Date of Award
2011
Document Type
Thesis
Degree Name
Bachelors
Department
Natural Sciences
First Advisor
Ruppeiner, George
Keywords
Wavelet, Simulation, Maxwell, Krylov, Lanczos
Area of Concentration
Physics
Abstract
Techniques which improve the efficiency of numerical simulations used to evaluate partial differential equations are especially important in creating realistic models of physical phenomena. In this thesis I examine the implementation of a wavelet basis in simulating the propagation of electromagnetic waves through a dielectric medium. I review the properties of a wavelet basis and its advantages over the traditional Fourier basis. I then explain the general method of projecting functions and operators into a given wavelet basis, and follow the construction of a Hamiltonian operator which defines the behavior of electromagnetic fields in a given system. This material supports the example propagation of an electromagnetic wave through a dielectric material using a variation of an iterative computational method known as the Lanczos Algorithm.
Recommended Citation
Keys, Kerry, "Simulating Electromagnetic Wave Propagation using Multi-Scale Time-Domain Methods and Iterative Algorithms" (2011). Theses & ETDs. 4390.
https://digitalcommons.ncf.edu/theses_etds/4390