{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/121461"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/121461","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Spectral element poisson preconditioners for heterogeneous architectures","abstract":"Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2023-12-04 without embargo terms","abstract_html":"Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2023-12-04 without embargo terms","abstract_has_math":false,"creators":["Phillips, Malachi"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Computer Science","degree_department":null,"school":null,"contributors":["Lottes, James","Fischer, Paul","Olson, Luke","Kloeckner, Andreas","Kolev, Tzanio"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2023,"date_issued":"2023-08","date_published":"2023-08","updated_at":"2026-07-22T22:24:57Z","subjects":["Preconditioning","Multigrid","Poisson Equation","Navier-stokes Equations","Spectral Element Method","Heterogeneous Computing","High-performance Computing"],"languages":["en","eng"],"rights":["Copyright 2023 Malachi Phillips"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/2142/121461","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Lottes, James","Fischer, Paul","Olson, Luke","Kloeckner, Andreas","Kolev, Tzanio"]},{"key":"dc:creator","label":"Author","values":["Phillips, Malachi"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2023-08","2023-07-06"]},{"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":["Preconditioning","Multigrid","Poisson Equation","Navier-stokes Equations","Spectral Element Method","Heterogeneous Computing","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 2023 Malachi Phillips"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://hdl.handle.net/2142/121461"]}]},{"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 2023-12-04 without embargo terms","The student, Malachi Phillips, accepted the attached license on 2023-07-06 at 11:28.","The student, Malachi Phillips, submitted this Dissertation for approval on 2023-07-06 at 11:40.","This Dissertation was approved for publication on 2023-07-06 at 15:03.","DSpace SAF Submission Ingestion Package generated from Vireo submission #19530 on 2023-12-04 at 17:00:45","The solution to the Poisson equation arising from the spectral element discretization of the incompressible Navier-Stokes equation requires robust preconditioning strategies. Two classes of preconditioners prove most effective: geometric p-multigrid and low-order refined methods. Low-order refined preconditioners, moreover, require the use of algebraic multigrid to approximate the inverse of the operator. The communication associated with the multigrid coarse-grid solve hinders the parallel scalability of both classes of preconditioners, especially on heterogeneous architectures. To mitigate the coarse-grid solve cost, novel smoothing strategies are considered. The fourth-kind Chebyshev polynomial smoothing proposed by James Lottes is utilized to accelerate additive Schwarz-based smoothers in a geometric p-multigrid preconditioner. Through these techniques, we develop geometric p-multigrid preconditioners capable of achieving up to an 81% speedup over the state-of-the-art p-multigrid preconditioners on the Summit supercomputer.A p-multigrid approach with an additive coarse-grid solve specifically designed for heterogeneous architectures is considered. We also propose a hybrid p-multigrid and low-order refined preconditioner that improve the time-to-solution by as much as 86% compared to the low-order preconditioner. We demonstrate the effectiveness of these novel approaches on a variety of problems arising from the spectral element discretization of the incompressible Navier-Stokes equations on GPU architectures spanning to P > 1024 NVIDIA V100 GPUs on Summit."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Spectral element poisson preconditioners for heterogeneous architectures"]}]}],"canonical_facts":{"dc:contributor":["Lottes, James","Fischer, Paul","Olson, Luke","Kloeckner, Andreas","Kolev, Tzanio"],"dc:creator":["Phillips, Malachi"],"dc:date":["2023-08","2023-07-06"],"dc:description":["Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2023-12-04 without embargo terms","The student, Malachi Phillips, accepted the attached license on 2023-07-06 at 11:28.","The student, Malachi Phillips, submitted this Dissertation for approval on 2023-07-06 at 11:40.","This Dissertation was approved for publication on 2023-07-06 at 15:03.","DSpace SAF Submission Ingestion Package generated from Vireo submission #19530 on 2023-12-04 at 17:00:45","The solution to the Poisson equation arising from the spectral element discretization of the incompressible Navier-Stokes equation requires robust preconditioning strategies. Two classes of preconditioners prove most effective: geometric p-multigrid and low-order refined methods. Low-order refined preconditioners, moreover, require the use of algebraic multigrid to approximate the inverse of the operator. The communication associated with the multigrid coarse-grid solve hinders the parallel scalability of both classes of preconditioners, especially on heterogeneous architectures. To mitigate the coarse-grid solve cost, novel smoothing strategies are considered. The fourth-kind Chebyshev polynomial smoothing proposed by James Lottes is utilized to accelerate additive Schwarz-based smoothers in a geometric p-multigrid preconditioner. Through these techniques, we develop geometric p-multigrid preconditioners capable of achieving up to an 81% speedup over the state-of-the-art p-multigrid preconditioners on the Summit supercomputer.A p-multigrid approach with an additive coarse-grid solve specifically designed for heterogeneous architectures is considered. We also propose a hybrid p-multigrid and low-order refined preconditioner that improve the time-to-solution by as much as 86% compared to the low-order preconditioner. We demonstrate the effectiveness of these novel approaches on a variety of problems arising from the spectral element discretization of the incompressible Navier-Stokes equations on GPU architectures spanning to P > 1024 NVIDIA V100 GPUs on Summit."],"dc:format":["application/pdf"],"dc:identifier":["https://hdl.handle.net/2142/121461"],"dc:language":["en","eng"],"dc:rights":["Copyright 2023 Malachi Phillips"],"dc:subject":["Preconditioning","Multigrid","Poisson Equation","Navier-stokes Equations","Spectral Element Method","Heterogeneous Computing","High-performance Computing"],"dc:title":["Spectral element poisson preconditioners for heterogeneous architectures"],"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":"2026-07-22T22:24:57Z"}