{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/124245"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/124245","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Monolithic multigrid for saddle point systems","abstract":"Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2024-09-16 without embargo terms","abstract_html":"Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2024-09-16 without embargo terms","abstract_has_math":false,"creators":["Voronin, Alexey"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Computer Science","degree_department":null,"school":null,"contributors":["Olson, Luke N","Gropp, William D","Fischer, Paul","MacLachlan, Scott"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2024,"date_issued":"2024-05","date_published":"2024-05","updated_at":"2026-07-22T22:25:00Z","subjects":["Multigrid","Algebraic","Geometric","Iterative Methods","Preconditioning","Relaxation","Additive Schwarz","Vanka","Stokes Equation","High Order","Finite Elements","Saddle Point","Systems","Parallel","Mpi","High Performance Computing"],"languages":["en","eng"],"rights":["Copyright 2024 Alexey Voronin"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/2142/124245","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Olson, Luke N","Gropp, William D","Fischer, Paul","MacLachlan, Scott"]},{"key":"dc:creator","label":"Author","values":["Voronin, Alexey"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2024-05","2024-04-10"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Computer Science"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Multigrid","Algebraic","Geometric","Iterative Methods","Preconditioning","Relaxation","Additive Schwarz","Vanka","Stokes Equation","High Order","Finite Elements","Saddle Point","Systems","Parallel","Mpi","High Performance Computing"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en","eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2024 Alexey Voronin"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://hdl.handle.net/2142/124245"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2024-09-16 without embargo terms","The student, Alexey Voronin, accepted the attached license on 2024-04-09 at 13:28.","The student, Alexey Voronin, submitted this Dissertation for approval on 2024-04-09 at 13:57.","This Dissertation was approved for publication on 2024-04-10 at 16:19.","DSpace SAF Submission Ingestion Package generated from Vireo submission #20340 on 2024-09-16 at 00:33:54","In computational science and engineering, the discretization of coupled partial differential equations (PDEs) modeling multi-physics phenomena leads to large linear saddle-point systems. These systems encompass multiple interlinked unknowns, such as velocity, pressure, temperature, and charge, arising in simulations across domains like hydrocarbon extraction, biomedical engineering, and plasma physics. This dissertation focuses on developing a robust multigrid preconditioning framework for these systems using the Stokes equations as a representative model problem. A novel defect-correction approach is introduced for coupled systems, utilizing stable low-order re-discretizations to construct preconditioners for higher-order discretizations like Taylor-Hood and Scott-Vogelius elements. For Taylor-Hood, geometric multigrid performance is optimized through Local Fourier Analysis. Furthermore, a monolithic algebraic multigrid (AMG) method is developed, incorporating the defect-correction approach to robustly precondition these higher-order Stokes discretizations without relying on geometric information, unlike most existing approaches. To improve efficiency for high approximation orders, p-multigrid methods combining spatial and approximation order coarsening are presented. These methods outperform traditional spatial-only multigrid, especially for unstructured meshes. Different p-coarsening strategies are analyzed, and a robust approximate full-block factorization variant leveraging p-multigrid is introduced for the Scott-Vogelius discretization. Finally, patch relaxation techniques are proposed to reduce multigrid setup costs when solving sequences of related linear systems. This approach reuses patch factorizations between consecutive solves and updates only a subset of patches, minimizing overhead while maintaining fast convergence."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Monolithic multigrid for saddle point systems"]}]}],"canonical_facts":{"dc:contributor":["Olson, Luke N","Gropp, William D","Fischer, Paul","MacLachlan, Scott"],"dc:creator":["Voronin, Alexey"],"dc:date":["2024-05","2024-04-10"],"dc:description":["Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2024-09-16 without embargo terms","The student, Alexey Voronin, accepted the attached license on 2024-04-09 at 13:28.","The student, Alexey Voronin, submitted this Dissertation for approval on 2024-04-09 at 13:57.","This Dissertation was approved for publication on 2024-04-10 at 16:19.","DSpace SAF Submission Ingestion Package generated from Vireo submission #20340 on 2024-09-16 at 00:33:54","In computational science and engineering, the discretization of coupled partial differential equations (PDEs) modeling multi-physics phenomena leads to large linear saddle-point systems. These systems encompass multiple interlinked unknowns, such as velocity, pressure, temperature, and charge, arising in simulations across domains like hydrocarbon extraction, biomedical engineering, and plasma physics. This dissertation focuses on developing a robust multigrid preconditioning framework for these systems using the Stokes equations as a representative model problem. A novel defect-correction approach is introduced for coupled systems, utilizing stable low-order re-discretizations to construct preconditioners for higher-order discretizations like Taylor-Hood and Scott-Vogelius elements. For Taylor-Hood, geometric multigrid performance is optimized through Local Fourier Analysis. Furthermore, a monolithic algebraic multigrid (AMG) method is developed, incorporating the defect-correction approach to robustly precondition these higher-order Stokes discretizations without relying on geometric information, unlike most existing approaches. To improve efficiency for high approximation orders, p-multigrid methods combining spatial and approximation order coarsening are presented. These methods outperform traditional spatial-only multigrid, especially for unstructured meshes. Different p-coarsening strategies are analyzed, and a robust approximate full-block factorization variant leveraging p-multigrid is introduced for the Scott-Vogelius discretization. Finally, patch relaxation techniques are proposed to reduce multigrid setup costs when solving sequences of related linear systems. This approach reuses patch factorizations between consecutive solves and updates only a subset of patches, minimizing overhead while maintaining fast convergence."],"dc:format":["application/pdf"],"dc:identifier":["https://hdl.handle.net/2142/124245"],"dc:language":["en","eng"],"dc:rights":["Copyright 2024 Alexey Voronin"],"dc:subject":["Multigrid","Algebraic","Geometric","Iterative Methods","Preconditioning","Relaxation","Additive Schwarz","Vanka","Stokes Equation","High Order","Finite Elements","Saddle Point","Systems","Parallel","Mpi","High Performance Computing"],"dc:title":["Monolithic multigrid for saddle point systems"],"dc:type":["text"],"thesis:degree_discipline":["Computer Science"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:00Z"}