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dc.contributor.authorDriver, Maria Sosonkina Jr.en_US
dc.date.accessioned2014-03-14T20:22:34Z
dc.date.available2014-03-14T20:22:34Z
dc.date.issued1997-09-05en_US
dc.identifier.otheretd-81897-131850en_US
dc.identifier.urihttp://hdl.handle.net/10919/30718
dc.description.abstractGlobally convergent homotopy methods are used to solve difficult nonlinear systems of equations by tracking the zero curve of a homotopy map. Homotopy curve tracking involves solving a sequence of linear systems, which often vary greatly in difficulty. In this research, a popular iterative solution tool, GMRES(k), is adapted to deal with the sequence of such systems. The proposed adaptive strategy of GMRES(k) allows tuning of the restart parameter k based on the GMRES convergence rate for the given problem. Adaptive GMRES(k) is shown to be superior to several other iterative techniques on analog circuit simulation problems and on postbuckling structural analysis problems. Developing parallel techniques for robust but expensive sequential computations, such as globally convergent homotopy methods, is important. The design of these techniques encompasses the functionality of the iterative method (adaptive GMRES(k)) implemented sequentially and is based on the results of a parallel performance analysis of several implementations. An implementation of adaptive GMRES(k) with Householder reflections in its orthogonalization phase is developed. It is shown that the efficiency of linear system solution by the adaptive GMRES(k) algorithm depends on the change in problem difficulty when the problem is scaled. In contrast, a standard GMRES(k) implementation using Householder reflections maintains a constant efficiency with increase in problem size and number of processors, as concluded analytically and experimentally. The supporting numerical results are obtained on three distributed memory homogeneous parallel architectures: CRAY T3E, Intel Paragon, and IBM SP2.en_US
dc.publisherVirginia Techen_US
dc.relation.haspartmasha.pdfen_US
dc.rightsI hereby grant to Virginia Tech or its agents the right to archive and to make available my thesis or dissertation in whole or in part in the University Libraries in all forms of media, now or hereafter known. I retain all proprietary rights, such as patent rights. I also retain the right to use in future works (such as articles or books) all or part of this thesis or dissertation.en_US
dc.subjectKrylov subspace methodsen_US
dc.subjectscientific computingen_US
dc.subjectiterative methodsen_US
dc.titleParallel Sparse Linear Algebra for Homotopy Methodsen_US
dc.typeDissertationen_US
dc.contributor.departmentComputer Scienceen_US
dc.description.degreePh. D.en_US
thesis.degree.namePh. D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen_US
thesis.degree.disciplineComputer Scienceen_US
dc.contributor.committeechairWatson, Layne T.en_US
dc.contributor.committeememberJones, Mark T.en_US
dc.contributor.committeememberHeath, Lenwood S.en_US
dc.contributor.committeememberAllison, Donald C. S.en_US
dc.contributor.committeememberBeattie, Christopher A.en_US
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-81897-131850/en_US
dc.date.sdate1997-09-05en_US
dc.date.rdate1998-09-19
dc.date.adate1997-09-19en_US


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