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A FOM/ROM Hybrid Approach for Accelerating Numerical Simulations

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Abstract

The basis generation in reduced order modeling usually requires multiple high-fidelity large-scale simulations that could take a huge computational cost. In order to accelerate these numerical simulations, we introduce a FOM/ROM hybrid approach in this paper. It is developed based on an a posteriori error estimation for the output approximation of the dynamical system. By controlling the estimated error, the method dynamically switches between the full-order model and the reduced-oder model generated on the fly. Therefore, it reduces the computational cost of a high-fidelity simulation while achieving a prescribed accuracy level. Numerical tests on the non-parametric and parametric PDEs illustrate the efficacy of the proposed approach.

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Authors and Affiliations

  1. Max Planck Institute for Dynamics of Complex Technical Systems, 1 Sandtorstr, 39106, Magdeburg, Germany

    Lihong Feng

  2. Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN, 46556, USA

    Guosheng Fu

  3. Department of Mathematics, University of South Carolina, Columbia, SC, 29208, USA

    Zhu Wang

Authors
  1. Lihong Feng
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  2. Guosheng Fu
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  3. Zhu Wang
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Corresponding author

Correspondence to Zhu Wang.

Additional information

The authors acknowledge the support from the Institute for Computational and Experimental Research in Mathematics (ICERM) at Brown University for participating the “Model and dimension reduction in uncertain and dynamic systems" semester program in Spring 2020, which were supported by the National Science Foundation under Grant No. DMS-1439786 and the Simons Foundation Grant No. 50736. Z. Wang was partially supported by the National Science Foundation through Grants No. DMS-1913073, 2012469 and the U.S. Department of Energy Grant No. DE-SC0020270. The authors are grateful to the anonymous referees for their helpful comments and suggestions.

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Feng, L., Fu, G. & Wang, Z. A FOM/ROM Hybrid Approach for Accelerating Numerical Simulations. J Sci Comput 89, 61 (2021). https://doi.org/10.1007/s10915-021-01668-9

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  • DOI: https://doi.org/10.1007/s10915-021-01668-9

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