Dissertation/Thesis Abstract

An Improved 3D Complex-envelope Four-stage ADI-FDTD Using the Fundamental Scheme
by Liu, Qi, Ph.D., The University of Mississippi, 2019, 110; 13879181
Abstract (Summary)

The exponential operator splitting approach can be used to transform the two sub-steps based complex-envelope (CE) alternating-direction-implicit (ADI) FDTD algorithm into a four sub-steps based CE four-stages (4S) ADI-FDTD. In two dimensions the CE-4S-ADI-FDTD is more accurate than the CE-ADI-FDTD, but requires double the computation time due to the fixed time consumption in each sub-step.

Here, the existing 2D CE-4S-ADI-FDTD scheme is extended to three spatial dimensions. By incorporating the fundamental scheme into the 3D CE-4S-ADI-FDTD, the proposed 3D-4S-FADI-FDTD method is the result. In the fundamental scheme six auxiliary variables are defined, by which the number of terms and operations in the implicit equations is reduced. The computation time in each sub-step is reduced, and consequently the total computational time. The near perfectly matched layers (NPML) and the total field/scattered field schemes are incorporated into the 3D CE-4S-FADI-FDTD for modeling the problem with a boundless domain, and with a plane wave source respectively.

Three corresponding reference methods are developed. The CE explicit FDTD method is used to solve the problem with a point source and perfect electric conductor (PEC) boundaries. The problem with a point source and absorbing boundary conditions (ABC) is solved by the 3D free-space Green's function in the frequency domain, and then transformed to the time domain using the inverse fast Fourier transform (IFFT). For the problem with a plane wave and ABC, the frequency-domain solution is obtained using the volume integral equations and method of moments (VIE-MOM), and is then transformed into the time-domain solution using the IFFT. Comparison of the numerical results demonstrates the accuracy and computational effectiveness of the 3D CE-4S-FADI-FDTD algorithm.

Indexing (document details)
Advisor: Goggans, Paul M.
Commitee: Gordon, Richard, Hutchcraft, Elliott, Rodriguez, Vince, Diaz, Erwin M.
School: The University of Mississippi
Department: Electrical Engineering
School Location: United States -- Mississippi
Source: DAI-B 81/2(E), Dissertation Abstracts International
Subjects: Electromagnetics
Keywords: Spatial dimentions, Near perfectly matched layers, Perfect electric conductor
Publication Number: 13879181
ISBN: 9781085594110
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