Approved for public release; distribution is unlimited / This thesis investigates the viability of a new method for numerically computing the input impedance and the currents on simple antenna structures. This technique considers the antenna between two ground planes and uses multiregion cylindrical harmonic expansions with tangential field continuity to obtain the surface currents and input impedance. The computed results are compared to the results obtained from the Numerical Electromagnetics Code for various physical parameters to assess computational accuracy. / http://archive.org/details/computationofmon00hurl / Lieutenant, United States Navy

This thesis focuses on nonlinear robust process control synthesis and analysis. The theoretical fundamental is the L2 finite gain theory. The aim of this research is to gain better understanding of this theory and develop new process control synthesis and analysis methods for nonlinear processes with model uncertainties and unmeasured disturbances.The current nonlinear process control methods are examined in this thesis. The research scopes of this study are described as follows: 1/. To characterize the most common process control problems such as zero-offset requirement, presentation of model uncertainties and unknown disturbance in the L2 finite gain theory framework and solve the basic theoretical issues concerned in controller design. 2/. To solve numerical computation problems arising in the nonlinear controller. 3/. To investigate the relationship between robustness requirement and performance requirement for nonlinear systems in the L2 finite gain theory framework. 4/. To consider the common phenomenon such as time-delay in the new developed methods. 5/. To investigate the advantages of the controller based on the L2 finite gain theory over the current nonlinear control methods. A series of new systematic robust process control synthesis approaches are the main contributions of this study. Simulations show the potential of these newly developed methods. / Doctor of Philosophy (PhD)

<p> This thesis details the application of computational methods to the problem of determining custom data representations when building hardware accelerators for numerical computations. A majority of scientific applications which require hardware acceleration are implemented in IEEE-754 double precision. However, in many cases the error tolerance requirements of the application are much less than the accuracy which IEEE-754 double precision provides. By leveraging custom data representations, a more resource efficient hardware implementation arises thereby enabling greater parallelism and thus higher performance of the accelerator. </p> <p> The existing custom representation methods are unable to guarantee robust representations while at the same time adequately supporting ill-conditioned operators. Support for both of these scenarios is necessary for accelerating scientific calculations. To address this, we propose the use of a computational method based on Satisfiability-Modulo Theory (SMT). By capturing a calculation as a set of constraints, an SMT instance can be formulated which provides meaningful bounds even in the presence of ill-conditioned operators. At the same time, the analytical nature of SMT satisfies the need for robustness. Utilizing block vector arithmetic, our SMT approach is extended to provide scalability to large instances involving vector calculus which arise in scientific calculations. Atop this foundation, a unified error model is proposed which deals simultaneously with absolute and relative error, thereby providing the means of supporting both fixed-point and custom floating-point data types. Iterative algorithm analysis is leveraged to derive constraints for the SMT method. The application of the method to several scientific algorithms is discussed by way of case studies. </p> / Thesis / Doctor of Philosophy (PhD)

Studying chaotic behavior in nonlinear systems requires numerous computations in order to simulate the behavior of such systems. The Standard Map Machine was designed and implemented as a special computer for performing these intensive computations with high-speed and high-precision. Its impressive performance is due to its simple architecture specialized to the numerical computations required of nonlinear systems. This report discusses the design and implementation of the Standard Map Machine and its use in the study of nonlinear mappings; in particular, the study of the standard map.

Este trabajo resuelve el problema de gran interés para la industria aeronáutica: el cálculo de la sección recta (RCS) de blancos radar complejos en tiempo real. Para ello basta una estación de trabajo con un acelerador grafico 3-d hardware en lugar de los super-ordenadores vectoriales que requieren los métodos clásicos. El método desarrollado totalmente original e innovador, consiste en procesar gráficamente una imagen del blanco presente en la pantalla de la estación grafica. Con ello se consigue que el tiempo de cpu sea independiente del tamaño y complejidad del blanco, con lo que su principal aplicación es la estimación rápida de la RCS de blancos radar complejos. Este método, al que hemos denominado "procesado grafico", implementa las aproximaciones asintóticas de alta frecuencia que permiten obtener las principales contribuciones a la RCS: óptica física, para la reflexión en superficies; condiciones de contorno de impedancia, para la reflexión en recubrimientos absorbentes radar (RAM), método de las corrientes equivalentes para la disposición en aristas y un método grafico de iluminación global (radiosity) para las reflexiones múltiples entre superficies. Los resultados de este trabajo hacen posible, por vez primera, el diseño interactivo de formas de baja RCS "stealth" con una estación de trabajo, por lo que se ha conseguido una herramienta software para la industria aeronáutica de gran eficiencia y potencialidad en sus aplicaciones.

This paper deals with the applications of symbolic computation of Mathematica 7.0 (Wolfram, 2008) in distribution theory. The purpose of this study is twofold. Firstly, we will implement some functions to extend Mathematica capabilities to handle symbolic computations of the characteristic function for linear combination of independent univariate random variables. These functions utilizes pattern-matching codes that enhance Mathematica's ability to simplify expressions involving the product and summation of algebraic terms. Secondly, characteristic function can be classified into commonly used distributions, including six discrete distributions and seven continuous distributions, via the pattern-matching feature of Mathematica. Finally, several examples will be presented. The examples include calculating limit of characteristic function of linear combinations of independent random variables, and applications of coded functions and illustrate the central limit theorem, the law of large numbers and properties of some distributions.

