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Krylov's methods in function space for waveform relaxation.

by Wai-Shing Luk. / Thesis (Ph.D.)--Chinese University of Hong Kong, 1996. / Includes bibliographical references (leaves 104-113). / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Functional Extension of Iterative Methods --- p.2 / Chapter 1.2 --- Applications in Circuit Simulation --- p.2 / Chapter 1.3 --- Multigrid Acceleration --- p.3 / Chapter 1.4 --- Why Hilbert Space? --- p.4 / Chapter 1.5 --- Parallel Implementation --- p.5 / Chapter 1.6 --- Domain Decomposition --- p.5 / Chapter 1.7 --- Contributions of This Thesis --- p.6 / Chapter 1.8 --- Outlines of the Thesis --- p.7 / Chapter 2 --- Waveform Relaxation Methods --- p.9 / Chapter 2.1 --- Basic Idea --- p.10 / Chapter 2.2 --- Linear Operators between Banach Spaces --- p.14 / Chapter 2.3 --- Waveform Relaxation Operators for ODE's --- p.16 / Chapter 2.4 --- Convergence Analysis --- p.19 / Chapter 2.4.1 --- Continuous-time Convergence Analysis --- p.20 / Chapter 2.4.2 --- Discrete-time Convergence Analysis --- p.21 / Chapter 2.5 --- Further references --- p.24 / Chapter 3 --- Waveform Krylov Subspace Methods --- p.25 / Chapter 3.1 --- Overview of Krylov Subspace Methods --- p.26 / Chapter 3.2 --- Krylov Subspace methods in Hilbert Space --- p.30 / Chapter 3.3 --- Waveform Krylov Subspace Methods --- p.31 / Chapter 3.4 --- Adjoint Operator for WBiCG and WQMR --- p.33 / Chapter 3.5 --- Numerical Experiments --- p.35 / Chapter 3.5.1 --- Test Circuits --- p.36 / Chapter 3.5.2 --- Unstructured Grid Problem --- p.39 / Chapter 4 --- Parallel Implementation Issues --- p.50 / Chapter 4.1 --- DECmpp 12000/Sx Computer and HPF --- p.50 / Chapter 4.2 --- Data Mapping Strategy --- p.55 / Chapter 4.3 --- Sparse Matrix Format --- p.55 / Chapter 4.4 --- Graph Coloring for Unstructured Grid Problems --- p.57 / Chapter 5 --- The Use of Inexact ODE Solver in Waveform Methods --- p.61 / Chapter 5.1 --- Inexact ODE Solver for Waveform Relaxation --- p.62 / Chapter 5.1.1 --- Convergence Analysis --- p.63 / Chapter 5.2 --- Inexact ODE Solver for Waveform Krylov Subspace Methods --- p.65 / Chapter 5.3 --- Experimental Results --- p.68 / Chapter 5.4 --- Concluding Remarks --- p.72 / Chapter 6 --- Domain Decomposition Technique --- p.80 / Chapter 6.1 --- Introduction --- p.80 / Chapter 6.2 --- Overlapped Schwarz Methods --- p.81 / Chapter 6.3 --- Numerical Experiments --- p.83 / Chapter 6.3.1 --- Delay Circuit --- p.83 / Chapter 6.3.2 --- Unstructured Grid Problem --- p.86 / Chapter 7 --- Conclusions --- p.90 / Chapter 7.1 --- Summary --- p.90 / Chapter 7.2 --- Future Works --- p.92 / Chapter A --- Pseudo Codes for Waveform Krylov Subspace Methods --- p.94 / Chapter B --- Overview of Recursive Spectral Bisection Method --- p.101 / Bibliography --- p.104

Identiferoai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_321663
Date January 1996
ContributorsLuk, Wai-Shing., Chinese University of Hong Kong Graduate School. Division of Computer Science and Engineering.
PublisherChinese University of Hong Kong
Source SetsThe Chinese University of Hong Kong
LanguageEnglish
Detected LanguageEnglish
TypeText, bibliography
Formatprint, xiii, 113 leaves : ill. ; 30 cm.
RightsUse 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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