Extended convergence analysis for multi-grid algorithms and its application in mobility models
Abstract
The purpose of this thesis is to extend the Fourier-based convergence theory for multi-grid algorithms. The extension allows an efficient multi-grid algorithm to be configured for situations in which a system shows local variations that cannot be handled by Fourier analysis. The focus of this new convergence analysis is a precise description of aliasing effects on the system and the coarsening strategy of the algorithm. Particular cases where this new analysis can be applied are studied, including systems with square-wave eigen-vectors and mobility models based on correlated random walks. The application of the convergence analysis to a given system allows one to obtain the factors by which the modal components of the error in one multi-grid iteration are reduced (convergence factors) and mixed (aliasing factors). These factors show the strength and weakness of inter-grid operators used by the algorithm to transfer information between multiple levels of description of a system. Thus, the convergence analysis can be used to evaluate and design efficient inter-grid operators for the application of the multi-grid algorithm. An application of this theory to models of the mobility of vehicles in a city is considered. An algebraic multi-grid configuration is considered for computation of absorbing times that provide important information for the evaluation of communication protocols in Mobile Ad-hoc NETworks (MANETs). In simple cases, the convergence analysis can be applied to show the efficiency of the configuration and numerical results are provided for more complicated scenarios.
Degree
Ph.D.
Advisors
Bell, Purdue University.
Subject Area
Electrical engineering
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