{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/36499"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/36499","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"An Efficient Parallel Three-Level Preconditioner for Linear Partial Differential Equations","abstract":"The primary motivation of this research is to develop and investigate parallel preconditioners for linear elliptic partial differential equations. Three preconditioners are studied: block-Jacobi preconditioner (BJ), a two-level tangential preconditioner (D0), and a three-level preconditioner (D1). Performance and scalability on a distributed memory parallel computer are considered. Communication cost and redundancy are explored as well. After experiments and analysis, we find that the three-level preconditioner D1 is the most efficient and scalable parallel preconditioner, compared to BJ and D0. The D1 preconditioner reduces both the number of iterations and computational time substantially. A new hybrid preconditioner is suggested which may combine the best features of D0 and D1.","abstract_html":"The primary motivation of this research is to develop and investigate parallel preconditioners for linear elliptic partial differential equations. Three preconditioners are studied: block-Jacobi preconditioner (BJ), a two-level tangential preconditioner (D0), and a three-level preconditioner (D1). Performance and scalability on a distributed memory parallel computer are considered. Communication cost and redundancy are explored as well. After experiments and analysis, we find that the three-level preconditioner D1 is the most efficient and scalable parallel preconditioner, compared to BJ and D0. The D1 preconditioner reduces both the number of iterations and computational time substantially. A new hybrid preconditioner is suggested which may combine the best features of D0 and D1.","abstract_has_math":false,"creators":["Yao, Aixiang I Song"],"institution":"Virginia Tech","degree_name":"Master of Science","degree_level":"masters","degree_discipline":"Computer Science","degree_department":"Computer Science","school":null,"contributors":[],"advisors":[],"committee_chairs":["Ribbens, Calvin J."],"committee_members":["Beattie, Christopher A.","Watson, Layne T."],"year":1998,"date_issued":"1998-02-05","date_published":"1998-02-05","updated_at":"2026-07-22T22:20:35Z","subjects":["domain decomposition","preconditioner","parallel computing","PDE","distributed systems"],"languages":[],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-12398-18633"],"render_values":[{"text":"etd-12398-18633","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10919/36499","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeechair","label":"Committee Chair","values":["Ribbens, Calvin J."]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Beattie, Christopher A.","Watson, Layne T."]},{"key":"dc:contributor.department","label":"Department","values":["Computer Science"]},{"key":"dc:creator","label":"Author","values":["Yao, Aixiang I Song"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2014-03-14T20:50:56Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2014-03-14T20:50:56Z","1998-02-26"]},{"key":"dc:date.issued","label":"Date","values":["1998-02-05"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Tech"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Computer Science"]},{"key":"thesis:degree_level","label":"Degree Level","values":["masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Virginia Polytechnic Institute and State University"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["domain decomposition","preconditioner","parallel computing","PDE","distributed systems"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["In Copyright"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-12398-18633"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10919/36499"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The primary motivation of this research is to develop and investigate parallel preconditioners for linear elliptic partial differential equations. Three preconditioners are studied: block-Jacobi preconditioner (BJ), a two-level tangential preconditioner (D0), and a three-level preconditioner (D1). Performance and scalability on a distributed memory parallel computer are considered. Communication cost and redundancy are explored as well. After experiments and analysis, we find that the three-level preconditioner D1 is the most efficient and scalable parallel preconditioner, compared to BJ and D0. The D1 preconditioner reduces both the number of iterations and computational time substantially. A new hybrid preconditioner is suggested which may combine the best features of D0 and D1."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Master of Science"]},{"key":"dc:title","label":"Title","values":["An Efficient Parallel Three-Level Preconditioner for Linear Partial Differential Equations"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Ribbens, Calvin J."],"dc:contributor.committeemember":["Beattie, Christopher A.","Watson, Layne T."],"dc:contributor.department":["Computer Science"],"dc:creator":["Yao, Aixiang I Song"],"dc:date.accessioned":["2014-03-14T20:50:56Z"],"dc:date.available":["2014-03-14T20:50:56Z","1998-02-26"],"dc:date.issued":["1998-02-05"],"dc:description.abstract":["The primary motivation of this research is to develop and investigate parallel preconditioners for linear elliptic partial differential equations. 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