A Modified Balanced POD Model Reduction Algorithm for Parabolic PDEs with Unbounded Inputs
We develop an algorithm to approximate the balanced reduced order model for linear parabolic PDE systems with an unbounded input operator and a bounded output operator. We use balanced POD, a widely used simulation-based algorithm for balanced truncation, however we modify the algorithm to avoid unusual and challenging simulations due to the unbounded input operator. We develop the modified algorithm for two classes of unbounded input operators; the first class includes Neumann boundary input operators, and the second class includes Dirichlet boundary input operators. We present numerical results for a convection diffusion equation.
W. Hu and J. R. Singler, "A Modified Balanced POD Model Reduction Algorithm for Parabolic PDEs with Unbounded Inputs," Proceedings of the American Control Conference (2014, Portland, OR), Institute of Electrical and Electronics Engineers (IEEE), Jun 2014.
The definitive version is available at https://doi.org/10.1109/ACC.2014.6859087
American Control Conference (2014: Jun. 4-6, Portland, OR)
Mathematics and Statistics
Center for High Performance Computing Research
Keywords and Phrases
Computational Methods; Control; Balanced Truncation; Convection-Diffusion Equations; Dirichlet Boundary; Distributed Parameter Systems; Modified Algorithms; Numerical Results; Reduced Order Models; Simulation-Based Algorithms; Algorithms
International Standard Book Number (ISBN)
International Standard Serial Number (ISSN)
Article - Conference proceedings
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01 Jun 2014