{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/95519"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/95519","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Multi-scale problems: an improved non-intrusive algorithm that enhances FEA platforms with the generalized finite element method; An improved preconditioned conjugate gradient solver for hierarchical generalized finite element systems of equations","abstract":"The finite element method (FEM) discretizes an object of interest, say a cube, and solves for its dis placement and stress under a certain loading. The FEM is used by many commercial softwares. The generalized FEM (GFEM) adds information in the solution process that improves the displacement and stress results, and is not fully available in commercial software, but in third-party software. A GFEM method that transfers small scale information to larger scales is called GFEM global-local (GFEM gl ). The process of adding GFEM gl functionality to commercial software without modifying the commercial software is called a non-intrusive algorithm. This thesis presents a new non-intrusive algorithm, the hierarchical non-intrusive algorithm (HNA), that allows the combination of powerful FEM softwares with current and future state-of-the-art GFEM gl software, allowing the user to enjoy the capabilities of each software. The HNA is better than previous non-intrusive methods because it is faster, uses less memory, and is easy to use. In this thesis, the HNA is outlined and its accuracy is verified. It can be used to improve the simulation of vehicles flying at hyper-sonic speeds, greater than five times the speed of sound. A procedure that reduces the negative effects of machine precision (condition number) in solving GFEM gl systems of equations is called the Stable GFEM gl (SGFEM gl ). This thesis presents results on the ability of SGFEM gl to not only reduce the condition number, but improve solution accuracy over GFEM gl . The reduced conditioning from SGFEM gl systems of equations makes feasible iterative schemes that solve SGFEM gl linear system of equations. The reduced memory requirements of iterative solvers over direct solvers, combined with improved speed, make larger-scale simulations possible. An iterative solver called the preconditioned conjugate gradient method is investigated within this context, and a preconditioner is proposed for the method. This thesis shows that its proposed iterative solver is faster than previous iterative solvers. The proposed iterative solver is also shown to be faster than a sparse direct solver.","abstract_html":"The finite element method (FEM) discretizes an object of interest, say a cube, and solves for its dis placement and stress under a certain loading. The FEM is used by many commercial softwares. The generalized FEM (GFEM) adds information in the solution process that improves the displacement and stress results, and is not fully available in commercial software, but in third-party software. A GFEM method that transfers small scale information to larger scales is called GFEM global-local (GFEM gl ). The process of adding GFEM gl functionality to commercial software without modifying the commercial software is called a non-intrusive algorithm. This thesis presents a new non-intrusive algorithm, the hierarchical non-intrusive algorithm (HNA), that allows the combination of powerful FEM softwares with current and future state-of-the-art GFEM gl software, allowing the user to enjoy the capabilities of each software. The HNA is better than previous non-intrusive methods because it is faster, uses less memory, and is easy to use. In this thesis, the HNA is outlined and its accuracy is verified. It can be used to improve the simulation of vehicles flying at hyper-sonic speeds, greater than five times the speed of sound. A procedure that reduces the negative effects of machine precision (condition number) in solving GFEM gl systems of equations is called the Stable GFEM gl (SGFEM gl ). This thesis presents results on the ability of SGFEM gl to not only reduce the condition number, but improve solution accuracy over GFEM gl . The reduced conditioning from SGFEM gl systems of equations makes feasible iterative schemes that solve SGFEM gl linear system of equations. The reduced memory requirements of iterative solvers over direct solvers, combined with improved speed, make larger-scale simulations possible. An iterative solver called the preconditioned conjugate gradient method is investigated within this context, and a preconditioner is proposed for the method. This thesis shows that its proposed iterative solver is faster than previous iterative solvers. The proposed iterative solver is also shown to be faster than a sparse direct solver.","abstract_has_math":false,"creators":["Fillmore, Travis"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"M.S.","degree_level":"Thesis","degree_discipline":"Civil Engineering","degree_department":null,"school":null,"contributors":["Duarte, Carlos A."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2017,"date_issued":"2017-03-01T16:37:11Z","date_published":"2017-03-01T16:37:11Z","updated_at":"2026-07-22T22:26:37Z","subjects":["Multi-scale","Non-intrusive","Generalized finite element method (GFEM)","Finite element method (FEM)","Stable generalized finite element method (SGFEM)","Iterative","Preconditioned conjugate gradient (PCG)"],"languages":["en"],"rights":["Copyright 2016 Travis Fillmore"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/95519","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Duarte, Carlos A."]