Keywords and Phrases
Error Analysis; Finite Element Method; Incremental Algorithm; Proper Orthogonal Decomposition; Weighted Norm
"We propose an incremental algorithm to compute the proper orthogonal decomposition (POD) of simulation data for a partial differential equation. Specifically, we modify an incremental matrix SVD algorithm of Brand to accommodate data arising from Galerkin-type simulation methods for time dependent PDEs. We introduce an incremental SVD algorithm with respect to a weighted inner product to compute the proper orthogonal decomposition (POD). The algorithm is applicable to data generated by many numerical methods for PDEs, including finite element and discontinuous Galerkin methods. We also modify the algorithm to initialize and incrementally update both the SVDand an error bound during the time stepping in a PDE solver without storing the simulation data. We show the algorithm produces the exact SVD of an approximate data matrix, and the operator norm error between the approximate and exact data matrices is bounded above by the computed error bound. This error bound also allows us to bound the error in the incrementally computed singular values and singular vectors. We demonstrate the effectiveness of the algorithm using finite element computations for a 1D Burgers' equation, a 1D FitzHugh-Nagumo PDE system, and a 2D Navier-Stokes problem"--Abstract, page iv.
Singler, John R.
Mathematics and Statistics
Ph. D. in Mathematics
Missouri University of Science and Technology
Journal article titles appearing in thesis/dissertation
- Incremental proper orthogonal decomposition for PDE simulation data
- Error analysis of an incremental POD algorithm for PDE simulation data
x, 96 pages
© 2018 Hiba Ghassan Fareed, All rights reserved.
Dissertation - Open Access
Electronic OCLC #
Fareed, Hiba, "Incremental proper orthogonal decomposition for PDE simulation data: Algorithms and analysis" (2018). Doctoral Dissertations. 2671.