Doctoral Dissertations

Hiba Fareed

Keywords and Phrases

Error Analysis; Finite Element Method; Incremental Algorithm; Proper Orthogonal Decomposition; Weighted Norm

Abstract

"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.

Advisor(s)

Singler, John R.

Committee Member(s)

He, Xiaoming
Zhang, Yanzhi
Paige, Robert
Leopold, Jennifer

Department(s)

Mathematics and Statistics

Degree Name

Ph. D. in Mathematics

Publisher

Missouri University of Science and Technology

Publication Date

Spring 2018

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

Pagination

x, 96 pages

Note about bibliography

Includes bibliographic references.

Rights

© 2018 Hiba Ghassan Fareed, All rights reserved.

Document Type

Dissertation - Open Access

File Type

text

Language

English

Thesis Number

T 11278

Electronic OCLC #

1041858451

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Included in

Mathematics Commons

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