{"id":{"repo_id":"rice","oai_identifier":"oai:repository.rice.edu:1911/103704"},"canonical_url":"https://search.dev.ndltd.org/etd/rice/oai:repository.rice.edu:1911/103704","repository":{"repo_id":"rice","name":"Rice University","base_url":"https://repository.rice.edu/server/oai/request"},"display":{"title":"A survey of discontinuous Galerkin methods for solving the time domain Maxwell's equations","abstract":"The discontinuous Galerkin (DG) method with different numerical fluxes is applied to the square wave guide problem to avoid spurious modes that arise from the application of standard finite element methods. These numerical fluxes are the central, upwind and Lax-Friedrichs found in the literature. A new scheme, called penalty DG, is presented. Each scheme is tested with and without a locally divergence-free basis for the magnetic field. The spectral properties of the DG spatial discretization matrix for each flux are surmised by considering three different meshes and example eigenvalue plots. The convergence rate of the first ten eigenvalues is observed for h - and p -refinements. The central flux scheme is determined to be a poor choice for problems involving Maxwell's equations. It is proved that the kernel is empty for the DG spatial discretization matrix corresponding to the Lax-Friedrichs divergence-free scheme.","abstract_html":"The discontinuous Galerkin (DG) method with different numerical fluxes is applied to the square wave guide problem to avoid spurious modes that arise from the application of standard finite element methods. These numerical fluxes are the central, upwind and Lax-Friedrichs found in the literature. A new scheme, called penalty DG, is presented. Each scheme is tested with and without a locally divergence-free basis for the magnetic field. The spectral properties of the DG spatial discretization matrix for each flux are surmised by considering three different meshes and example eigenvalue plots. The convergence rate of the first ten eigenvalues is observed for h - and p -refinements. The central flux scheme is determined to be a poor choice for problems involving Maxwell's equations. It is proved that the kernel is empty for the DG spatial discretization matrix corresponding to the Lax-Friedrichs divergence-free scheme.","abstract_has_math":false,"creators":["Binford, Tommy L., Jr."],"institution":"Rice University","degree_name":"Master of Arts","degree_level":"Masters","degree_discipline":"Engineering","degree_department":null,"school":null,"contributors":[],"advisors":["Warburton, Tim"],"committee_chairs":[],"committee_members":[],"year":2006,"date_issued":"2006","date_published":"2006","updated_at":"2026-07-24T04:10:22Z","subjects":["Mathematics","Pure sciences"],"languages":["eng"],"rights":["Copyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/1911/103704","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Warburton, Tim"]},{"key":"dc:creator","label":"Author","values":["Binford, Tommy L., Jr."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2018-12-03T18:32:51Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2018-12-03T18:32:51Z"]},{"key":"dc:date.issued","label":"Date","values":["2006"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Arts"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Rice University"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics","Pure sciences"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright is held by the author, unless otherwise indicated. 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The spectral properties of the DG spatial discretization matrix for each flux are surmised by considering three different meshes and example eigenvalue plots. The convergence rate of the first ten eigenvalues is observed for h - and p -refinements. The central flux scheme is determined to be a poor choice for problems involving Maxwell's equations. It is proved that the kernel is empty for the DG spatial discretization matrix corresponding to the Lax-Friedrichs divergence-free scheme."]},{"key":"dc:title","label":"Title","values":["A survey of discontinuous Galerkin methods for solving the time domain Maxwell's equations"]}]}],"canonical_facts":{"dc:contributor.advisor":["Warburton, Tim"],"dc:creator":["Binford, Tommy L., Jr."],"dc:date.accessioned":["2018-12-03T18:32:51Z"],"dc:date.available":["2018-12-03T18:32:51Z"],"dc:date.issued":["2006"],"dc:description.abstract":["The discontinuous Galerkin (DG) method with different numerical fluxes is applied to the square wave guide problem to avoid spurious modes that arise from the application of standard finite element methods. These numerical fluxes are the central, upwind and Lax-Friedrichs found in the literature. A new scheme, called penalty DG, is presented. Each scheme is tested with and without a locally divergence-free basis for the magnetic field. The spectral properties of the DG spatial discretization matrix for each flux are surmised by considering three different meshes and example eigenvalue plots. The convergence rate of the first ten eigenvalues is observed for h - and p -refinements. The central flux scheme is determined to be a poor choice for problems involving Maxwell's equations. It is proved that the kernel is empty for the DG spatial discretization matrix corresponding to the Lax-Friedrichs divergence-free scheme."],"dc:identifier.uri":["https://hdl.handle.net/1911/103704"],"dc:language.iso":["eng"],"dc:rights":["Copyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder."],"dc:subject":["Mathematics","Pure sciences"],"dc:title":["A survey of discontinuous Galerkin methods for solving the time domain Maxwell's equations"],"dc:type":["Thesis"],"thesis:degree_discipline":["Engineering"],"thesis:degree_level":["Masters"],"thesis:degree_name":["Master of Arts"],"thesis:institution_name":["Rice University"]},"updated_at":"2026-07-24T04:10:22Z"}