{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/69594"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/69594","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"The SAS Domain Decomposition Method for Structural Analysis","abstract":"A new domain decomposition method for the efficient and parallelizable numerical handling of plate bending and three dimensional elasticity problem is developed via the discovery of two special classes of matrices. The first class of matrices, say $A\\in{\\cal C}\\sp{n\\times n}$, has the relation A = P A P and the second, the counterpart of the first class of matrices A, say $B\\in{\\cal C}\\sp{n\\times n}$, satisfies the relation B = $-$P B P where P is some symmetrical signed permutation matrix. Also introduced are four special classes of linear vector subspaces which are closely related to this approach. Two of these four subspaces contain vectors as their elements and the other two consist of matrices as their elements.","abstract_html":"A new domain decomposition method for the efficient and parallelizable numerical handling of plate bending and three dimensional elasticity problem is developed via the discovery of two special classes of matrices. The first class of matrices, say $A\\in{\\cal C}\\sp{n\\times n}$, has the relation A = P A P and the second, the counterpart of the first class of matrices A, say $B\\in{\\cal C}\\sp{n\\times n}$, satisfies the relation B = $-$P B P where P is some symmetrical signed permutation matrix. Also introduced are four special classes of linear vector subspaces which are closely related to this approach. Two of these four subspaces contain vectors as their elements and the other two consist of matrices as their elements.","abstract_has_math":true,"creators":["Chen, Hsin-Chu"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Computer Science","degree_department":null,"school":null,"contributors":["Sameh, Ahmed H."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-12-15T19:26:04Z","date_published":"2014-12-15T19:26:04Z","updated_at":"2026-07-22T22:26:01Z","subjects":["Computer Science"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(UMI)AAI8823098"],"render_values":[{"text":"(UMI)AAI8823098","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/69594","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Sameh, Ahmed H."]},{"key":"dc:creator","label":"Author","values":["Chen, Hsin-Chu"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014-12-15T19:26:04Z","10000-01-01","1988"]},{"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":["Computer Science"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/69594","(UMI)AAI8823098"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["A new domain decomposition method for the efficient and parallelizable numerical handling of plate bending and three dimensional elasticity problem is developed via the discovery of two special classes of matrices. The first class of matrices, say $A\\in{\\cal C}\\sp{n\\times n}$, has the relation A = P A P and the second, the counterpart of the first class of matrices A, say $B\\in{\\cal C}\\sp{n\\times n}$, satisfies the relation B = $-$P B P where P is some symmetrical signed permutation matrix. Also introduced are four special classes of linear vector subspaces which are closely related to this approach. Two of these four subspaces contain vectors as their elements and the other two consist of matrices as their elements.","This new approach has its origin in the idea of the traditional symmetrical and antisymmetrical approach and that of generalized coordinate transformations. It can be viewed physically as a special domain decomposition method, which takes advantage of the symmetry or partial symmetry of a physical problem. This approach is, therefore, referred to as the symmetrical and antisymmetrical (SAS) domain decomposition method, or simply the SAS approach. The SAS domain decomposition method is a very efficient approach for problems which are symmetrically discretizable. The application of this method in conjunction with other domain decomposition techniques to problems which cannot be symmetrically discretized is still promising, although the advantage over the non-SAS approach is not as great as that for symmetrical problems.","Made available in DSpace on 2014-12-15T19:26:04Z (GMT). No. of bitstreams: 1 8823098.pdf: 3403938 bytes, checksum: 6b588a648a8b92ac820cd40ea9bb5189 (MD5) Previous issue date: 1988","Embargo set by: Seth Robbins for item 69760 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","121 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1988."]},{"key":"dc:title","label":"Title","values":["The SAS Domain Decomposition Method for Structural Analysis"]}]}],"canonical_facts":{"dc:contributor":["Sameh, Ahmed H."],"dc:creator":["Chen, Hsin-Chu"],"dc:date":["2014-12-15T19:26:04Z","10000-01-01","1988"],"dc:description":["A new domain decomposition method for the efficient and parallelizable numerical handling of plate bending and three dimensional elasticity problem is developed via the discovery of two special classes of matrices. The first class of matrices, say $A\\in{\\cal C}\\sp{n\\times n}$, has the relation A = P A P and the second, the counterpart of the first class of matrices A, say $B\\in{\\cal C}\\sp{n\\times n}$, satisfies the relation B = $-$P B P where P is some symmetrical signed permutation matrix. Also introduced are four special classes of linear vector subspaces which are closely related to this approach. Two of these four subspaces contain vectors as their elements and the other two consist of matrices as their elements.","This new approach has its origin in the idea of the traditional symmetrical and antisymmetrical approach and that of generalized coordinate transformations. It can be viewed physically as a special domain decomposition method, which takes advantage of the symmetry or partial symmetry of a physical problem. This approach is, therefore, referred to as the symmetrical and antisymmetrical (SAS) domain decomposition method, or simply the SAS approach. The SAS domain decomposition method is a very efficient approach for problems which are symmetrically discretizable. The application of this method in conjunction with other domain decomposition techniques to problems which cannot be symmetrically discretized is still promising, although the advantage over the non-SAS approach is not as great as that for symmetrical problems.","Made available in DSpace on 2014-12-15T19:26:04Z (GMT). No. of bitstreams: 1 8823098.pdf: 3403938 bytes, checksum: 6b588a648a8b92ac820cd40ea9bb5189 (MD5) Previous issue date: 1988","Embargo set by: Seth Robbins for item 69760 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","121 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1988."],"dc:identifier":["http://hdl.handle.net/2142/69594","(UMI)AAI8823098"],"dc:subject":["Computer Science"],"dc:title":["The SAS Domain Decomposition Method for Structural Analysis"],"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":"2026-07-22T22:26:01Z"}