UMD Theses and Dissertations

Permanent URI for this collectionhttp://hdl.handle.net/1903/3

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 given thesis/dissertation in DRUM.

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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.
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    ELECTROMAGNETIC MODELING WITH A NEW 3D ALTERNATING-DIRECTION-IMPLICIT (ADI) MAXWELL EQUATION SOLVER
    (2004-08-10) Shao, Xi; Goldsman, Neil; Electrical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
    We introduce a time-domain method to simulate the digital signal propagation along on-chip interconnects, aperture radiation, and indoor-communication by solving the Maxwell equation with the Alternating-Direction-Implicit (ADI) method. With this method, we are able to resolve the large scale (i.e. electromagnetic wave propagation) and fine scale (i.e. metal skin depth, substrate current, coating material) structure in the same simulation, and the simulation time step is not limited by the Courant condition. The simulations allow us to calculate in detail parasitic current flow inside the substrate; propagation losses, skin-depth and dispersion of digital signals on non-ideal interconnects; detailed surface current and standing wave pattern in aperture radiation problem; signal power map and propagation delay in complicated in-door communication scenarios