HDG-POD Reduced Order Model of the Heat Equation
Abstract
We propose a new hybridizable discontinuous Galerkin (HDG) model order reduction technique based on proper orthogonal decomposition (POD). We consider the heat equation as a test problem and prove error bounds that converge to zero as the number of POD modes increases. We present 2D and 3D numerical results to illustrate the convergence analysis.
Recommended Citation
J. Shen et al., "HDG-POD Reduced Order Model of the Heat Equation," Journal of Computational and Applied Mathematics, vol. 362, pp. 663 - 679, Elsevier, Dec 2019.
The definitive version is available at https://doi.org/10.1016/j.cam.2018.09.031
Department(s)
Mathematics and Statistics
Research Center/Lab(s)
Center for High Performance Computing Research
Keywords and Phrases
Error analysis; Heat transfer; Partial differential equations; Principal component analysis; Convergence analysis; Discontinuous galerkin; Discontinuous Galerkin methods; Heat equation; Model order reduction; Numerical results; Proper orthogonal decompositions; Reduced order models; Galerkin methods; Hybridizable discontinuous Galerkin method
International Standard Serial Number (ISSN)
0377-0427
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2018 Elsevier, All rights reserved.
Publication Date
01 Dec 2019
Comments
J. Singler and Y. Zhang were supported in part by National Science Foundation, United States, grant DMS-1217122.