},{"key":"dc:creator","label":"Author","values":["Fillmore, Travis"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2017-03-01T16:37:11Z","2019-03-02T10:15:27Z","2016-12-08","2016-12"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Civil 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":["Multi-scale","Non-intrusive","Generalized finite element method (GFEM)","Finite element method (FEM)","Stable generalized finite element method (SGFEM)","Iterative","Preconditioned conjugate gradient (PCG)"]}]},{"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 Travis Fillmore"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/95519"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["The finite element method (FEM) discretizes an object of interest, say a cube, and solves for its dis placement and stress under a certain loading. The FEM is used by many commercial softwares. The generalized FEM (GFEM) adds information in the solution process that improves the displacement and stress results, and is not fully available in commercial software, but in third-party software. A GFEM method that transfers small scale information to larger scales is called GFEM global-local (GFEM gl ). The process of adding GFEM gl functionality to commercial software without modifying the commercial software is called a non-intrusive algorithm. This thesis presents a new non-intrusive algorithm, the hierarchical non-intrusive algorithm (HNA), that allows the combination of powerful FEM softwares with current and future state-of-the-art GFEM gl software, allowing the user to enjoy the capabilities of each software. The HNA is better than previous non-intrusive methods because it is faster, uses less memory, and is easy to use. In this thesis, the HNA is outlined and its accuracy is verified. It can be used to improve the simulation of vehicles flying at hyper-sonic speeds, greater than five times the speed of sound. A procedure that reduces the negative effects of machine precision (condition number) in solving GFEM gl systems of equations is called the Stable GFEM gl (SGFEM gl ). This thesis presents results on the ability of SGFEM gl to not only reduce the condition number, but improve solution accuracy over GFEM gl . The reduced conditioning from SGFEM gl systems of equations makes feasible iterative schemes that solve SGFEM gl linear system of equations. The reduced memory requirements of iterative solvers over direct solvers, combined with improved speed, make larger-scale simulations possible. An iterative solver called the preconditioned conjugate gradient method is investigated within this context, and a preconditioner is proposed for the method. This thesis shows that its proposed iterative solver is faster than previous iterative solvers. The proposed iterative solver is also shown to be faster than a sparse direct solver.","Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2018-12-01","The student, Travis Fillmore, accepted the attached license on 2016-12-07 at 12:07.","The student, Travis Fillmore, submitted this Thesis for approval on 2016-12-07 at 12:19.","This Thesis was approved for publication on 2016-12-08 at 13:53.","DSpace SAF Submission Ingestion Package generated from Vireo submission #10468 on 2017-02-28 at 14:37:37","Made available in DSpace on 2017-03-01T16:37:11Z (GMT). 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The FEM is used by many commercial softwares. The generalized FEM (GFEM) adds information in the solution process that improves the displacement and stress results, and is not fully available in commercial software, but in third-party software. A GFEM method that transfers small scale information to larger scales is called GFEM global-local (GFEM gl ). The process of adding GFEM gl functionality to commercial software without modifying the commercial software is called a non-intrusive algorithm. This thesis presents a new non-intrusive algorithm, the hierarchical non-intrusive algorithm (HNA), that allows the combination of powerful FEM softwares with current and future state-of-the-art GFEM gl software, allowing the user to enjoy the capabilities of each software. The HNA is better than previous non-intrusive methods because it is faster, uses less memory, and is easy to use. In this thesis, the HNA is outlined and its accuracy is verified. It can be used to improve the simulation of vehicles flying at hyper-sonic speeds, greater than five times the speed of sound. A procedure that reduces the negative effects of machine precision (condition number) in solving GFEM gl systems of equations is called the Stable GFEM gl (SGFEM gl ). This thesis presents results on the ability of SGFEM gl to not only reduce the condition number, but improve solution accuracy over GFEM gl . The reduced conditioning from SGFEM gl systems of equations makes feasible iterative schemes that solve SGFEM gl linear system of equations. The reduced memory requirements of iterative solvers over direct solvers, combined with improved speed, make larger-scale simulations possible. An iterative solver called the preconditioned conjugate gradient method is investigated within this context, and a preconditioner is proposed for the method. This thesis shows that its proposed iterative solver is faster than previous iterative solvers. The proposed iterative solver is also shown to be faster than a sparse direct solver.","Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2018-12-01","The student, Travis Fillmore, accepted the attached license on 2016-12-07 at 12:07.","The student, Travis Fillmore, submitted this Thesis for approval on 2016-12-07 at 12:19.","This Thesis was approved for publication on 2016-12-08 at 13:53.","DSpace SAF Submission Ingestion Package generated from Vireo submission #10468 on 2017-02-28 at 14:37:37","Made available in DSpace on 2017-03-01T16:37:11Z (GMT). No. of bitstreams: 2 FILLMORE-THESIS-2016.pdf: 5730797 bytes, checksum: a16f2e7dda92c593974ec0f45032e09c (MD5) LICENSE.txt: 4212 bytes, checksum: 5bdfaf8ee6ec5c913173e23265e6e034 (MD5) Previous issue date: 2016-12-08","Embargo set by: Seth Robbins for item 98635 Lift date: 2019-03-01T16:37:19Z Reason: Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD system","U of I Only Restriction Lifted for Item 98635 on 2019-03-02T10:15:27Z."],"dc:format":["application/pdf"],"dc:identifier":["http://hdl.handle.net/2142/95519"],"dc:language":["en"],"dc:rights":["Copyright 2016 Travis Fillmore"],"dc:subject":["Multi-scale","Non-intrusive","Generalized finite element method (GFEM)","Finite element method (FEM)","Stable generalized finite element method (SGFEM)","Iterative","Preconditioned conjugate gradient (PCG)"],"dc:title":["Multi-scale problems: an improved non-intrusive algorithm that enhances FEA platforms with the generalized finite element method; An improved preconditioned conjugate gradient solver for hierarchical generalized finite element systems of equations"],"dc:type":["text"],"thesis:degree_discipline":["Civil Engineering"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["M.S."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:26:37Z"}