{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/26201"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/26201","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Stable numerical methods for hyperbolic partial differential equations using overlapping domain decomposition","abstract":"Overlapping domain decomposition methods, otherwise known as overset or chimera methods, are useful approaches for simplifying the discretizations of partial differential equations in or around complex geometries. While in wide use, the methods are prone to numerical instability unless numerical diffusion or some other form of regularization is used. This is especially true for higher-order methods. To address this, high-order, provably stable, overlapping domain decomposition methods are derived for hyperbolic initial-boundary-value problems. The overlap is treated by splitting the domain into pieces and using newly derived generalized summation-by-parts derivative operators and polynomial interpolation. Numerical regularization is not required for stability in the linear limit. Applications to linear and nonlinear problems in one and two dimensions are presented and new high-order generalized summation-by-parts derivative operators are derived.","abstract_html":"Overlapping domain decomposition methods, otherwise known as overset or chimera methods, are useful approaches for simplifying the discretizations of partial differential equations in or around complex geometries. While in wide use, the methods are prone to numerical instability unless numerical diffusion or some other form of regularization is used. This is especially true for higher-order methods. To address this, high-order, provably stable, overlapping domain decomposition methods are derived for hyperbolic initial-boundary-value problems. The overlap is treated by splitting the domain into pieces and using newly derived generalized summation-by-parts derivative operators and polynomial interpolation. Numerical regularization is not required for stability in the linear limit. Applications to linear and nonlinear problems in one and two dimensions are presented and new high-order generalized summation-by-parts derivative operators are derived.","abstract_has_math":false,"creators":["Reichert, Adam H."],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Computer Science","degree_department":null,"school":null,"contributors":["Bodony, Daniel J.","Olson, Luke N.","Heath, Michael T.","Henshaw, William","Gropp, William D."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-08-25T22:18:30Z","date_published":"2011-08-25T22:18:30Z","updated_at":"2026-07-22T22:25:26Z","subjects":["High order finite difference methods","Overlapping domain decomposition","Numerical stability","Generalized summation-by-parts"],"languages":["en"],"rights":["Copyright 2011 Adam H. Reichert"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/26201","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Bodony, Daniel J.","Olson, Luke N.","Heath, Michael T.","Henshaw, William","Gropp, William D."]},{"key":"dc:creator","label":"Author","values":["Reichert, Adam H."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-08-25T22:18:30Z","2011-08"]},{"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":["High order finite difference methods","Overlapping domain decomposition","Numerical stability","Generalized summation-by-parts"]}]},{"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 Adam H. Reichert"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/26201"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Overlapping domain decomposition methods, otherwise known as overset or chimera methods, are useful approaches for simplifying the discretizations of partial differential equations in or around complex geometries. While in wide use, the methods are prone to numerical instability unless numerical diffusion or some other form of regularization is used. This is especially true for higher-order methods. To address this, high-order, provably stable, overlapping domain decomposition methods are derived for hyperbolic initial-boundary-value problems. The overlap is treated by splitting the domain into pieces and using newly derived generalized summation-by-parts derivative operators and polynomial interpolation. Numerical regularization is not required for stability in the linear limit. Applications to linear and nonlinear problems in one and two dimensions are presented and new high-order generalized summation-by-parts derivative operators are derived.","Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2011-07-11T17:10:49Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Reichert_Adam.pdf: 1933194 bytes, checksum: 21934ab1ee27d883b3d365654b6a831b (MD5)","Made available in DSpace on 2011-08-25T22:18:30Z (GMT). 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To address this, high-order, provably stable, overlapping domain decomposition methods are derived for hyperbolic initial-boundary-value problems. The overlap is treated by splitting the domain into pieces and using newly derived generalized summation-by-parts derivative operators and polynomial interpolation. Numerical regularization is not required for stability in the linear limit. Applications to linear and nonlinear problems in one and two dimensions are presented and new high-order generalized summation-by-parts derivative operators are derived.","Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2011-07-11T17:10:49Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Reichert_Adam.pdf: 1933194 bytes, checksum: 21934ab1ee27d883b3d365654b6a831b (MD5)","Made available in DSpace on 2011-08-25T22:18:30Z (GMT). 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