Analysis of Projective-Iterative Methods for Solving Multidimensional Transport Problems

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dc.contributor.advisor Semyon V. Tsynkov, Committee Member en_US
dc.contributor.advisor Paul J. Turinsky, Committee Member en_US
dc.contributor.advisor Dmitriy Y. Anistratov, Committee Chair en_US Constantinescu, Adrian Cornel en_US 2010-04-02T18:08:14Z 2010-04-02T18:08:14Z 2006-07-19 en_US
dc.identifier.other etd-07172006-075005 en_US
dc.description.abstract The particle transport equation has a wide range of applications: nuclear engineering, astrophysics, atmospheric science, medical physics, microelectronics manufacturing, etc. It is an integro-differential equation with seven independent variables: 3 spatial, 2 angular, energy, and time, which cannot be solved analytically in most of the cases of interest. The way to solve this equation is to discretize it in space, angle, energy, and time. In practical cases, this leads to a huge sparse matrix. Iterative methods should be used even for solving transport problems on the most powerful computers available nowadays. The need to analyze the behavior of these methods is obvious: knowledge about behavior of methods can help us to improve them and avoid their use in cases in which they are not efficient. Also, if we can predict what should happen in specific cases, we can verify and validate transport codes. Analysis of iterative methods' behavior in highly scattering and strong heterogeneous medium is very important from the point of view of solving various radiative and particle transport problems. It became important for solving neutron transport equation in full-core, due to current industry's interest in obtaining very detailed transport solution without homogenization. For these reasons, the main target of this thesis was to analyze the convergence rate of four methods used to solve the steady state transport equation. We were interested in studying behavior of these methods in case of one and two dimensional strong heterogeneous and highly scattering medium with periodic structure, on rectangular grids. In order to understand better these methods, we analyzed them as well in cases of homogeneous and low scattering medium, uniform grids, etc. The main tool that we used is Fourier analysis. Iteration matrix analysis was a secondary tool that we consider. It proved to be restrictive in some cases but provided a good insight of the methods behavior. In several diffcult cases the Fourier analysis predicted degradation in efficiency or even divergence for the methods that we've studied. In most of the cases, the numerical results were consistent with the analytic predictions. In order to cover various areas where the transport equation is used, we spanned wide ranges for parameters of transport equation. Most of the cases in which the considered methods demonstrate slow convergence or even divergence are not specific to nuclear reactors. It means that one can apply these methods for solving reactor-physics problems. en_US
dc.rights I hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to NC State University or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report. en_US
dc.subject stability analysis en_US
dc.subject iterative methods en_US
dc.subject particle transport equation en_US
dc.title Analysis of Projective-Iterative Methods for Solving Multidimensional Transport Problems en_US MS en_US thesis en_US Nuclear Engineering en_US

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