O solos saproliticos sÃo encontrados no fundo das escavaÃÃes de jazidas que sÃo normalmente usadas na construcao de barragens de terra. NÃo sÃo normalmente utilizados pelo desconhecimentos de suas propriedades adequadas para gerar uma estrutura de vedaÃÃo. Em algumas situaÃÃes por inexistÃncias de solos residuais maduros suficientes para construÃÃo da barragem ou por questÃes de distancia e possÃvel construir a barragem com solos pouco desenvolvidos (solos residuais jovens). Este foi a motivaÃao para realizaÃÃo deste pesquisa. Foram realizados todos os ensaios de caracterizaÃÃo e mecÃnicos em amostras solos jovens (saproliticos) e a partir do conhecimento de suas propriedades foram realizadas simulaÃÃes numÃricas para demonstrar ser possÃvel construir pequenas barragens com solo residual jovem com o atendimento das questoes relativas a seguranÃa e a reduÃÃo provavel de custos. Os resultados experimentais e numÃricos comprovaram essa possibilidade / The saprolite soils are found on the bottom of the excavation of deposits that are commonly used in the construction of earth dams. Are not normally used by the unknowns of their suitable properties to generate a sealing structure. In some situations by inexistÃncias sufficient mature residual soils for construction of the dam or distance issues and possible to build the dam with poorly developed soils (young residual soils). This was the motivation for conducting this research. All mechanical and characterization tests on soil samples young (saprolite) and from knowledge of its properties numerical simulations were performed to demonstrate possible to build small dams with young residual soil with the care of the issues related to safety and reduction were performed probable costs. The experimental and numerical results confirmed this possibility

Deng, Xiaomao. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 98-104). / Chapter 1 --- Introduction to Inverse Scattering Problems --- p.6 / Chapter 1.1 --- Direct Problems --- p.6 / Chapter 1.1.1 --- Far-field Patterns --- p.10 / Chapter 1.2 --- Inverse Problems --- p.16 / Chapter 1.2.1 --- Introduction --- p.16 / Chapter 2 --- Numerical Methods in Inverse Obstacle Scattering --- p.19 / Chapter 2.1 --- Linear Sampling Method --- p.19 / Chapter 2.1.1 --- History Review --- p.19 / Chapter 2.1.2 --- Numerical Scheme of LSM --- p.21 / Chapter 2.1.3 --- Theoretic Justification --- p.25 / Chapter 2.1.4 --- Summarize --- p.38 / Chapter 2.2 --- Point Source Method --- p.38 / Chapter 2.2.1 --- Historical Review --- p.38 / Chapter 2.2.2 --- Superposition of Plane Waves --- p.40 / Chapter 2.2.3 --- Approximation of Domains --- p.42 / Chapter 2.2.4 --- Algorithm --- p.44 / Chapter 2.2.5 --- Summarize --- p.49 / Chapter 2.3 --- Singular Source Method --- p.49 / Chapter 2.3.1 --- Historical Review --- p.49 / Chapter 2.3.2 --- Algorithm --- p.51 / Chapter 2.3.3 --- Far-field Data --- p.54 / Chapter 2.3.4 --- Summarize --- p.55 / Chapter 2.4 --- Probe Method --- p.57 / Chapter 2.4.1 --- Historical Review --- p.57 / Chapter 2.4.2 --- Needle --- p.58 / Chapter 2.4.3 --- Algorithm --- p.59 / Chapter 3 --- Numerical Experiments --- p.61 / Chapter 3.1 --- Discussions on Linear Sampling Method --- p.61 / Chapter 3.1.1 --- Regularization Strategy --- p.61 / Chapter 3.1.2 --- Cut off Value --- p.70 / Chapter 3.1.3 --- Far-field data --- p.76 / Chapter 3.2 --- Numerical Verification of PSM and SSM --- p.80 / Chapter 3.3 --- Inverse Medium Scattering --- p.83 / Bibliography --- p.98

