Chan Kit Hung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves 90-93). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Model Elliptic Boundary-Value Problems --- p.2 / Chapter 1.2 --- Applications of the Model Boundary-Value Problem --- p.4 / Chapter 1.2.1 --- Curl-Curl Formulation --- p.4 / Chapter 1.2.2 --- Vector Potential Formulation --- p.6 / Chapter 1.2.3 --- Darwin Model and Quasistatic Model --- p.7 / Chapter 1.3 --- Spurious Solutions --- p.8 / Chapter 2 --- Finite Element Formulation --- p.11 / Chapter 2.1 --- Preliminaries --- p.11 / Chapter 2.2 --- Weak Formulation --- p.14 / Chapter 2.2.1 --- Galerkin Method --- p.17 / Chapter 2.2.2 --- The Rayleigh-Ritz Method --- p.19 / Chapter 2.3 --- H1(Ω) Conforming Finite Element Method --- p.23 / Chapter 2.3.1 --- The Dirichlet Problem --- p.24 / Chapter 2.3.2 --- The Neumann Problem --- p.27 / Chapter 3 --- Numerical Implementations --- p.29 / Chapter 3.1 --- Introduction --- p.29 / Chapter 3.2 --- Implementation of Boundary Conditions --- p.32 / Chapter 3.3 --- Numerical Integration Formula --- p.39 / Chapter 3.4 --- Discrete L2-norms --- p.40 / Chapter 3.5 --- Solution of Linear System of Equations --- p.42 / Chapter 3.6 --- Automatic Mesh Generation --- p.43 / Chapter 3.6.1 --- The Cubic Domain Ω --- p.44 / Chapter 3.6.2 --- The Spherical Shell Domain Ωs --- p.44 / Chapter 4 --- Numerical Experiments --- p.50 / Chapter 4.1 --- Numerical Experiments for Dirichlet Problem --- p.50 / Chapter 4.1.1 --- Original Formulation --- p.50 / Chapter 4.1.2 --- Experiments --- p.52 / Chapter 4.1.3 --- Penalty Factor Effect --- p.56 / Chapter 4.2 --- Numerical Experiment for Neumann Problem --- p.61 / Chapter 4.2.1 --- Original Formulation --- p.61 / Chapter 4.2.2 --- Experiments --- p.62 / Chapter 4.2.3 --- Penalty Factor Effect --- p.66 / Chapter 4.2.4 --- Comparison with the Dirichlet Problem --- p.70 / Chapter 4.3 --- Numerical Experiment of Dirichlet Problem with Boundary Condition E = E --- p.71 / Chapter 4.3.1 --- Original Formulation --- p.71 / Chapter 4.3.2 --- Experiments --- p.73 / Chapter 4.3.3 --- Penalty Factor Effect --- p.76 / Chapter 4.4 --- Numerical Experiment on Spherical Shell Domain --- p.81 / Chapter 4.4.1 --- The Spherical Shell Domain --- p.81 / Chapter 4.4.2 --- Dirichlet Problem --- p.82 / Chapter 4.5 --- Some Numerical Phenomena --- p.86 / Chapter 4.5.1 --- GMRES Convergence Accelerator --- p.86 / Chapter 4.5.2 --- Sparsity Improvement --- p.88 / Bibliography --- p.90 / List of Tables --- p.94
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_322832 |
| Date | January 1999 |
| Contributors | Chan, Kit Hung., Chinese University of Hong Kong Graduate School. Division of Mathematics. |
| Source Sets | The Chinese University of Hong Kong |
| Language | English, Chinese |
| Detected Language | English |
| Type | Text, bibliography |
| Format | print, viii, 96 leaves : ill. ; 30 cm. |
| Rights | Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/) |
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