HDG-POD Reduced Order Model of the Heat Equation
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.
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
Mathematics and Statistics
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)
Article - Journal
© 2018 Elsevier, All rights reserved.
01 Dec 2019