Maxwell’s equations are a set of partial differential equations that describe the classic electromagnetic problems, electrodynamics etc. Effective numerical methods are derived to solve the equations in the past decades, and continued to be of great interest to be developed to its completion. In this thesis, we introduce and propose numerical methods using staggered meshes that deal with both two dimensional and three dimensional space problem in polygonal and general curved domains. / Finite difference method, finite volume method, spectral method and staggered discontinuous Galerkin method are discussed in the thesis. A forth order finite difference method using Taylor expansion technic is proposed. The integral form of the original Maxwell’s equations give rise to methods based on more general domain. For the finite volume method, covolume methods both on the cyclic polygon elements and noncyclic polygon elements are derived. To derive a higher order accurate method, staggered discontinuous Galerkin method based on the same domain decomposition present in the finite volume method use Nedelec elements is derived in two dimensional space, and spectral method using nodal high-order method operate on a general domain in 3D with flexible domain geometry is introduced. Numerical results are shown to show the performance oft he above mentioned approximation methods in 2D case. / 麥克斯韋方程組是一組描述經典電磁問題，電磁力學的偏微分方程。在過去數十年，行之有效的偏微分方程數值解已經被推導出並用於求解該方程，該問題現在仍然吸引著學者極大的興趣，並日臻完善。在這篇論文中，我們介紹並提出一些運用曲域交錯網格數值方法在二維和三維的多面體和更一般幾何體處理麥克斯韋方程組問題。 / 本論文對有限差分法，有限體積法，光譜法和交錯間斷有限元方法進行了討論。利用泰勒展開式這一方法推導出一個二維的四階有限差分方法。基於原來的麥克斯韋方程組的積分形式所得到的數值方法更適用於更普遍的域。對於有限體積法，對循環多邊形元素和非環狀多邊形元素的有限體積方法都將被導出。為了得到一個更高階準確的方法，基於有限體積法中使用的域分解方法，使用Nedelec元素，推導了二維空間的高階有限元方法。基於頂點高階數值方法的光譜法對於三維一般定義域的幾何形態更為靈活適用。在二維的定義域中，數值模擬結果驗證上述數值方法的精確性。 / Jian, Fangqiong. / Thesis M.Phil. Chinese University of Hong Kong 2014. / Includes bibliographical references (leaves 62-65). / Abstracts also in Chinese. / Title from PDF title page (viewed on 07, October, 2016). / Detailed summary in vernacular field only. / Detailed summary in vernacular field only.

Cheung, Man Wah. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (leaves 89-91). / Abstracts in English and Chinese. / Chapter 1 --- Introduction to Inverse Problems --- p.1 / Chapter 1.1 --- Major properties --- p.1 / Chapter 1.2 --- Typical examples --- p.3 / Chapter 1.3 --- Thesis outline --- p.5 / Chapter 2 --- Some Operator Theory --- p.6 / Chapter 2.1 --- Fredholm integral equation of the first kind --- p.6 / Chapter 2.2 --- Compact operator theory --- p.8 / Chapter 2.3 --- Singular system --- p.12 / Chapter 2.4 --- Moore-Penrose generalized inverse --- p.14 / Chapter 3 --- Regularization Theory for First Kind Equations --- p.19 / Chapter 3.1 --- General regularization theory --- p.19 / Chapter 3.2 --- Tikhonov regularization --- p.24 / Chapter 3.3 --- Landweber iteration --- p.26 / Chapter 3.4 --- TSVD --- p.28 / Chapter 4 --- Multilevel Algorithms for Ill-posed Problems --- p.30 / Chapter 4.1 --- Basic assumptions and definitions --- p.31 / Chapter 4.2 --- Multilevel analysis --- p.33 / Chapter 4.3 --- Applications --- p.37 / Chapter 4.3.1 --- Preconditioned iterative methods with nonzero regularization parameter --- p.38 / Chapter 4.3.2 --- Preconditioned iterative methods with zero regularization parameter --- p.38 / Chapter 4.3.3 --- Full multilevel algorithm --- p.40 / Chapter 5 --- Numerical Experiments --- p.41 / Chapter 5.1 --- Integral equations --- p.41 / Chapter 5.1.1 --- Discretization --- p.42 / Chapter 5.1.2 --- Test problems --- p.43 / Chapter 5.1.3 --- "Singular values, singular vectors and condition numbers" --- p.45 / Chapter 5.1.4 --- Effect of condition numbers on numerical accuracies --- p.49 / Chapter 5.2 --- Differential equations --- p.50 / Chapter 5.2.1 --- Discretization --- p.51 / Chapter 5.2.2 --- "Singular values, singular vectors and condition numbers" --- p.53 / Chapter 5.3 --- Numerical experiments by classical methods --- p.55 / Chapter 5.3.1 --- Tikhonov regularization --- p.55 / Chapter 5.3.2 --- TSVD --- p.56 / Chapter 5.3.3 --- Landweber iteration --- p.63 / Chapter 5.4 --- Numerical experiments by multilevel methods --- p.63 / Chapter 5.4.1 --- General convergence --- p.63 / Chapter 5.4.2 --- Numerical results --- p.65 / Chapter 5.4.3 --- Effect of multilevel parameters on convergence --- p.76 / Bibliography --- p.89

