A survey of discontinuous Galerkin methods for solving the time domain Maxwell's equations

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dc.contributor.advisorWarburton, Tim
dc.creatorBinford, Tommy L., Jr.
dc.date.accessioned2018-12-03T18:32:51Z
dc.date.available2018-12-03T18:32:51Z
dc.date.issued2006
dc.description.abstractThe 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.format.extent87 pp
dc.identifier.callnoTHESIS MATH.SCI. 2007 BINFORD
dc.identifier.citationBinford, Tommy L., Jr.. "A survey of discontinuous Galerkin methods for solving the time domain Maxwell's equations." (2006) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/103704">https://hdl.handle.net/1911/103704</a>.
dc.identifier.digital305274055
dc.identifier.urihttps://hdl.handle.net/1911/103704
dc.language.isoeng
dc.rightsCopyright 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.subjectMathematics
dc.subjectPure sciences
dc.titleA survey of discontinuous Galerkin methods for solving the time domain Maxwell's equations
dc.typeThesis
dc.type.materialText
thesis.degree.departmentMathematical Sciences
thesis.degree.disciplineEngineering
thesis.degree.grantorRice University
thesis.degree.levelMasters
thesis.degree.nameMaster of Arts
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