Newman, James C., III
Sreenivas, Kidambi; Webster, Robert
College of Engineering and Computer Science
University of Tennessee at Chattanooga
Place of Publication
A well known nodal discontinuous Galerkin finite element method has been extended for higher order temporal accuracy using several schemes. While common in computational fluid dynamics, less research has been conducted with these methods for computational electromagnetics. A stabilized finite element method utilizing the Streamline/Upwind Petrov-Galerkin approach is explored. This work examines several higher order temporally accurate schemes to test their viability for the Maxwell equations. Only the one-dimensional case is considered. The temporal integration methods utilized are the first two backward differentiation formula (BDF), second through fourth order modified extended backward differentiation formula (MEBDF), and second through fourth order explicit first stage singly diagonally implicit Runge- Kutta (ESDIRK) schemes. A problem using a simple Gaussian pulse to which the analytical solution is known is used to verify the desired order of accuracy. Fifth-order spatial integration using Legendre polynomials, so spatial errors will be much smaller than temporal errors.
M. S.; A thesis submitted to the faculty of the University of Tennessee at Chattanooga in partial fulfillment of the requirements of the degree of Master of Science.
Maxwell equations; Finite element method; Numerical analysis
iv, 40 leaves
Cox, Jeffrey D., "Error analysis of higher order time-domain finite element methods for the one-dimensional Maxwell's equations" (2016). Masters Theses and Doctoral Dissertations.