The Upper Mississippi River is in interest to river managers and biologists' dues to its vast ecosystem and past anthropogenic impacts. In order to help restore the river to its once natural state, river managers and biologists need a strong understanding of the hydrodynamics of the system. A two-dimensional hydrodynamic model was developed in Pool 8 of the Upper Mississippi River and utilized for river management applications. The model was constructed using SMS 10.0 grid generation software and processed with SRH-2D software. SRH-2D used Manning's roughness coefficients to calibrate the model to observed water surface elevation data collected by the USGS. The model was validated to an observed water surface elevation profile and percent discharge through 17 transects within the model. The calibrated and validated model was used for river management and biological applications; hypothetical island, drawdown scenarios, residence time study, and habitat suitability assessment. The results showed that the two-dimensional hydrodynamic model could accurately represent a hypothetical island within the lower pool, simulate drawdown scenarios, develop stream traces for particle tracking and residence time calculation, and the creation of habitat suitability maps based on field data. The completion of these applications with the two-dimensional model shows the efficiently and accuracy of the model, and how two-dimensional numerical models are important tools in bridging the gap between engineers and scientists.

In this thesis we shall investigate the numerical solutions to several important practical static and dynamic optimization problems in engineering and physics. The thesis is organized as follows.In Chapter 1 a general literature review is presented, including motivation and development of the problems, and existing results. Furthermore, some existing computational methods for optimal control problems are also discussed.In Chapter 2 the design of a semiconductor device is posed as an optimization problem: given an ideal voltage-current (V - I) characteristic, find one or more physical and geometrical parameters so that the V-I characteristic of the device matches the ideal one optimally with respect to a prescribed performance criterion. The voltage-current characteristic of a semiconductor device is governed by a set of nonlinear partial differential equations (PDE), and thus a black-box approach is taken for the numerical solution to the PDEs. Various existing numerical methods are proposed for the solution of the nonlinear optimization problem. The Jacobian of the cost function is ill-conditioned and a scaling technique is thus proposed to stabilize the resulting linear system. Numerical experiments, performed to show the usefulness of this approach, demonstrate that the approach always gives optimal or near-optimal solutions to the test problems in both two and three dimensions.In Chapter 3 we propose an efficient approach to numerical integration in one and two dimensions, where a grid set with a fixed number of vertices is to be chosen so that the error between the numerical integral and the exact integral is minimized. For one dimensional problem two schemes are developed for sufficiently smooth functions based on the mid-point rectangular quadrature rule and the trapezoidal rule respectively, and another method is also developed for integrands which are not ++ / sufficiently smooth. For two dimensional problems two schemes are first developed for sufficiently smooth functions. One is based on the barycenter rule on a rectangular partition, while the other is on a triangular partition. A scheme for insufficiently smooth functions is also developed. For illustration, several examples are solved using the proposed schemes, and the numerical results show the effectiveness of the approach.Chapter 4 deals with optimal recharge and driving plans for a battery-powered electric vehicle. A major problem facing battery-powered electric vehicles is in their batteries: weight and charge capacity. Thus a battery-powered electric vehicle only has a short driving range. To travel for a longer distance, the batteries are required to be recharged frequently. In this chapter we construct a model for a battery-powered electric vehicle, in which driving strategy is to be obtained so that the total traveling time between two locations is minimized. The problem is formulated as an unconventional optimization problem. However, by using the control