{"id":{"repo_id":"maryland","oai_identifier":"oai:drum.lib.umd.edu:1903/8743"},"canonical_url":"https://search.dev.ndltd.org/etd/maryland/oai:drum.lib.umd.edu:1903/8743","repository":{"repo_id":"maryland","name":"University of Maryland","base_url":"https://api.drum.lib.umd.edu/server/oai/request"},"display":{"title":"Fast Solvers for Models of Fluid Flow with Spectral Elements","abstract":"We introduce a preconditioning technique based on Domain Decomposition and the Fast Diagonalization Method that can be applied to tensor product based discretizations of the steady convection-diffusion and the linearized Navier-Stokes equations. The method is based on iterative substructuring where fast diagonalization is used to efficiently eliminate the interior degrees of freedom and subsidiary subdomain solves. We demonstrate the effectiveness of this preconditioner in numerical simulations using a spectral element discretization. This work extends the use of Fast Diagonalization to steady convection-diffusion systems. We also extend the \"least-squares commutator\" preconditioner, originally developed for the finite element method, to a matrix-free spectral element framework. We show that these two advances, when used together, allow for efficient computation of steady-state solutions the the incompressible Navier-Stokes equations using high-order spectral element discretizations.","abstract_html":"We introduce a preconditioning technique based on Domain Decomposition and the Fast Diagonalization Method that can be applied to tensor product based discretizations of the steady convection-diffusion and the linearized Navier-Stokes equations. The method is based on iterative substructuring where fast diagonalization is used to efficiently eliminate the interior degrees of freedom and subsidiary subdomain solves. We demonstrate the effectiveness of this preconditioner in numerical simulations using a spectral element discretization. This work extends the use of Fast Diagonalization to steady convection-diffusion systems. We also extend the "least-squares commutator" preconditioner, originally developed for the finite element method, to a matrix-free spectral element framework. We show that these two advances, when used together, allow for efficient computation of steady-state solutions the the incompressible Navier-Stokes equations using high-order spectral element discretizations.","abstract_has_math":false,"creators":["Lott, Paul Aaron"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":"Applied Mathematics and Scientific Computation","school":null,"contributors":[],"advisors":["Elman, Howard","Deane, Anil"],"committee_chairs":[],"committee_members":[],"year":2008,"date_issued":"2008-09-02","date_published":"2008-09-02","updated_at":"2026-07-24T03:02:25Z","subjects":[],"languages":["en_US"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/1903/8743","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Elman, Howard","Deane, Anil"]},{"key":"dc:contributor.department","label":"Department","values":["Applied Mathematics and Scientific Computation"]},{"key":"dc:creator","label":"Author","values":["Lott, Paul Aaron"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2009-01-24T06:34:14Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2009-01-24T06:34:14Z"]},{"key":"dc:date.issued","label":"Date","values":["2008-09-02"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en_US"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/1903/8743"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["We introduce a preconditioning technique based on Domain Decomposition and the Fast Diagonalization Method that can be applied to tensor product based discretizations of the steady convection-diffusion and the linearized Navier-Stokes equations. The method is based on iterative substructuring where fast diagonalization is used to efficiently eliminate the interior degrees of freedom and subsidiary subdomain solves. We demonstrate the effectiveness of this preconditioner in numerical simulations using a spectral element discretization. This work extends the use of Fast Diagonalization to steady convection-diffusion systems. We also extend the \"least-squares commutator\" preconditioner, originally developed for the finite element method, to a matrix-free spectral element framework. We show that these two advances, when used together, allow for efficient computation of steady-state solutions the the incompressible Navier-Stokes equations using high-order spectral element discretizations."]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Fast Solvers for Models of Fluid Flow with Spectral Elements"]}]}],"canonical_facts":{"dc:contributor.advisor":["Elman, Howard","Deane, Anil"],"dc:contributor.department":["Applied Mathematics and Scientific Computation"],"dc:creator":["Lott, Paul Aaron"],"dc:date.accessioned":["2009-01-24T06:34:14Z"],"dc:date.available":["2009-01-24T06:34:14Z"],"dc:date.issued":["2008-09-02"],"dc:description.abstract":["We introduce a preconditioning technique based on Domain Decomposition and the Fast Diagonalization Method that can be applied to tensor product based discretizations of the steady convection-diffusion and the linearized Navier-Stokes equations. The method is based on iterative substructuring where fast diagonalization is used to efficiently eliminate the interior degrees of freedom and subsidiary subdomain solves. We demonstrate the effectiveness of this preconditioner in numerical simulations using a spectral element discretization. This work extends the use of Fast Diagonalization to steady convection-diffusion systems. We also extend the \"least-squares commutator\" preconditioner, originally developed for the finite element method, to a matrix-free spectral element framework. We show that these two advances, when used together, allow for efficient computation of steady-state solutions the the incompressible Navier-Stokes equations using high-order spectral element discretizations."],"dc:format.mimetype":["application/pdf"],"dc:identifier.uri":["http://hdl.handle.net/1903/8743"],"dc:language.iso":["en_US"],"dc:title":["Fast Solvers for Models of Fluid Flow with Spectral Elements"],"dc:type":["Dissertation"]},"updated_at":"2026-07-24T03:02:25Z"}