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dc.contributorVirginia Tech
dc.contributor.authorParks, M. L.
dc.contributor.authorDe Sturler, E.
dc.contributor.authorMackey, G.
dc.contributor.authorJohnson, D. D.
dc.contributor.authorMaiti, S.
dc.date.accessioned2014-05-28T18:35:10Z
dc.date.available2014-05-28T18:35:10Z
dc.date.issued2006
dc.identifier.citationParks, M. L.; De Sturler, E.; Mackey, G.; Johnson, D. D.; Maiti, S., " Recycling Krylov subspaces for sequences of linear systems," SIAM J. Sci. Comput., 28(5), 1651-1674, (2006). DOI: 10.1137/040607277
dc.identifier.issn1064-8275
dc.identifier.urihttp://hdl.handle.net/10919/48161
dc.description.abstractMany problems in science and engineering require the solution of a long sequence of slowly changing linear systems. We propose and analyze two methods that significantly reduce the total number of matrix-vector products required to solve all systems. We consider the general case where both the matrix and right-hand side change, and we make no assumptions regarding the change in the right-hand sides. Furthermore, we consider general nonsingular matrices, and we do not assume that all matrices are pairwise close or that the sequence of matrices converges to a particular matrix. Our methods work well under these general assumptions, and hence form a significant advancement with respect to related work in this area. We can reduce the cost of solving subsequent systems in the sequence by recycling selected subspaces generated for previous systems. We consider two approaches that allow for the continuous improvement of the recycled subspace at low cost. We consider both Hermitian and non-Hermitian problems, and we analyze our algorithms both theoretically and numerically to illustrate the effects of subspace recycling. We also demonstrate the effectiveness of our algorithms for a range of applications from computational mechanics, materials science, and computational physics.
dc.description.sponsorshipUnited States Department of Energy under contract DE-AC04-94-AL8500
dc.description.sponsorshipComputational Science and Engineering program at UIUC through two CSE fellowships
dc.description.sponsorshipMaterials Computation Center (UIUC) through grants NSF DMR 99-76550, DMR-0325939
dc.description.sponsorshipCenter for Simulation of Advanced Rockets (UIUC) through grant DOE LLNL B341494
dc.language.isoen_US
dc.publisherSiam Publications
dc.subjectsequence of linear systems
dc.subjectlinear solvers
dc.subjectkrylov methods
dc.subjecttruncation
dc.subjectrestarting
dc.subjectkrylov subspace recycling
dc.subjectiterative methods
dc.subjectconjugate-gradient algorithm
dc.subjectscale nonlinear problems
dc.subjectright-hand
dc.subjectsides
dc.subjectsuperlinear convergence
dc.subjectnonsymmetric systems
dc.subjectiterative
dc.subjectsolution
dc.subjectarnoldi methods
dc.subjectgmres
dc.subjectpreconditioner
dc.subjectstrategies
dc.subjectmathematics, applied
dc.titleRecycling Krylov subspaces for sequences of linear systems
dc.typeArticle - Refereed
dc.identifier.urlhttp://epubs.siam.org/doi/abs/10.1137/040607277
dc.date.accessed2014-05-27
dc.title.serialSiam Journal on Scientific Computing
dc.identifier.doihttps://doi.org/10.1137/040607277


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