{"id":{"repo_id":"unm","oai_identifier":"oai:digitalrepository.unm.edu:math_etds-1003"},"canonical_url":"https://search.dev.ndltd.org/etd/unm/oai:digitalrepository.unm.edu:math_etds-1003","repository":{"repo_id":"unm","name":"University of New Mexico","base_url":"https://digitalrepository.unm.edu/do/oai/"},"display":{"title":"Studies of Coherent Synchrotron Radiation with the Discontinuous Galerkin Method","abstract":"In this thesis, we present methods for integrating Maxwell's equations in Frenet-Serret coordinates in several settings using discontinuous Galerkin (DG) finite element method codes in 1D, 2D, and 3D. We apply these routines to the study of coherent synchrotron radiation, an important topic in accelerator physics. We build upon the published computational work of T. Agoh and D. Zhou in solving Maxwell's equations in the frequency-domain using a paraxial approximation which reduces Maxwell's equations to a Schrödinger-like system. We also evolve Maxwell's equations in the time-domain using a Fourier series decomposition with 2D DG motivated by an experiment performed at the Canadian Light Source. A comparison between theory and experiment has been published (Phys. Rev. Lett. 114, 204801 (2015)). Lastly, we devise a novel approach to integrating Maxwell's equations with 3D DG using a Galilean transformation and demonstrate proof-of-concept. In the above studies, we examine the accuracy, efficiency, and convergence of DG.","abstract_html":"In this thesis, we present methods for integrating Maxwell's equations in Frenet-Serret coordinates in several settings using discontinuous Galerkin (DG) finite element method codes in 1D, 2D, and 3D. We apply these routines to the study of coherent synchrotron radiation, an important topic in accelerator physics. We build upon the published computational work of T. Agoh and D. Zhou in solving Maxwell's equations in the frequency-domain using a paraxial approximation which reduces Maxwell's equations to a Schrödinger-like system. We also evolve Maxwell's equations in the time-domain using a Fourier series decomposition with 2D DG motivated by an experiment performed at the Canadian Light Source. A comparison between theory and experiment has been published (Phys. Rev. Lett. 114, 204801 (2015)). Lastly, we devise a novel approach to integrating Maxwell's equations with 3D DG using a Galilean transformation and demonstrate proof-of-concept. In the above studies, we examine the accuracy, efficiency, and convergence of DG.","abstract_has_math":false,"creators":["Bizzozero, David"],"institution":null,"degree_name":"Mathematics","degree_level":"Doctoral","degree_discipline":"Mathematics & Statistics","degree_department":null,"school":null,"contributors":["Lau, Stephen","Stephen Lau","James Auby Ellison","Daniel Appelö","Robert Warnock"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2016,"date_issued":"2016-02-01T08:00:00Z","date_published":"2016-02-01T08:00:00Z","updated_at":"2026-07-24T05:27:37Z","subjects":["Maxwell","discontinuous Galerkin","coherent synchrotron radiation","electromagnetic"],"languages":["English"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalrepository.unm.edu/math_etds/4"],"render_values":[{"text":"https://digitalrepository.unm.edu/math_etds/4","href":"https://digitalrepository.unm.edu/math_etds/4","code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/1928/31705","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Lau, Stephen","Stephen Lau","James Auby Ellison","Daniel Appelö","Robert Warnock"]},{"key":"dc:creator","label":"Author","values":["Bizzozero, David"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics & Statistics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Doctoral","Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Mathematics"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Maxwell","discontinuous Galerkin","coherent synchrotron radiation","electromagnetic"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/1928/31705","https://digitalrepository.unm.edu/math_etds/4"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this thesis, we present methods for integrating Maxwell's equations in Frenet-Serret coordinates in several settings using discontinuous Galerkin (DG) finite element method codes in 1D, 2D, and 3D. We apply these routines to the study of coherent synchrotron radiation, an important topic in accelerator physics. We build upon the published computational work of T. Agoh and D. Zhou in solving Maxwell's equations in the frequency-domain using a paraxial approximation which reduces Maxwell's equations to a Schrödinger-like system. We also evolve Maxwell's equations in the time-domain using a Fourier series decomposition with 2D DG motivated by an experiment performed at the Canadian Light Source. A comparison between theory and experiment has been published (Phys. Rev. Lett. 114, 204801 (2015)). Lastly, we devise a novel approach to integrating Maxwell's equations with 3D DG using a Galilean transformation and demonstrate proof-of-concept. In the above studies, we examine the accuracy, efficiency, and convergence of DG."]},{"key":"dc:title","label":"Title","values":["Studies of Coherent Synchrotron Radiation with the Discontinuous Galerkin Method"]}]}],"canonical_facts":{"dc:contributor":["Lau, Stephen","Stephen Lau","James Auby Ellison","Daniel Appelö","Robert Warnock"],"dc:creator":["Bizzozero, David"],"dc:description.abstract":["In this thesis, we present methods for integrating Maxwell's equations in Frenet-Serret coordinates in several settings using discontinuous Galerkin (DG) finite element method codes in 1D, 2D, and 3D. We apply these routines to the study of coherent synchrotron radiation, an important topic in accelerator physics. We build upon the published computational work of T. Agoh and D. Zhou in solving Maxwell's equations in the frequency-domain using a paraxial approximation which reduces Maxwell's equations to a Schrödinger-like system. We also evolve Maxwell's equations in the time-domain using a Fourier series decomposition with 2D DG motivated by an experiment performed at the Canadian Light Source. A comparison between theory and experiment has been published (Phys. Rev. Lett. 114, 204801 (2015)). Lastly, we devise a novel approach to integrating Maxwell's equations with 3D DG using a Galilean transformation and demonstrate proof-of-concept. In the above studies, we examine the accuracy, efficiency, and convergence of DG."],"dc:identifier":["http://hdl.handle.net/1928/31705","https://digitalrepository.unm.edu/math_etds/4"],"dc:language":["English"],"dc:subject":["Maxwell","discontinuous Galerkin","coherent synchrotron radiation","electromagnetic"],"dc:title":["Studies of Coherent Synchrotron Radiation with the Discontinuous Galerkin Method"],"thesis:degree_discipline":["Mathematics & Statistics"],"thesis:degree_level":["Doctoral","Dissertation"],"thesis:degree_name":["Mathematics"]},"updated_at":"2026-07-24T05:27:37Z"}