Year: 2024
Author: Qijia Zhai, Qingguo Hong, Xiaoping Xie
Advances in Applied Mathematics and Mechanics, Vol. 16 (2024), Iss. 6 : pp. 1328–1357
Abstract
In this paper, we develop a new reduced basis (RB) method, named as Single Eigenvalue Acceleration Method (SEAM), for second order parabolic equations with homogeneous Dirichlet boundary conditions. The high-fidelity numerical method adopts the backward Euler scheme and conforming simplicial finite elements for the temporal and spatial discretizations, respectively. Under the assumption that the time step size is sufficiently small and time steps are not very large, we show that the singular value distribution of the high-fidelity solution matrix $U$ is close to that of a rank one matrix. We select the eigenfunction associated to the principal eigenvalue of the matrix $U^TU$ as the basis of Proper Orthogonal Decomposition (POD) method so as to obtain SEAM and a parallel SEAM. Numerical experiments confirm the efficiency of the new method.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2023-0053
Advances in Applied Mathematics and Mechanics, Vol. 16 (2024), Iss. 6 : pp. 1328–1357
Published online: 2024-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 30
Keywords: Reduced basis method proper orthogonal decomposition singular value second order parabolic equation.
Author Details
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A projection-based time-segmented reduced order model for fluid-structure interactions
Zhai, Qijia
Zhang, Shiquan
Sun, Pengtao
Xie, Xiaoping
Journal of Computational Physics, Vol. 520 (2025), Iss. P.113481
https://doi.org/10.1016/j.jcp.2024.113481 [Citations: 0]