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dc.contributor.authorHou, Peter S.en_US
dc.date.accessioned2014-03-14T20:34:35Z
dc.date.available2014-03-14T20:34:35Z
dc.date.issued2005-04-27en_US
dc.identifier.otheretd-04292005-144622en_US
dc.identifier.urihttp://hdl.handle.net/10919/32026
dc.description.abstractThe availability of high performance computing clusters has allowed scientists and engineers to study more challenging problems. However, new algorithms need to be developed to take advantage of the new computer architecture (in particular, distributed memory clusters). Since the solution of linear systems still demands most of the computational effort in many problems (such as the approximation of partial differential equation models) iterative methods and, in particular, efficient preconditioners need to be developed. In this study, we consider application of incomplete LU (ILU) preconditioners for finite element models to partial differential equations. Since finite elements lead to large, sparse systems, reordering the node numbers can have a substantial influence on the effectiveness of these preconditioners. We study two implementations of the ILU preconditioner: a stucturebased method and a threshold-based method. The main emphasis of the thesis is to test a variety of breadth-first ordering strategies on the convergence properties of the preconditioned systems. These include conventional Cuthill-McKee (CM) and Reverse Cuthill-McKee (RCM) orderings as well as strategies related to the physical distance between nodes and post-processing methods based on relative sizes of associated matrix entries. Although the success of these methods were problem dependent, a number of tendencies emerged from which we could make recommendations. Finally, we perform a preliminary study of the multi-processor case and observe the importance of partitioning quality and the parallel ILU reordering strategy.en_US
dc.publisherVirginia Techen_US
dc.relation.haspartphou_thesis.pdfen_US
dc.rightsI 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 Virginia Tech 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.subjectIterative Solveren_US
dc.subjectScientific Computingen_US
dc.subjectUnstructured Meshen_US
dc.subjectFinite Element Methoden_US
dc.subjectPreconditioneren_US
dc.subjectNodal Reordering Strategyen_US
dc.titleNodal Reordering Strategies to Improve Preconditioning for Finite Element Systemsen_US
dc.typeThesisen_US
dc.contributor.departmentMathematicsen_US
dc.description.degreeMaster of Scienceen_US
thesis.degree.nameMaster of Scienceen_US
thesis.degree.levelmastersen_US
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen_US
thesis.degree.disciplineMathematicsen_US
dc.contributor.committeechairBorggaard, Jeffrey T.en_US
dc.contributor.committeememberIliescu, Traianen_US
dc.contributor.committeememberGugercin, Serkanen_US
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-04292005-144622/en_US
dc.date.sdate2005-04-29en_US
dc.date.rdate2005-05-05
dc.date.adate2005-05-05en_US


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