With the changing perceptions in coastal engineering in recent time, creation of bay beach for recreation by combining artificial headlands with nourishment has become one of the favorable options for mitigating erosion and shore protection in several foreign countries advanced in coastal engineering. To achieve this goal, hydraulic model tests and numerical simulations have been applied for the planning and design of stable bay beaches. While using the latter approach, numerical computation includes four major components, these being the waves, topography changes, flow field and sediment transport. This study utilizes the so-called Modified Hsu3D model developed by Serizawa et al. (1996) and Kumada et al. (2002) in Japan for the bathymetry within a static equilibrium bay beach defined by Hsu and Evans (1989). This model enables the direct calculation of bottom bathymetry within a static bay without using not only iterative numerical steps for wave transformation and current distribution, but also the continuity equation for total sediment transport. The results of this simplified approach can be used to estimate the distribution of erosion and accretion within a static bay, hence, suitable for pre-assessment of an artificial beach nourishment project. Prior to applying the Modified Hsu3D model to a bay beach undertaken in this study, sensitivity tests are performed on the setting of several key parameters associated with this model, such as limiting slope on land , limiting slope in the water , height of the berm , alignment angle at downdrift of the bay beach, and wave incident angle . The verification results are then adopted to compare with that reported in Serizawa et al. (2000), as well as to investigate the effects of each parameters on the accuracy of the modeling, in order to enhance the reliability of this model and the setting of the parameters. Finally, the Modified Hsu3D model is applied to simulate the changes in the shoreline and bathymetry for the Sizihwan Bay in Kaohsiung, under the action of normal incident waves during summer monsoon. This study also takes the advantage of the Modified Hsu3D model to explore the effect of oblique wave incidence on the deviation of downdrift control point of a static bay, in order to assist the prediction of downdrift control point for beach changes on an artificially nourished bay beach. The results reveal that the downdrift control point does not shift, under normal incident waves with different for the breaker. On the other hand, under oblique wave action within from the external boundary line of 20 m depth offshore of a bay beach comprising sediment 0.2~0.5 mm, the offset of point (i.e., and coordinates from the original origin) versus wave incident angle can be established. By establishing a regression equation between and versus , the result can be used to assist the determination, more precisely without guess work, on locating the downdrift control point of a bay beach, while working on the MEPBAY (Klein, et al., 2003) on computer screen to assess its stability.

Yes / For the abutment bed scour to reach its equilibrium state, a long flow time is needed. Hence, the employment of usual strategy of simulating such scouring event using the 3D numerical model is very time consuming and less practical. In order to develop an applicable model to consider temporally long abutment scouring process, this study modifies the common approach of 2D shallow water equations (SWEs) model to account for the sediment transport and turbulence, and provides a realistic approach to simulate the long scouring process to reach the full scour equilibrium. Due to the high demand of the 2D SWEs numerical scheme performance to simulate the abutment bed scouring, a recently proposed surface gradient upwind method (SGUM) was also used to improve the simulation of the numerical source terms. The abutment scour experiments of this study were conducted using the facility of Hydraulics Laboratory at Nanyang Technological University, Singapore to compare with the presented 2D SGUM-SWEs model. Fifteen experiments were conducted over a total period of 3059.7 hours experimental time (over 4.2 months). The comparison shows that the 2D SGUM-SWEs model gives good representation to the experimental results with the practical advantage.

We study numerical methods for solving the nonlinear porous medium and Navier-Lame problems. When coupled together, these equations model the flow of exhaust through a porous medium, soil, and the effects that the pressure has on the soil in terms of spatial displacement. For the porous medium equation we use the Crank-Nicolson time stepping method with a spectral discretization in space. Since the Navier-Lame equation is a boundary value problem, it is solved using a finite element method where the spatial domain is represented by a triangulation of discrete points. The two problems are coupled by using approximations of solutions to the porous medium equation to define the forcing term in the Navier-Lame equation. The spatial displacement solutions can be used to approximate the strain and stress imposed on the soil. An analysis of these physical properties shows whether or not the material ceases to act as an elastic material and instead behaves like a plastic which will tell us if the soil has failed and a crater has formed. Analytical as well as experimental tests are used to find a good balance for solving the porous medium and Navier-Lame equations both accurately and efficiently.

Neste trabalho, as restrições de estabilidade transitória são incorporadas ao problema de Fluxo de Potência Ótimo (FPO) por meio da aproximação de equações diferenciais do problema de estabilidade por um conjunto de equações algébricas provenientes de procedimentos de integração numérica. Uma contribuição original desta dissertação é a proposição de um procedimento de otimização multi-passos que minimiza problemas de convergência e acelera o processo computacional. O procedimento de otimização proposto foi testado com sucesso num sistema pequeno de 3 geradores, tendo as potências geradas como variáveis de controle. / In this work, transient stability constraints are incorporated into the Optimal Power Flow (OPF) problem by approximating differential equations constraints by a set of equivalent algebraic equations originated from numerical integration procedures. A contribution of this dissertation is the proposal of a multi-step optimization procedure, which minimizes convergence problems and speeds up computation. The proposed optimization procedure was successfully tested on a small 3-machine power system, having the generated powers as control variables.