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

Jonggeon Lee, Euiyoung Kim and Jaehun Lee ()
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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

Mathematics, 2022, vol. 10, issue 20, 1-16

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.

Keywords: reduced-order model; proper orthogonal decomposition; radial basis function; discrete Fourier transformations; non-intrusive method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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