Theses and Dissertations from UMD

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New submissions to the thesis/dissertation collections are added automatically as they are received from the Graduate School. Currently, the Graduate School deposits all theses and dissertations from a given semester after the official graduation date. This means that there may be up to a 4 month delay in the appearance of a give thesis/dissertation in DRUM

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Author: search.filters.author.Haeri Kermani, MohammadSubject: search.filters.subject.Physics, Radiation

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    The ADI-FDTD Method for High Accuracy Electrophysics Applications
    (2006-11-24) Haeri Kermani, Mohammad; Ramahi, Omar M; Electrical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
    The Finite-Difference Time-Domain (FDTD) is a dependable method to simulate a wide range of problems from acoustics, to electromagnetics, and to photonics, amongst others. The execution time of an FDTD simulation is inversely proportional to the time-step size. Since the FDTD method is explicit, its time-step size is limited by the well-known Courant-Friedrich-Levy (CFL) stability limit. The CFL stability limit can render the simulation inefficient for very fine structures. The Alternating Direction Implicit FDTD (ADI-FDTD) method has been introduced as an unconditionally stable implicit method. Numerous works have shown that the ADI-FDTD method is stable even when the CFL stability limit is exceeded. Therefore, the ADI-FDTD method can be considered an efficient method for special classes of problems with very fine structures or high gradient fields. Whenever the ADI-FDTD method is used to simulate open-region radiation or scattering problems, the implementation of a mesh-truncation scheme or absorbing boundary condition becomes an integral part of the simulation. These truncation techniques represent, in essence, differential operators that are discretized using a distinct differencing scheme which can potentially affect the stability of the scheme used for the interior region. In this work, we show that the ADI-FDTD method can be rendered unstable when higher-order mesh truncation techniques such as Higdon's Absorbing Boundary Condition (ABC) or Complementary Derivatives Method (COM) are used. When having large field gradients within a limited volume, a non-uniform grid can reduce the computational domain and, therefore, it decreases the computational cost of the FDTD method. However, for high-accuracy problems, different grid sizes increase the truncation error at the boundary of domains having different grid sizes. To address this problem, we introduce the Complementary Derivatives Method (CDM), a second-order accurate interpolation scheme. The CDM theory is discussed and applied to numerical examples employing the FDTD and ADI-FDTD methods.