Physical Sciences and Mathematics Commons^™

Accuracy Of Wave Speeds Computed From The Dpg And Hdg Methods For Electromagnetic And Acoustic Waves, Nicole Michelle Olivares

Dissertations and Theses

We study two finite element methods for solving time-harmonic electromagnetic and acoustic problems: the discontinuous Petrov-Galerkin (DPG) method and the hybrid discontinuous Galerkin (HDG) method.

The DPG method for the Helmholtz equation is studied using a test space normed by a modified graph norm. The modification scales one of the terms in the graph norm by an arbitrary positive scaling parameter. We find that, as the parameter approaches zero, better results are obtained, under some circumstances. A dispersion analysis on the multiple interacting stencils that form the DPG method shows that the discrete wavenumbers of the method are complex, explaining …