Optimization of Plane Wave Directions in Plane Wave Discontinuous Galerkin Methods for the Helmholtz Equation

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dc.contributor.advisorHoppe, Ronald W.
dc.contributor.committeeMemberKuznetsov, Yuri
dc.contributor.committeeMemberHeinkenschloss, Matthias
dc.contributor.committeeMemberQiu, Jingmei
dc.creatorAgrawal, Akshay 1990-
dc.date.accessioned2021-07-15T04:12:40Z
dc.date.available2021-07-15T04:12:40Z
dc.date.createdMay 2016
dc.date.issued2016-05
dc.date.submittedMay 2016
dc.date.updated2021-07-15T04:12:41Z
dc.description.abstractRecently, the use of special local test functions other than polynomials in Discontinuous Galerkin (DG) approaches has attracted a lot of attention and became known as DG-Trefftz methods. In particular, for the 2D Helmholtz equation, plane waves have been used to derive an Interior Penalty (IP) type Plane Wave DG (PWDG) method and to provide an a priori error analysis of its p-version with respect to equidistributed plane wave directions. However, the dependence on the distribution of the plane wave directions has not been studied. In this thesis, we study the dependence by formulating the choice of the directions as an optimal control problem with a tracking type objective functional and the variational formulation of the PWDG method as a constraint. The necessary optimality conditions are derived and numerically solved by a projected gradient method. Numerical results are given which illustrate the benefits of the approach.
dc.description.departmentMathematics, Department of
dc.format.digitalOriginborn digital
dc.format.mimetypeapplication/pdf
dc.identifier.urihttps://hdl.handle.net/10657/7884
dc.language.isoeng
dc.rightsThe author of this work is the copyright owner. UH Libraries and the Texas Digital Library have their permission to store and provide access to this work. Further transmission, reproduction, or presentation of this work is prohibited except with permission of the author(s).
dc.subjectPWDG
dc.subjectPlane Wave Discontinuous Galerkin
dc.subjectHelmholtz
dc.subjectOptimization of Plane Wave Directions
dc.titleOptimization of Plane Wave Directions in Plane Wave Discontinuous Galerkin Methods for the Helmholtz Equation
dc.type.dcmiText
dc.type.genreThesis
thesis.degree.collegeCollege of Natural Sciences and Mathematics
thesis.degree.departmentMathematics, Department of
thesis.degree.disciplineMathematics
thesis.degree.grantorUniversity of Houston
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy

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