{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/95421"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/95421","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Asynchronous parallel solver for hyperbolic problems via the Spacetime Discontinuous Galerkin method","abstract":"This thesis presents a parallel Space Time Discontinuous Galerkin (SDG) finite element method which makes use of the method's unstructured mesh generation and localized solution technique to achieve a high level of parallel scalability. Our SDG method is different from most traditional adaptive finite element methods in that the solution process generates fully unstructured spacetime grids that satisfy a special causality constraint ensuring that computations can occur locally on small cluster of spacetime elements. The resulting asynchronous solution scheme offers several desirable features: element-wise conservation of solution quantities, strong stability properties without the need for explicit stabilization, local mesh adaptivity operations and linear complexity in the number of spacetime elements. In this thesis we propose an algorithm that effectively parallelizes the Tent Pitcher algorithm developed by [1] using the POSIX Thread (or Pthread) parallel execution model. Multiple software threads can simultaneously and asynchronously perform patch computations by advancing vertices in time. By enforcing the causality constraint on the time step, we can guarantee that each thread only performs calculations using data computed previously. Additionally, improvements to the adaptivity scheme allow for local mesh refinement and coarsening while maintaining globally conforming triangulation. Numerical tests show that our algorithm achieves high parallel scalability using shared-memory parallelization.","abstract_html":"This thesis presents a parallel Space Time Discontinuous Galerkin (SDG) finite element method which makes use of the method's unstructured mesh generation and localized solution technique to achieve a high level of parallel scalability. Our SDG method is different from most traditional adaptive finite element methods in that the solution process generates fully unstructured spacetime grids that satisfy a special causality constraint ensuring that computations can occur locally on small cluster of spacetime elements. The resulting asynchronous solution scheme offers several desirable features: element-wise conservation of solution quantities, strong stability properties without the need for explicit stabilization, local mesh adaptivity operations and linear complexity in the number of spacetime elements. In this thesis we propose an algorithm that effectively parallelizes the Tent Pitcher algorithm developed by [1] using the POSIX Thread (or Pthread) parallel execution model. Multiple software threads can simultaneously and asynchronously perform patch computations by advancing vertices in time. By enforcing the causality constraint on the time step, we can guarantee that each thread only performs calculations using data computed previously. Additionally, improvements to the adaptivity scheme allow for local mesh refinement and coarsening while maintaining globally conforming triangulation. Numerical tests show that our algorithm achieves high parallel scalability using shared-memory parallelization.","abstract_has_math":false,"creators":["Madhukar, Amit"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"M.S.","degree_level":"Thesis","degree_discipline":"Mechanical Engineering","degree_department":null,"school":null,"contributors":["Haber, Robert B."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2017,"date_issued":"2017-03-01T15:49:35Z","date_published":"2017-03-01T15:49:35Z","updated_at":"2026-07-22T22:26:37Z","subjects":["Spacetime Discontinuous Galerkin Finite Element Method","Parallel","Thread Pool","Asynchronous","Unstructured Meshing"],"languages":["en"],"rights":["Copyright 2016 Amit Madhukar"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/95421","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Haber, Robert B."]},{"key":"dc:creator","label":"Author","values":["Madhukar, Amit"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2017-03-01T15:49:35Z","2016-12-08","2016-12"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mechanical Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["M.S."]},{"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":["Spacetime Discontinuous Galerkin Finite Element Method","Parallel","Thread Pool","Asynchronous","Unstructured Meshing"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2016 Amit Madhukar"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/95421"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["This thesis presents a parallel Space Time Discontinuous Galerkin (SDG) finite element method which makes use of the method's unstructured mesh generation and localized solution technique to achieve a high level of parallel scalability. Our SDG method is different from most traditional adaptive finite element methods in that the solution process generates fully unstructured spacetime grids that satisfy a special causality constraint ensuring that computations can occur locally on small cluster of spacetime elements. The resulting asynchronous solution scheme offers several desirable features: element-wise conservation of solution quantities, strong stability properties without the need for explicit stabilization, local mesh adaptivity operations and linear complexity in the number of spacetime elements. In this thesis we propose an algorithm that effectively parallelizes the Tent Pitcher algorithm developed by [1] using the POSIX Thread (or Pthread) parallel execution model. Multiple software threads can simultaneously and asynchronously perform patch computations by advancing vertices in time. By enforcing the causality constraint on the time step, we can guarantee that each thread only performs calculations using data computed previously. Additionally, improvements to the adaptivity scheme allow for local mesh refinement and coarsening while maintaining globally conforming triangulation. Numerical tests show that our algorithm achieves high parallel scalability using shared-memory parallelization.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2017-02-28 without embargo terms","The student, Amit Madhukar, accepted the attached license on 2016-12-08 at 13:57.","The student, Amit Madhukar, submitted this Thesis for approval on 2016-12-08 at 14:09.","This Thesis was approved for publication on 2016-12-08 at 14:43.","DSpace SAF Submission Ingestion Package generated from Vireo submission #10493 on 2017-02-28 at 15:03:52","Made available in DSpace on 2017-03-01T15:49:35Z (GMT). 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Our SDG method is different from most traditional adaptive finite element methods in that the solution process generates fully unstructured spacetime grids that satisfy a special causality constraint ensuring that computations can occur locally on small cluster of spacetime elements. The resulting asynchronous solution scheme offers several desirable features: element-wise conservation of solution quantities, strong stability properties without the need for explicit stabilization, local mesh adaptivity operations and linear complexity in the number of spacetime elements. In this thesis we propose an algorithm that effectively parallelizes the Tent Pitcher algorithm developed by [1] using the POSIX Thread (or Pthread) parallel execution model. Multiple software threads can simultaneously and asynchronously perform patch computations by advancing vertices in time. By enforcing the causality constraint on the time step, we can guarantee that each thread only performs calculations using data computed previously. Additionally, improvements to the adaptivity scheme allow for local mesh refinement and coarsening while maintaining globally conforming triangulation. Numerical tests show that our algorithm achieves high parallel scalability using shared-memory parallelization.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2017-02-28 without embargo terms","The student, Amit Madhukar, accepted the attached license on 2016-12-08 at 13:57.","The student, Amit Madhukar, submitted this Thesis for approval on 2016-12-08 at 14:09.","This Thesis was approved for publication on 2016-12-08 at 14:43.","DSpace SAF Submission Ingestion Package generated from Vireo submission #10493 on 2017-02-28 at 15:03:52","Made available in DSpace on 2017-03-01T15:49:35Z (GMT). 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