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dc.contributor.advisorSzyld, Daniel
dc.creatorLadenheim, Scott Aaron
dc.date.accessioned2020-11-04T16:09:59Z
dc.date.available2020-11-04T16:09:59Z
dc.date.issued2015
dc.identifier.other931912279
dc.identifier.urihttp://hdl.handle.net/20.500.12613/3156
dc.description.abstractThis thesis is concerned with the fast iterative solution of linear systems of equations of saddle point form. Saddle point problems are a ubiquitous class of matrices that arise in a host of computational science and engineering applications. The focus here is on improving the convergence of iterative methods for these problems by preconditioning. Preconditioning is a way to transform a given linear system into a different problem for which iterative methods converge faster. Saddle point matrices have a very specific block structure and many preconditioning strategies for these problems exploit this structure. The preconditioners considered in this thesis are constraint preconditioners. This class of preconditioner mimics the structure of the original saddle point problem. In this thesis, we prove norm- and field-of-values-equivalence for constraint preconditioners associated to saddle point matrices with a particular structure. As a result of these equivalences, the number of iterations needed for convergence of a constraint preconditioned minimal residual Krylov subspace method is bounded, independent of the size of the matrix. In particular, for saddle point systems that arise from the finite element discretization of partial differential equations (p.d.e.s), the number of iterations it takes for GMRES to converge for theses constraint preconditioned systems is bounded (asymptotically), independent of the size of the mesh width. Moreover, we extend these results when appropriate inexact versions of the constraint preconditioner are used. We illustrate this theory by presenting numerical experiments on saddle point matrices that arise from the finite element solution of coupled Stokes-Darcy flow. This is a system of p.d.e.s that models the coupling of a free flow to a porous media flow by conditions across the interface of the two flow regions. We present experiments in both two and three dimensions, using different types of elements (triangular, quadrilateral), different finite element schemes (continuous, discontinuous Galerkin methods), and different geometries. In all cases, the effectiveness of the constraint preconditioner is demonstrated.
dc.format.extent88 pages
dc.language.isoeng
dc.publisherTemple University. Libraries
dc.relation.ispartofTheses and Dissertations
dc.rightsIN COPYRIGHT- This Rights Statement can be used for an Item that is in copyright. Using this statement implies that the organization making this Item available has determined that the Item is in copyright and either is the rights-holder, has obtained permission from the rights-holder(s) to make their Work(s) available, or makes the Item available under an exception or limitation to copyright (including Fair Use) that entitles it to make the Item available.
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/
dc.subjectMathematics
dc.subjectFinite Element Methods
dc.subjectNumerical Linear Algebra
dc.subjectPreconditioning
dc.subjectSaddle Point Matrices
dc.subjectScientific Computing
dc.titleConstraint Preconditioning of Saddle Point Problems
dc.typeText
dc.type.genreThesis/Dissertation
dc.contributor.committeememberSeibold, Benjamin
dc.contributor.committeememberKlapper, Isaac
dc.contributor.committeememberChidyagwai, Prince
dc.description.departmentMathematics
dc.relation.doihttp://dx.doi.org/10.34944/dspace/3138
dc.ada.noteFor Americans with Disabilities Act (ADA) accommodation, including help with reading this content, please contact scholarshare@temple.edu
dc.description.degreePh.D.
refterms.dateFOA2020-11-04T16:09:59Z


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