doi.org/10.1007/s42493-020-00048-z

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  • DOI: https://doi.org/10.1007/s42493-020-00048-z

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