Nodal Reordering Strategies to Improve Preconditioning for Finite Element Systems

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dc.contributor.authorHou, Peter S.en
dc.contributor.committeechairBorggaard, Jeffrey T.en
dc.contributor.committeememberIliescu, Traianen
dc.contributor.committeememberGugercin, Serkanen
dc.contributor.departmentMathematicsen
dc.date.accessioned2014-03-14T20:34:35Zen
dc.date.adate2005-05-05en
dc.date.available2014-03-14T20:34:35Zen
dc.date.issued2005-04-27en
dc.date.rdate2005-05-05en
dc.date.sdate2005-04-29en
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
dc.description.degreeMaster of Scienceen
dc.identifier.otheretd-04292005-144622en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-04292005-144622/en
dc.identifier.urihttp://hdl.handle.net/10919/32026en
dc.publisherVirginia Techen
dc.relation.haspartphou_thesis.pdfen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectIterative Solveren
dc.subjectScientific Computingen
dc.subjectUnstructured Meshen
dc.subjectFinite element methoden
dc.subjectPreconditioneren
dc.subjectNodal Reordering Strategyen
dc.titleNodal Reordering Strategies to Improve Preconditioning for Finite Element Systemsen
dc.typeThesisen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.levelmastersen
thesis.degree.nameMaster of Scienceen

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