Krylov Subspace Spectral (KSS) Methods have been demonstrated to be highly scalable time-stepping methods for stiff nonlinear PDEs. However, ensuring this scalability requires analytic computation of frequency-dependent quadrature nodes from the coefficients of the spatial differential operator. This thesis describes how this process can be automated for various classes of differential operators to facilitate public-domain software implementation.
","abstract_html":"<p>Krylov Subspace Spectral (KSS) Methods have been demonstrated to be highly scalable time-stepping methods for stiff nonlinear PDEs. However, ensuring this scalability requires analytic computation of frequency-dependent quadrature nodes from the coefficients of the spatial differential operator. This thesis describes how this process can be automated for various classes of differential operators to facilitate public-domain software implementation.</p>","abstract_has_math":false,"creators":["Montiforte, Vivian Ashley"],"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":2018,"date_issued":"2018-05-01T07:00:00Z","date_published":"2018-05-01T07:00:00Z","updated_at":"2026-07-24T05:44:50Z","subjects":["Partial Differential Equations","Krylov Subspace Spectral Methods","Frequency-Dependent Nodes","Stiff","Nonlinear","Quadrature Nodes","Numerical Analysis and Computation"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://aquila.usm.edu/masters_theses/343","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":["Montiforte, Vivian Ashley"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2018-03-28T07:00:00Z"]},{"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":["Partial Differential Equations","Krylov Subspace Spectral Methods","Frequency-Dependent Nodes","Stiff","Nonlinear","Quadrature Nodes","Numerical Analysis and Computation"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://aquila.usm.edu/masters_theses/343"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Krylov Subspace Spectral (KSS) Methods have been demonstrated to be highly scalable time-stepping methods for stiff nonlinear PDEs. However, ensuring this scalability requires analytic computation of frequency-dependent quadrature nodes from the coefficients of the spatial differential operator. This thesis describes how this process can be automated for various classes of differential operators to facilitate public-domain software implementation.
"]},{"key":"dc:title","label":"Title","values":["Automatic Construction of Scalable Time-Stepping Methods for Stiff PDES"]}]}],"canonical_facts":{"dc:contributor":["James Lambers","Haiyan Tian","Huiqing Zhu"],"dc:creator":["Montiforte, Vivian Ashley"],"dc:date.available":["2018-03-28T07:00:00Z"],"dc:description.abstract":["Krylov Subspace Spectral (KSS) Methods have been demonstrated to be highly scalable time-stepping methods for stiff nonlinear PDEs. However, ensuring this scalability requires analytic computation of frequency-dependent quadrature nodes from the coefficients of the spatial differential operator. This thesis describes how this process can be automated for various classes of differential operators to facilitate public-domain software implementation.
"],"dc:identifier":["https://aquila.usm.edu/masters_theses/343"],"dc:subject":["Partial Differential Equations","Krylov Subspace Spectral Methods","Frequency-Dependent Nodes","Stiff","Nonlinear","Quadrature Nodes","Numerical Analysis and Computation"],"dc:title":["Automatic Construction of Scalable Time-Stepping Methods for Stiff PDES"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Masters Thesis"],"thesis:degree_name":["Master of Science (MS)"]},"updated_at":"2026-07-24T05:44:50Z"}