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

Recently, 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.

Name thesis:degree_name

Doctor of Philosophy

Level thesis:degree_level

Doctoral

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Houston

Year dc:date.issued

2016

Author dc:creator

• Agrawal, Akshay 1990-

Advisor dc:contributor.advisor

• Hoppe, Ronald W.

Committee members dc:contributor.committeemember

• Kuznetsov, Yuri
• Heinkenschloss, Matthias
• Qiu, Jingmei

• PWDG
• Plane Wave Discontinuous Galerkin
• Helmholtz
• Optimization of Plane Wave Directions

Statement dc:rights

• The 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).

Language dc:language.iso

eng

Handle dc:identifier.uri

https://hdl.handle.net/10657/7884

OAI identifier oai:identifier

oai:uh-ir.tdl.org:10657/7884