Award Date
12-15-2019
Degree Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Mathematical Sciences
First Committee Member
Jichun Li
Second Committee Member
Hongtao Yang
Third Committee Member
Monika Neda
Fourth Committee Member
Pengtao Sun
Fifth Committee Member
Yi-Tung Chen
Number of Pages
103
Abstract
This dissertation investigates two different mathematical models based on the time-domain Maxwell's equations: the Drude model for metamaterials and an equivalent Berenger's perfectly matched layer (PML) model. We develop both an explicit high order finite difference scheme and a compact implicit scheme to solve both models. We develop a systematic technique to prove stability and error estimate for both schemes. Extensive numerical results supporting our analysis are presented. To our best knowledge, our convergence theory and stability results are novel and provide the first error estimate for the high-order finite difference methods for Maxwell's equations.
Keywords
finite difference method; fourth order method; Maxwell's equations; metamaterial; Perfectly Matched Layer
Disciplines
Mathematics
File Format
File Size
3.1 MB
Degree Grantor
University of Nevada, Las Vegas
Language
English
Repository Citation
Chen, Min, "Arbitrary High Order Finite Difference Methods with Applications to Wave Propagation Modeled by Maxwell's Equations" (2019). UNLV Theses, Dissertations, Professional Papers, and Capstones. 3790.
http://dx.doi.org/10.34917/18608611
Rights
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