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Data Reconstruction-Based Two-Step Non-Intrusive Reduced-Order Modeling Using Fourier Transform and Interpolations

Author

Listed:
  • Jonggeon Lee

    (Department of Mechanical Engineering, Seoul National University, Seoul 08826, Korea)

  • Euiyoung Kim

    (Mechanical Systems Safety Research Division, Department of System Dynamics, Korea Institute of Machinery & Materials, Daejeon 34103, Korea)

  • Jaehun Lee

    (Department of Mechanical, Robotics and Energy Engineering, Dongguk University, Seoul 04620, Korea)

Abstract

This study presents a data reconstruction-based two-step non-intrusive reduced-order modeling (ROM) based on discrete Fourier transformation (DFT) and proper orthogonal decomposition-radial basis function (POD-RBF) interpolation. To efficiently approximate a system for various parametric inputs, two offline and one online stage are proposed. The first offline stage adjusts and reconstructs sampled data using a scaling factor. During the adjusting procedure, the fast Fourier transform operation is used to transform a domain between the time and frequency, and the POD-RBF interpolation method efficiently generates adjusted data. The second offline stage constructs multiple ROMs in the frequency domain for interpolation with respect to the parameter. Finally, in the online stage, the solution field depending on the changes in input parameters, is approximated using the POD-RBF interpolation and the inverse Fourier transformation. The accuracy and efficiency of the proposed method are verified using the 2-D unsteady incompressible Newtonian fluid problems and are compared to the OpenFOAM software program showing remarkable efficiencies in computing approximated solutions.

Suggested Citation

  • Jonggeon Lee & Euiyoung Kim & Jaehun Lee, 2022. "Data Reconstruction-Based Two-Step Non-Intrusive Reduced-Order Modeling Using Fourier Transform and Interpolations," Mathematics, MDPI, vol. 10(20), pages 1-16, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:20:p:3738-:d:939126
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    References listed on IDEAS

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    1. Peter Rashkov, 2022. "Reduced Basis Approximation for a Spatial Lotka-Volterra Model," Mathematics, MDPI, vol. 10(12), pages 1-12, June.
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    Cited by:

    1. Jaehun Lee & Younggeun Park & Yeji Lee & Seongmin Chang, 2023. "An Adaptive Frequency Sampling Algorithm for Dynamic Condensation-Based Frequency Response Analysis," Mathematics, MDPI, vol. 11(12), pages 1-18, June.

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