{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/72084"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/72084","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Efficient Solution of Large Sparse Eigenvalue Problems in Microelectronic Simulation","abstract":"We present a new Chebyshev-Arnoldi algorithm for finding the lowest energy eigen-functions of an elliptic operator. The algorithm, which is essentially the same for symmetric, nonsymmetric, and complex nonhermitian matrices, is adapted to a specific problem by two subroutines which encapsulate the problem-specific definition of energy, plus the discretization and matrix-vector multiply routines. We adapt the algorithm to two important problems, the self-consistent Schrodinger-Poisson model of quantum-effect devices, and the vector Helmholtz equation for a dielectric waveguide, addressing other important physical, numerical and computational issues as they arise. An asymptotic convergence estimate is derived which shows the Chebyshev-Arnoldi algorithm to be superior to Chebyshev-preconditioned subspace iteration. We also examine Newton methods for general large sparse eigenvalue problems satisfying the overdamping condition and show how to use sparse iterative solvers more effectively in them.","abstract_html":"We present a new Chebyshev-Arnoldi algorithm for finding the lowest energy eigen-functions of an elliptic operator. The algorithm, which is essentially the same for symmetric, nonsymmetric, and complex nonhermitian matrices, is adapted to a specific problem by two subroutines which encapsulate the problem-specific definition of energy, plus the discretization and matrix-vector multiply routines. We adapt the algorithm to two important problems, the self-consistent Schrodinger-Poisson model of quantum-effect devices, and the vector Helmholtz equation for a dielectric waveguide, addressing other important physical, numerical and computational issues as they arise. An asymptotic convergence estimate is derived which shows the Chebyshev-Arnoldi algorithm to be superior to Chebyshev-preconditioned subspace iteration. We also examine Newton methods for general large sparse eigenvalue problems satisfying the overdamping condition and show how to use sparse iterative solvers more effectively in them.","abstract_has_math":false,"creators":["Galick, Albert Thomas"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Computer Science","degree_department":null,"school":null,"contributors":["Kerkhoven, Thomas"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1993,"date_issued":"1993","date_published":"1993","updated_at":"2026-07-22T22:26:06Z","subjects":["Mathematics","Computer Science"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(UMI)AAI9329034"],"render_values":[{"text":"(UMI)AAI9329034","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/72084","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Kerkhoven, Thomas"]},{"key":"dc:creator","label":"Author","values":["Galick, Albert Thomas"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["1993","2014-12-17T20:00:38Z","10000-01-01"]},{"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":["Mathematics","Computer Science"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/72084","(UMI)AAI9329034"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["We present a new Chebyshev-Arnoldi algorithm for finding the lowest energy eigen-functions of an elliptic operator. The algorithm, which is essentially the same for symmetric, nonsymmetric, and complex nonhermitian matrices, is adapted to a specific problem by two subroutines which encapsulate the problem-specific definition of energy, plus the discretization and matrix-vector multiply routines. We adapt the algorithm to two important problems, the self-consistent Schrodinger-Poisson model of quantum-effect devices, and the vector Helmholtz equation for a dielectric waveguide, addressing other important physical, numerical and computational issues as they arise. An asymptotic convergence estimate is derived which shows the Chebyshev-Arnoldi algorithm to be superior to Chebyshev-preconditioned subspace iteration. We also examine Newton methods for general large sparse eigenvalue problems satisfying the overdamping condition and show how to use sparse iterative solvers more effectively in them.","Made available in DSpace on 2014-12-17T20:00:38Z (GMT). No. of bitstreams: 1 9329034.pdf: 4382424 bytes, checksum: 9c10d05faf91199c7d1ea1e84698a594 (MD5) Previous issue date: 1993","Embargo set by: Seth Robbins for item 72252 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","133 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1993."]},{"key":"dc:title","label":"Title","values":["Efficient Solution of Large Sparse Eigenvalue Problems in Microelectronic Simulation"]}]}],"canonical_facts":{"dc:contributor":["Kerkhoven, Thomas"],"dc:creator":["Galick, Albert Thomas"],"dc:date":["1993","2014-12-17T20:00:38Z","10000-01-01"],"dc:description":["We present a new Chebyshev-Arnoldi algorithm for finding the lowest energy eigen-functions of an elliptic operator. The algorithm, which is essentially the same for symmetric, nonsymmetric, and complex nonhermitian matrices, is adapted to a specific problem by two subroutines which encapsulate the problem-specific definition of energy, plus the discretization and matrix-vector multiply routines. We adapt the algorithm to two important problems, the self-consistent Schrodinger-Poisson model of quantum-effect devices, and the vector Helmholtz equation for a dielectric waveguide, addressing other important physical, numerical and computational issues as they arise. An asymptotic convergence estimate is derived which shows the Chebyshev-Arnoldi algorithm to be superior to Chebyshev-preconditioned subspace iteration. We also examine Newton methods for general large sparse eigenvalue problems satisfying the overdamping condition and show how to use sparse iterative solvers more effectively in them.","Made available in DSpace on 2014-12-17T20:00:38Z (GMT). No. of bitstreams: 1 9329034.pdf: 4382424 bytes, checksum: 9c10d05faf91199c7d1ea1e84698a594 (MD5) Previous issue date: 1993","Embargo set by: Seth Robbins for item 72252 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","133 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1993."],"dc:identifier":["http://hdl.handle.net/2142/72084","(UMI)AAI9329034"],"dc:subject":["Mathematics","Computer Science"],"dc:title":["Efficient Solution of Large Sparse Eigenvalue Problems in Microelectronic Simulation"],"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":"2026-07-22T22:26:06Z"}