Krylov Subspace Spectral (KSS) methods are traditionally used to solve time-dependent, variable-coefficient PDEs. They are high-order accurate, component-wise methods that are efficient with variable input sizes.
This thesis will demonstrate how one can make KSS methods even more efficient by using a Multigrid-like approach for low-frequency components. The essential ingredients of Multigrid, such as restriction, residual correction, and prolongation, are adapted to the timedependent case. Then a comparison of KSS, KSS with Multigrid, KSS-EPI and standard Krylov projection methods will be demonstrated.
","abstract_html":"<p>Krylov Subspace Spectral (KSS) methods are traditionally used to solve time-dependent, variable-coefficient PDEs. They are high-order accurate, component-wise methods that are efficient with variable input sizes.</p> <p>This thesis will demonstrate how one can make KSS methods even more efficient by using a Multigrid-like approach for low-frequency components. The essential ingredients of Multigrid, such as restriction, residual correction, and prolongation, are adapted to the timedependent case. Then a comparison of KSS, KSS with Multigrid, KSS-EPI and standard Krylov projection methods will be demonstrated.</p>","abstract_has_math":false,"creators":["Dozier, Haley Renee"],"institution":null,"degree_name":"Master of Science (MS)","degree_level":"Masters Thesis","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["James Lambers","Haiyan Tian","Huiqing Zhu"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2016,"date_issued":"2016-08-01T07:00:00Z","date_published":"2016-08-01T07:00:00Z","updated_at":"2026-07-24T05:44:34Z","subjects":["KSS Methods","Numerical Methods for Partial Differential Equations","Numerical Analysis and Computation","Partial Differential Equations"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://aquila.usm.edu/masters_theses/205","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["James Lambers","Haiyan Tian","Huiqing Zhu"]},{"key":"dc:creator","label":"Author","values":["Dozier, Haley Renee"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2016-06-30T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Masters Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science (MS)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["KSS Methods","Numerical Methods for Partial Differential Equations","Numerical Analysis and Computation","Partial Differential Equations"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://aquila.usm.edu/masters_theses/205"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Krylov Subspace Spectral (KSS) methods are traditionally used to solve time-dependent, variable-coefficient PDEs. They are high-order accurate, component-wise methods that are efficient with variable input sizes.
This thesis will demonstrate how one can make KSS methods even more efficient by using a Multigrid-like approach for low-frequency components. The essential ingredients of Multigrid, such as restriction, residual correction, and prolongation, are adapted to the timedependent case. Then a comparison of KSS, KSS with Multigrid, KSS-EPI and standard Krylov projection methods will be demonstrated.
"]},{"key":"dc:title","label":"Title","values":["Krylov Subspace Spectral Method with Multigrid for a Time-Dependent, Variable-Coefficient Partial Differential Equation"]}]}],"canonical_facts":{"dc:contributor":["James Lambers","Haiyan Tian","Huiqing Zhu"],"dc:creator":["Dozier, Haley Renee"],"dc:date.available":["2016-06-30T07:00:00Z"],"dc:description.abstract":["Krylov Subspace Spectral (KSS) methods are traditionally used to solve time-dependent, variable-coefficient PDEs. They are high-order accurate, component-wise methods that are efficient with variable input sizes.
This thesis will demonstrate how one can make KSS methods even more efficient by using a Multigrid-like approach for low-frequency components. The essential ingredients of Multigrid, such as restriction, residual correction, and prolongation, are adapted to the timedependent case. Then a comparison of KSS, KSS with Multigrid, KSS-EPI and standard Krylov projection methods will be demonstrated.
"],"dc:identifier":["https://aquila.usm.edu/masters_theses/205"],"dc:subject":["KSS Methods","Numerical Methods for Partial Differential Equations","Numerical Analysis and Computation","Partial Differential Equations"],"dc:title":["Krylov Subspace Spectral Method with Multigrid for a Time-Dependent, Variable-Coefficient Partial Differential Equation"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Masters Thesis"],"thesis:degree_name":["Master of Science (MS)"]},"updated_at":"2026-07-24T05:44:34Z"}