{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/29810"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/29810","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Adaptive unstructured spacetime meshing for four-dimensional spacetime discontinuous Galerkin finite element methods","abstract":"We describe the spacetime discontinuous Galerkin method, a new type of finite-element method which promises dramatic improvement in solution speed for hyperbolic problems. These methods require the generation of spacetime meshes that satisfy a special causality constraint. This work focuses on the extension of the existing 2d×time spacetime meshing algorithm known as TentPitcher to 3d×time problems. We review existing work based on TentPitcher. Then, we extend TentPitcher to 3d×time and derive methods for handling mesh adaptivity operations. Next, we describe the software we have developed to implement our algorithms and give preliminary results of testing. We also identify unresolved theoretical and engineering issues associated with our new methods and suggest directions for further research.","abstract_html":"We describe the spacetime discontinuous Galerkin method, a new type of finite-element method which promises dramatic improvement in solution speed for hyperbolic problems. These methods require the generation of spacetime meshes that satisfy a special causality constraint. This work focuses on the extension of the existing 2d×time spacetime meshing algorithm known as TentPitcher to 3d×time problems. We review existing work based on TentPitcher. Then, we extend TentPitcher to 3d×time and derive methods for handling mesh adaptivity operations. Next, we describe the software we have developed to implement our algorithms and give preliminary results of testing. We also identify unresolved theoretical and engineering issues associated with our new methods and suggest directions for further research.","abstract_has_math":false,"creators":["Mont, Alexander D."],"institution":"University of Illinois at Urbana-Champaign","degree_name":"M.S.","degree_level":"Thesis","degree_discipline":"Computer Science","degree_department":null,"school":null,"contributors":["Erickson, Jeff G."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2012,"date_issued":"2012-02-06T20:18:29Z","date_published":"2012-02-06T20:18:29Z","updated_at":"2026-07-22T22:25:29Z","subjects":["spacetime meshing","discontinuous Galerkin","adaptive meshing","advancing front"],"languages":["en"],"rights":["Copyright 2011 Alexander Mont."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/29810","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Erickson, Jeff G."]},{"key":"dc:creator","label":"Author","values":["Mont, Alexander D."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2012-02-06T20:18:29Z","2011-12"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Computer Science"]},{"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 meshing","discontinuous Galerkin","adaptive meshing","advancing front"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2011 Alexander Mont."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/29810"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["We describe the spacetime discontinuous Galerkin method, a new type of finite-element method which promises dramatic improvement in solution speed for hyperbolic problems. 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