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Numerical Heat Transfer, Part B: Fundamentals
An International Journal of Computation and Methodology
Volume 48, 2005 - Issue 2
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Original Articles

Solving Transient Nonlinear Heat Conduction Problems by Proper Orthogonal Decomposition and the Finite-Element Method

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Pages 103-124 | Received 03 Dec 2004, Accepted 30 Dec 2004, Published online: 01 Sep 2006

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Yazhou Wang, Guoliang Qin, Kumar K. Tamma, Dean Maxam & David Tae. (2021) Numerical investigations on model order reduction to SEM based on POD-DEIM to linear/nonlinear heat transfer problems. Numerical Heat Transfer, Part B: Fundamentals 80:3-4, pages 39-52.
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Qiang-Hua Zhu, Yu Liang & Xiao-Wei Gao. (2020) A proper orthogonal decomposition analysis method for transient nonlinear heat conduction problems. Part 2: Advanced algorithm. Numerical Heat Transfer, Part B: Fundamentals 77:2, pages 116-137.
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Qiang-Hua Zhu, Yu Liang & Xiao-Wei Gao. (2020) A proper orthogonal decomposition analysis method for transient nonlinear heat conduction problems. Part 1: Basic algorithm. Numerical Heat Transfer, Part B: Fundamentals 77:2, pages 87-115.
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Jing Cao, Hui Zhao & Gaoming Yu. (2016) Generation of low-order reservoir models using Krylov-enhanced proper orthogonal decomposition method. Geosystem Engineering 19:6, pages 302-311.
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Gerda Jankevičiūtė, Teresė Leonavičienė, Raimondas Čiegis & Andrej Bugajev. (2013) Reduced Order Models Based on Pod Method for Schrödinger Equations. Mathematical Modelling and Analysis 18:5, pages 694-707.
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Bo Yu, Guojun Yu, Zhizhu Cao, Dongxu Han & Qianqian Shao. (2013) Fast Calculation of the Soil Temperature Field around a Buried Oil Pipeline using a Body-Fitted Coordinates-Based POD-Galerkin Reduced-Order Model. Numerical Heat Transfer, Part A: Applications 63:10, pages 776-794.
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Craig A. Rogers, Alain J. Kassab, Eduardo A. Divo, Ziemowit Ostrowski & Ryszard A. Bialecki. (2012) An inverse POD-RBF network approach to parameter estimation in mechanics. Inverse Problems in Science and Engineering 20:5, pages 749-767.
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Vijay Anand, B.S. V. Patnaik & B.N. Rao. (2012) Efficient Extraction of Vortex Structures by Coupling Proper Orthogonal Decomposition (POD) and High–Dimensional Model Representation (HDMR) Techniques. Numerical Heat Transfer, Part B: Fundamentals 61:3, pages 229-257.
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Tien-Mo Shih, Martinus Arie & Derrick Ko. (2011) Literature Survey of Numerical Heat Transfer (2000–2009): Part II. Numerical Heat Transfer, Part A: Applications 60:11-12, pages 883-1096.
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F. Joly, O. Quéméner & A. Neveu. (2008) Modal Reduction of an Advection-Diffusion Model Using a Branch Basis. Numerical Heat Transfer, Part B: Fundamentals 53:5, pages 466-485.
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Z. Ostrowski, R. A. Białecki & A. J. Kassab. (2008) Solving inverse heat conduction problems using trained POD-RBF network inverse method. Inverse Problems in Science and Engineering 16:1, pages 39-54.
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S. Deng & Y. Hwang. (2007) Solving the Temperature Distribution Field in Nonlinear Heat Conduction Problems Using the Hopfield Neural Network. Numerical Heat Transfer, Part B: Fundamentals 51:4, pages 375-389.
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