by Lai Chi Wai. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1998. / Includes bibliographical references (leaves [104]-107). / Text in English; abstract also in Chinese. / by Lai Chi Wai. / Abstract --- p.i / Acknowledgment --- p.iv / List of Figures --- p.xi / List of Tables --- p.xii / Chapter 1 --- Introduction to Numerical Relativity --- p.1 / Chapter 1.1 --- The need for numerical approach --- p.2 / Chapter 1.2 --- A brief history of numerical relativity --- p.3 / Chapter 1.3 --- What this thesis concern --- p.4 / Chapter 2 --- Mathematical Formulation --- p.6 / Chapter 2.1 --- The initial value problem --- p.6 / Chapter 2.2 --- The space-plus-time (3+1) formalism --- p.8 / Chapter 3 --- Methods in Numerical Relativity --- p.17 / Chapter 3.1 --- General numerical methods --- p.17 / Chapter 3.2 --- Consistency and stability --- p.18 / Chapter 3.3 --- Difficulties and limitations --- p.20 / Chapter 3.4 --- Strategies specific to numerical relativity --- p.21 / Chapter 3.5 --- Boundary conditions --- p.27 / Chapter 4 --- Detweiler's Scheme --- p.29 / Chapter 4.1 --- Constrainted evolution in numerical relativity --- p.29 / Chapter 4.2 --- Detweiler's Scheme --- p.31 / Chapter 5 --- Constraint Enforcement in Plane Waves --- p.36 / Chapter 5.1 --- General solution for a linearized plane wave --- p.36 / Chapter 5.2 --- Code test --- p.40 / Chapter 5.3 --- Comparison of results with and without Detweiler's scheme --- p.41 / Chapter 5.4 --- Stability of evolution --- p.46 / Chapter 5.5 --- Comparison of Detweiler's scheme and simple diffusion method --- p.50 / Chapter 5.6 --- Two parameter extension of Detweiler's scheme --- p.55 / Chapter 5.7 --- Long time behavior --- p.59 / Chapter 5.8 --- Comparison of Hamiltonian and momentum constraint --- p.63 / Chapter 5.9 --- Indicator of Detweiler's scheme --- p.67 / Chapter 5.10 --- The maximal slicing condition --- p.70 / Chapter 5.11 --- The leaking problem --- p.73 / Chapter 5.12 --- The near-linear plane waves --- p.75 / Chapter 6 --- Constraint Enforcement in MTW Waves --- p.83 / Chapter 6.1 --- MTW waves --- p.83 / Chapter 6.2 --- Linear regime --- p.85 / Chapter 6.3 --- Comparison of results with and without Detweiler's scheme --- p.85 / Chapter 6.4 --- The indicator --- p.90 / Chapter 6.5 --- A comparison of simple diffusion method and Detweiler's scheme with a large amplitude wave --- p.92 / Chapter 7 --- Summary and Conclusion --- p.97 / Chapter A --- The Numerical Scheme of the Code --- p.98 / Chapter B --- Convergence Test --- p.100 / Chapter B.1 --- Plane wave --- p.100 / Chapter B.2 --- MTW wave --- p.102 / Bibliography --- p.104
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_322299 |
| Date | January 1998 |
| Contributors | Lai, Chi Wai., Chinese University of Hong Kong Graduate School. Division of Physics. |
| Source Sets | The Chinese University of Hong Kong |
| Language | English, Chinese |
| Detected Language | English |
| Type | Text, bibliography |
| Format | print, xi, 107 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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