Numerical Boundary Conditions for the Fourth -Order Accurate Finite -Difference Time -Domain Solution of Maxwell's Equations
Hwang, Kyu-Pyung
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https://hdl.handle.net/2142/80793
Description
Title
Numerical Boundary Conditions for the Fourth -Order Accurate Finite -Difference Time -Domain Solution of Maxwell's Equations
Author(s)
Hwang, Kyu-Pyung
Issue Date
2002
Doctoral Committee Chair(s)
Cangellaris, Andreas C.
Department of Study
Electrical Engineering
Discipline
Electrical Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Electronics and Electrical
Language
eng
Abstract
Development of accurate numerical boundary conditions for metallic boundaries and dielectric interfaces is the key to the proper implementation of high-order finite-difference time-domain (FDTD) methods for Maxwell's equations. In this dissertation, a new set of numerical boundary conditions at perfectly conducting walls and dielectric interfaces is proposed for Fang's fourth-order FDTD schemes. The eigenvalue analysis of the fully discrete systems shows the influence of boundary conditions on the original fourth-order schemes. Numerical experiments using two- and three-dimensional rectangular cavities verify that the proposed numerical boundary conditions preserve the fourth-order accuracy of Fang's schemes. Simulations of electromagnetic wave propagations through rectangular waveguides demonstrate that the enhanced high-order schemes produce much smaller phase errors compared to the second-order FDTD methods. As a consequence, the enhanced fourth-order Fang's schemes reduce the computational cost by more than two orders of magnitude in practical time domain electromagnetic simulations of three-dimensional structures composed of conductors and dielectrics. Applications in nonradiative dielectric (NRD) waveguide structures illustrate the promising capabilities of the enhanced fourth-order FDTD schemes for time domain simulations of electrically long microwave/millimeter wave and optoelectronic devices.
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