TY - JOUR
T1 - Data Reconstruction-Based Two-Step Non-Intrusive Reduced-Order Modeling Using Fourier Transform and Interpolations
AU - Lee, Jonggeon
AU - Kim, Euiyoung
AU - Lee, Jaehun
N1 - Publisher Copyright:
© 2022 by the authors.
PY - 2022/10
Y1 - 2022/10
N2 - 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.
AB - 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.
KW - discrete Fourier transformations
KW - non-intrusive method
KW - proper orthogonal decomposition
KW - radial basis function
KW - reduced-order model
UR - http://www.scopus.com/inward/record.url?scp=85140650011&partnerID=8YFLogxK
U2 - 10.3390/math10203738
DO - 10.3390/math10203738
M3 - Article
AN - SCOPUS:85140650011
SN - 2227-7390
VL - 10
JO - Mathematics
JF - Mathematics
IS - 20
M1 - 3738
ER -