{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/20158"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/20158","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"A parallelization of an equation-based algorithm for multicomponent separation calculations","abstract":"Multicomponent separation calculations, whether for single columns or for complexly interlinked systems of multiple columns, represent large scale computational problems and are thus attractive applications for the parallel computing architectures of modern supercomputers. Frequently, these problems are formulated as a large set of nonlinear equations solved by a Newton-Raphson or comparable successive linearization technique. They thus require the solution of a very large system of sparse linear equations, which often represents a large fraction of the overall computing time. An efficient parallel technique for the solution of such large sparse systems, based on an ordering of equations by plate, is presented. The resulting linear systems take on an almost block tridiagonal (BTD) form, with off-BTD blocks arising from recycle streams or tower sidestreams. Extensions to a current multiprocessor scheme for BTD systems, the Sameh method, are also given.","abstract_html":"Multicomponent separation calculations, whether for single columns or for complexly interlinked systems of multiple columns, represent large scale computational problems and are thus attractive applications for the parallel computing architectures of modern supercomputers. Frequently, these problems are formulated as a large set of nonlinear equations solved by a Newton-Raphson or comparable successive linearization technique. They thus require the solution of a very large system of sparse linear equations, which often represents a large fraction of the overall computing time. An efficient parallel technique for the solution of such large sparse systems, based on an ordering of equations by plate, is presented. The resulting linear systems take on an almost block tridiagonal (BTD) form, with off-BTD blocks arising from recycle streams or tower sidestreams. Extensions to a current multiprocessor scheme for BTD systems, the Sameh method, are also given.","abstract_has_math":false,"creators":["O'Neill, Alfred John"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Chemical Engineering","degree_department":null,"school":null,"contributors":["Stadtherr, Mark A."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-05-07T12:30:39Z","date_published":"2011-05-07T12:30:39Z","updated_at":"2026-07-22T22:25:15Z","subjects":["Engineering, Chemical","Computer Science"],"languages":["eng"],"rights":["Copyright 1991 O'Neill, Alfred John"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9210940","(UMI)AAI9210940"],"render_values":[{"text":"AAI9210940","href":null,"code":true},{"text":"(UMI)AAI9210940","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/20158","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Stadtherr, Mark A."]},{"key":"dc:creator","label":"Author","values":["O'Neill, Alfred John"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-05-07T12:30:39Z","10000-01-01","1991"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Chemical Engineering"]},{"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":["Engineering, Chemical","Computer Science"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 1991 O'Neill, Alfred John"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9210940","(UMI)AAI9210940","http://hdl.handle.net/2142/20158"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Multicomponent separation calculations, whether for single columns or for complexly interlinked systems of multiple columns, represent large scale computational problems and are thus attractive applications for the parallel computing architectures of modern supercomputers. Frequently, these problems are formulated as a large set of nonlinear equations solved by a Newton-Raphson or comparable successive linearization technique. They thus require the solution of a very large system of sparse linear equations, which often represents a large fraction of the overall computing time. An efficient parallel technique for the solution of such large sparse systems, based on an ordering of equations by plate, is presented. The resulting linear systems take on an almost block tridiagonal (BTD) form, with off-BTD blocks arising from recycle streams or tower sidestreams. Extensions to a current multiprocessor scheme for BTD systems, the Sameh method, are also given.","\"A close examination of the regular structure of the linear system reveals the possibility of a further improvement in the methd: a pretreatment of the matrix to reduce both the cost of system reduction and the overhead inherent in the parallel technique. The separate approaches result in three competing methods, which are compared on a parallel machine for a variety of problems. The results of this system of tests leads to an \"\"advanced\"\" method which incorporates the best features of the successful algorithms.\"","Made available in DSpace on 2011-05-07T12:30:39Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9210940.pdf: 4144200 bytes, checksum: 25e1902dcf62f982869bedec858a5072 (MD5) Previous issue date: 1991","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:41:57Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:18:13-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission","ETDs are only available to UIUC Users without author permission","U of I Only"]},{"key":"dc:title","label":"Title","values":["A parallelization of an equation-based algorithm for multicomponent separation calculations"]}]}],"canonical_facts":{"dc:contributor":["Stadtherr, Mark A."],"dc:creator":["O'Neill, Alfred John"],"dc:date":["2011-05-07T12:30:39Z","10000-01-01","1991"],"dc:description":["Multicomponent separation calculations, whether for single columns or for complexly interlinked systems of multiple columns, represent large scale computational problems and are thus attractive applications for the parallel computing architectures of modern supercomputers. Frequently, these problems are formulated as a large set of nonlinear equations solved by a Newton-Raphson or comparable successive linearization technique. They thus require the solution of a very large system of sparse linear equations, which often represents a large fraction of the overall computing time. An efficient parallel technique for the solution of such large sparse systems, based on an ordering of equations by plate, is presented. The resulting linear systems take on an almost block tridiagonal (BTD) form, with off-BTD blocks arising from recycle streams or tower sidestreams. Extensions to a current multiprocessor scheme for BTD systems, the Sameh method, are also given.","\"A close examination of the regular structure of the linear system reveals the possibility of a further improvement in the methd: a pretreatment of the matrix to reduce both the cost of system reduction and the overhead inherent in the parallel technique. The separate approaches result in three competing methods, which are compared on a parallel machine for a variety of problems. The results of this system of tests leads to an \"\"advanced\"\" method which incorporates the best features of the successful algorithms.\"","Made available in DSpace on 2011-05-07T12:30:39Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9210940.pdf: 4144200 bytes, checksum: 25e1902dcf62f982869bedec858a5072 (MD5) Previous issue date: 1991","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:41:57Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:18:13-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission","ETDs are only available to UIUC Users without author permission","U of I Only"],"dc:identifier":["AAI9210940","(UMI)AAI9210940","http://hdl.handle.net/2142/20158"],"dc:language":["eng"],"dc:rights":["Copyright 1991 O'Neill, Alfred John"],"dc:subject":["Engineering, Chemical","Computer Science"],"dc:title":["A parallelization of an equation-based algorithm for multicomponent separation calculations"],"dc:type":["text"],"thesis:degree_discipline":["Chemical Engineering"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:15Z"}