Multigrid methods for parameter identification in heat conduction systems.

• Other Authors: Chan, Kai Yam.
• Format: Others
• Language: English; Chinese
• Published: 2001
• Subjects: Multigrid methods (Numerical analysis); Heat > Conduction > Mathematics; System identification; Parameter estimation
• Online Access: http://library.cuhk.edu.hk/record=b5890661; http://repository.lib.cuhk.edu.hk/en/item/cuhk-323521

Chan Kai Yam. === Thesis (M.Phil.)--Chinese University of Hong Kong, 2001. === Includes bibliographical references (leaves 80-82). === Abstracts in English and Chinese. === Chapter 1 --- Introduction --- p.1 === Chapter 1.1 --- Parameter Identification in Heat Conduction Systems --- p.1 === Chapter 1.2 --- Inverse Problems --- p.3 === Chapter 1.3 --- Challenges in Inverse Problems --- p.6 === Chapter 2 --- Tools in Parameter Identification --- p.9 === Chapter 2.1 --- Output Least Squares Method --- p.10 === Chapter 2.2 --- Tikhonov Regularization --- p.11 === Chapter 2.3 --- Our Approach --- p.14 === Chapter 3 --- Numerical Implementations --- p.20 === Chapter 3.1 --- Finite Element Discretization and Its Convergence --- p.20 === Chapter 3.2 --- Steepest Descent Method --- p.22 === Chapter 3.3 --- Multigrid Techniques --- p.26 === Chapter 4 --- Numerical Experiments --- p.29 === Chapter 4.1 --- One Dimensional Examples --- p.30 === Chapter 4.1.1 --- Selection of mk --- p.31 === Chapter 4.1.2 --- Selection of nk --- p.34 === Chapter 4.1.3 --- Selection of Number of Levels in the Coarse Grid Correction Step --- p.37 === Chapter 4.1.4 --- Convergence with Different Regularization Pa- rameters γ --- p.39 === Chapter 4.1.5 --- Convergence with Different Initial Guesses --- p.42 === Chapter 4.1.6 --- Comparisons between MG and SG Methods --- p.44 === Chapter 4.1.7 --- Comparisons between MG and RMG Methods --- p.46 === Chapter 4.1.8 --- More Examples --- p.49 === Chapter 4.1.9 --- Coarse Grid Correction in Another Approach --- p.60 === Chapter 4.2 --- Two Dimensional Examples --- p.71 === Chapter 4.3 --- Conclusions --- p.78 === Bibliography --- p.80