Theses and Dissertations from UMD
Permanent URI for this communityhttp://hdl.handle.net/1903/2
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
More information is available at Theses and Dissertations at University of Maryland Libraries.
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Item Surface Tension Free Boundary Problems: Formulation, Optimal Control and Numerics(2013) Carlos, Patrick Sodré; Nochetto, Ricardo H; Applied Mathematics and Scientific Computation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)The goal of this work is to treat the formulation, optimal control and numerical analysis of free boundary problems with surface tension effects. From a formulation point of view, we introduce a (dimension independent) abstract framework which captures the essential behavior of free boundary problems with surface tension effects. We then apply this framework to two scenarios. The first is where the underlying bulk system is governed by the Laplacian with non-homogeneous essential boundary condition, and the second is modeled by the Stokes equations with slip and no-slip boundary conditions. We do not impose a fixed contact angle between the free surface and any fixed part of the boundary. Although the formulation and numerics involving the Laplacian was available in the literature, the Stokes free boundary problem in Rn is novel. To obtain this last result we also had to prove the existence and uniqueness in Sobolev spaces for the pure slip problem for domains of type C1,\epsilon. This is a significant improvement over the current best result involving C1,1 domains. The results from the abstract formulation also carry over to the optimal control aspect. We obtain differentiability conditions which guarantee existence and (local) uniqueness of a minimizer to well-behaved cost functions. In the Laplacian case we go beyond the theoretical results and give precise second-order sufficient conditions for the (local) uniqueness of a minimizer for cost functions of the tracking type. The contribution in this area is significant in the sense that sufficient conditions are usually only assumed to be true, while we actually show that it indeed holds for our specific problem. The last piece of this work is the numerical treatment of the free boundary optimal control problem based on the Laplace equation. We are able to prove optimal convergence results using the finite element method. Moreover, we construct experiments to study the behavior of various metrics associated with the optimization problem.Item MINIMIZING THE ACOUSTIC COUPLING OF FLUID LOADED PLATES USING TOPOLOGY OPTIMIZATION(2009) Almitani, Khalid Haza; Baz, Amr M; Mechanical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Optimization of the topology of a plate coupled with an acoustic cavity is investigated in an attempt to minimize the fluid-structure interactions at different structural frequencies. A mathematical model is developed to simulate such fluid-structure interactions based on the theory of finite elements. The model is integrated with a topology optimization approach which utilizes the Moving Asymptotes Method. The obtained results demonstrate the effectiveness of the proposed approach in simultaneously attenuating the structural vibration and the sound pressure inside the acoustic domain at several structural frequencies by proper redistribution of the plate material. Prototypes of plates with optimized topologies are manufactured at tested to validate the developed theoretical model. The performance characteristics of plates optimized for different frequency ranges are determined and compared with the theoretical predictions of the developed mathematical model. A close agreement is observed between theory and experiments. The presented topology optimization approach can be an invaluable tool in the design of a wide variety of critical structures which must operate quietly when subjected to fluid loading.Item The Equilibrium Geometry Theory for Bone Fracture Healing(2008-04-29) Yew, Alvin Garwai; Hsieh, Adam H; Mechanical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Models describing the impact of mechanical stimuli on bone fracture healing can be used to design improved fixation devices and optimize clinical treatment. Existing models however, are limited because they fail to consider the changing fracture callus morphology and probabilistic behavior of biological systems. To resolve these issues, the Equilibrium Geometry Theory (EGT) was conceptualized and when coupled with a mechanoregulation algorithm for differentiation, it provides a way to simulate cell processes at the fracture site. A three-dimensional, anisotropic random walk model with an adaptive finite element domain was developed for studying the entire course of fracture healing based on EGT fundamentals. Although a coarse cell dispersal lattice and finite element mesh were used for analyses, the computational platform provides exceptional latitude for visualizing the growth and remodeling of tissue. Preliminary parameter and sensitivity studies show that simulations can be fine-tuned for a wide variety of clinical and research applications.Item A Class of Stable, Efficient Navier-Stokes Solvers(2006-05-10) Liu, Jie; Liu, Jian-Guo; Mathematics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)We study a class of numerical schemes for Navier-Stokes equations (NSE) or Stokes equations (SE) for incompressible fluids in a bounded domain with given boundary value of velocity. The incompressibility constraint and non-slip boundary condition have made this problem very challenging. Their treatment by finite element method leads to the well-known inf-sup compatibility condition. Their treatment by finite difference method leads to the very popular projection method, which suffers from low resolution near the boundary. In [LLP], the authors propose an unconstrained formulation of NSE or SE, which replace the divergence-free constraint by a pressure equation with an appropriate boundary condition. All of the schemes in this thesis are based on this new formulation. In contrast to traditional methods, these schemes do not need to fulfill the traditional inf-sup compatibility condition between velocity space and pressure space. More importantly, they can achieve high-order accuracy very easily and are very efficient due to the decoupling of the update of velocity and pressure. They can even be proved to be unconditionally stable. There are two ways to analyze the schemes that we propose. The first is based upon the sharp estimate of the pressure in [LLP]. The second relies on a nice identity. Using the pressure estimates, we propose and study a $C^1$ finite element (FE) scheme for the steady-state SE as well as for the time-dependent NSE. For steady-state SE, we can either use an iterative scheme or solve velocity and pressure together. Using the nice identity, we prove that the semi-discrete iterative scheme for the steady-state SE converges ("semi-discrete" means that the spatial variable are kept continuous). This identity will also be crucial for our proofs of the stability and error estimates of the time-dependent $C^0$ FE schemes. Associated numerical computations demonstrate stability and accuracy of these schemes. We also present the numerical results of yet another $C^0$ FE scheme ([JL]) for the time-dependent NSE for which the theory of the fully discrete case is yet lacking.Item Microbridge Formation for Low Resistance Interline Connection Using Pulsed Laser Techniques(2005-12-13) Chung, Kuan-Jung; Bernstein, Joseph B; Mechanical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)MakeLink® technology has been applied in many semiconductor devices to achieve high performance. Sometimes one-type-link design doesn't make desirous links for all IC manufacturing processes. In this work, four new structures, called microbridge, were designed to form all types of link. Laser processing experiments were performed to verify the designs. The results show that two-lower-level-metal-line design has higher performance (low link resistance), higher productivity (broad energy window), and higher yield than the three-lower-level-metal-line design. Therefore, it can be considered as the optimal design from the processing point of view. Two-lower-level-metal-line with lateral gap structure provides better scalability and it can be used in next generation ICs. If high-speed is the primary concern, an advanced-lateral structure is best, corresponding to its much lower resistance. The reliability tests indicate that the median-times-to-failure of all test structures are greater than nine years in operating condition, presenting reasonable lifetimes for integrated circuits used in the market. A two-dimensional finite element plane models for microbridge formation is developed. Results are compared to the experiments with process windows to present their consistence. The model allowed for using different geometric parameters and metal-dielectric combinations optimizing the design. An optimal design diagram for the Al/SiO2 system is created to provide the designer with criteria to avoid the failure of structure. Trade-off requirements, such as process window and structure size, are also provided. Guidelines are obtained for the Cu/Low-K dielectric system.