{"id":{"repo_id":"ku","oai_identifier":"oai:kuscholarworks.ku.edu:1808/38234"},"canonical_url":"https://search.dev.ndltd.org/etd/ku/oai:kuscholarworks.ku.edu:1808/38234","repository":{"repo_id":"ku","name":"University of Kansas","base_url":"https://kuscholarworks.ku.edu/server/oai/request"},"display":{"title":"Domain Decomposition Methods for Convection-Diffusion-Reaction Equations with Finite Volume Discretizations","abstract":"In this dissertation, fast solvers for the convection-diffusion-reaction (CDR) model with the finite volume discretization are studied. Both overlapping and non-overlapping domain decom- position (DD) preconditioning methods are considered. With overlapping DD preconditioners, we work on a time dependent CDR model. The additive Runge-Kutta (ARK) scheme is used for the time discretization and the fourth-order finite volume is applied for the spacial discretization. With the non-overlapping DD methods, some preconditioners based on the Schur complement with low-rank corrections (SLR) are introduced. A time independent CDR model with the second-order finite volume discretization is studied by applying these non-overlapping DD preconditioners. In both overlapping and non-overlapping DD methods, two level preconditioners with a coarse prob- lem are introduced. We demonstrate the scalability of the two level preconditioners by numerical experiments. The finite volume element methods (FVEMs) is a special class of finite volume meth- ods. It shares properties of both finite element and finite volume methods. We develop an adaptive balancing domain decomposition by constraints (BDDC) preconditioner for the FVEMs and pro- vide an convergence analysis. Numerical experiments are provided to demonstrate our theoretical results.","abstract_html":"In this dissertation, fast solvers for the convection-diffusion-reaction (CDR) model with the finite volume discretization are studied. Both overlapping and non-overlapping domain decom- position (DD) preconditioning methods are considered. With overlapping DD preconditioners, we work on a time dependent CDR model. The additive Runge-Kutta (ARK) scheme is used for the time discretization and the fourth-order finite volume is applied for the spacial discretization. With the non-overlapping DD methods, some preconditioners based on the Schur complement with low-rank corrections (SLR) are introduced. A time independent CDR model with the second-order finite volume discretization is studied by applying these non-overlapping DD preconditioners. In both overlapping and non-overlapping DD methods, two level preconditioners with a coarse prob- lem are introduced. We demonstrate the scalability of the two level preconditioners by numerical experiments. The finite volume element methods (FVEMs) is a special class of finite volume meth- ods. It shares properties of both finite element and finite volume methods. We develop an adaptive balancing domain decomposition by constraints (BDDC) preconditioner for the FVEMs and pro- vide an convergence analysis. Numerical experiments are provided to demonstrate our theoretical results.","abstract_has_math":false,"creators":["Su, Yanru"],"institution":"University of Kansas","degree_name":"Ph.D.","degree_level":null,"degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":[],"advisors":["Tu, Xuemin"],"committee_chairs":[],"committee_members":[],"year":2022,"date_issued":"2022-01-01","date_published":"2022-01-01","updated_at":"2026-07-24T02:46:40Z","subjects":["BDDC preconditioner","domain decomposition methods","finite volume methods","Schur complement preconditioning"],"languages":["en"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["https://www.proquest.com/LegacyDocView/DISSNUM/29254328"],"render_values":[{"text":"https://www.proquest.com/LegacyDocView/DISSNUM/29254328","href":"https://www.proquest.com/LegacyDocView/DISSNUM/29254328","code":true}]}]},"links":{"outbound_url":"https://hdl.handle.net/1808/38234","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Tu, Xuemin"]},{"key":"dc:creator","label":"Author","values":["Su, Yanru"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2026-04-22T23:34:46Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2026-04-22T23:34:46Z"]},{"key":"dc:date.issued","label":"Date","values":["2022-01-01"]},{"key":"dc:publisher","label":"Institution","values":["University of Kansas"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["BDDC preconditioner","domain decomposition methods","finite volume methods","Schur complement preconditioning"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["https://www.proquest.com/LegacyDocView/DISSNUM/29254328"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/1808/38234"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this dissertation, fast solvers for the convection-diffusion-reaction (CDR) model with the finite volume discretization are studied. Both overlapping and non-overlapping domain decom- position (DD) preconditioning methods are considered. With overlapping DD preconditioners, we work on a time dependent CDR model. The additive Runge-Kutta (ARK) scheme is used for the time discretization and the fourth-order finite volume is applied for the spacial discretization. With the non-overlapping DD methods, some preconditioners based on the Schur complement with low-rank corrections (SLR) are introduced. A time independent CDR model with the second-order finite volume discretization is studied by applying these non-overlapping DD preconditioners. In both overlapping and non-overlapping DD methods, two level preconditioners with a coarse prob- lem are introduced. We demonstrate the scalability of the two level preconditioners by numerical experiments. The finite volume element methods (FVEMs) is a special class of finite volume meth- ods. It shares properties of both finite element and finite volume methods. We develop an adaptive balancing domain decomposition by constraints (BDDC) preconditioner for the FVEMs and pro- vide an convergence analysis. Numerical experiments are provided to demonstrate our theoretical results."]},{"key":"dc:title","label":"Title","values":["Domain Decomposition Methods for Convection-Diffusion-Reaction Equations with Finite Volume Discretizations"]}]}],"canonical_facts":{"dc:contributor.advisor":["Tu, Xuemin"],"dc:creator":["Su, Yanru"],"dc:date.accessioned":["2026-04-22T23:34:46Z"],"dc:date.available":["2026-04-22T23:34:46Z"],"dc:date.issued":["2022-01-01"],"dc:description.abstract":["In this dissertation, fast solvers for the convection-diffusion-reaction (CDR) model with the finite volume discretization are studied. Both overlapping and non-overlapping domain decom- position (DD) preconditioning methods are considered. With overlapping DD preconditioners, we work on a time dependent CDR model. The additive Runge-Kutta (ARK) scheme is used for the time discretization and the fourth-order finite volume is applied for the spacial discretization. With the non-overlapping DD methods, some preconditioners based on the Schur complement with low-rank corrections (SLR) are introduced. A time independent CDR model with the second-order finite volume discretization is studied by applying these non-overlapping DD preconditioners. In both overlapping and non-overlapping DD methods, two level preconditioners with a coarse prob- lem are introduced. We demonstrate the scalability of the two level preconditioners by numerical experiments. The finite volume element methods (FVEMs) is a special class of finite volume meth- ods. It shares properties of both finite element and finite volume methods. We develop an adaptive balancing domain decomposition by constraints (BDDC) preconditioner for the FVEMs and pro- vide an convergence analysis. Numerical experiments are provided to demonstrate our theoretical results."],"dc:identifier.other":["https://www.proquest.com/LegacyDocView/DISSNUM/29254328"],"dc:identifier.uri":["https://hdl.handle.net/1808/38234"],"dc:language.iso":["en"],"dc:publisher":["University of Kansas"],"dc:subject":["BDDC preconditioner","domain decomposition methods","finite volume methods","Schur complement preconditioning"],"dc:title":["Domain Decomposition Methods for Convection-Diffusion-Reaction Equations with Finite Volume Discretizations"],"dc:type":["Dissertation"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_name":["Ph.D."]},"updated_at":"2026-07-24T02:46:40Z"}