parameterization enhancing transformation (CPET) (see [100]) it is shown that this unconventional optimization is equivalent to a conventional optimal parameter selection problem. Numerical examples are solved using the proposed method.In Chapter 5 we consider the numerical solution to a class of optimal control problems involving variable time points in their cost functions. The CPET is first used to convert the optimal control problem with variable time points into an equivalent optimal control problem with fixed multiple characteristic times (MCT). Using the control parameterization technique, the time horizon is partitioned into several subintervals. Let the partition points also be taken as decision variables. The control functions are approximated by piecewise constant or piecewise linear functions ++ / in accordance with these variable partition points. We thus obtain a finite dimensional optimization problem. The CPET transform is again used to convert approximate optimal control problems with variable partition points into equivalent standard optimal control problems with MCT, where the control functions are piecewise constant or piecewise linear functions with pre-fixed partition points. The transformed problems are essentially optimal parameter selection problems with MCT. The gradient formulae are obtained for the objective function as well as the constraint functions with respect to relevant decision variables. Numerical examples are solved using the proposed method.A numerical approach is proposed in Chapter 6 for constructing an approximate optimal feedback control law of a class of nonlinear optimal control problems. In this approach, the state space is partitioned into subdivisions, and the controllers are approximated by a linear combination of the 3rd order B-spline basis functions. Furthermore, the partition points are also taken as decision variables in this formulation. To show the effectiveness of the proposed approach, a two dimensional and a three dimensional examples are solved by the approach. The numerical results demonstrate that the method is superior to the existing methods with fixed partition points.

A mathematical study has been undertaken to model various kinds of granular flows including the perfect plasticity flow and the viscous elasto-plasticity flow. The work is mainly based on the double-shearing theory originated by Spencer and developed by many others. The focus of the project is on the formulation of the theory, the construction of mathematical models and the development of robust simulation techniques.Based on a general formulation of the double-shearing theory, the perfect plasticity flow is shown to be governed by a set of highly nonlinear first order hyperbolic partial differential equations with two distinct characteristics. A sophisticated numerical algorithm is then developed based on the method of characteristics to determine the stress discontinuity and the velocity and stress fields. With the method developed, a numerical study is then undertaken to model the flow of granular materials in a hopper in the presence of stress discontinuity and to investigate the influence of various parameters on the distribution of hopper wall pressures.Utilising the double shearing theory, a set of stress-strain constitutive equations in explicit form has been derived, which makes it possible to formulate the double-shearing theory within the framework of the finite element method. Thus, consequently, a sophisticated finite element technique has been developed to solve the general boundary value problem governing the viscous elasto-plasticity flows obeying the double-shearing theory. Numerical implementation of the frictional boundary condition is also presented. The model is then illustrated with a numerical example demonstrating the influence of wall friction on the distribution of pressures on silo walls throughout the dynamic process of material discharge from silos.

Includes bibliographical references (leaves 158-163). Concerns the development of high-order finite-difference methods on a uniform rectangular grid for advection and diffuse problems with smooth variable coefficients. This technique has been successfully applied to variable-coefficient advection and diffusion problems. Demonstrates that the new schemes may readily be incorporated into multi-dimensional problems by using locally one-dimensional techniques, or that they may be used in process splitting algorithms to solve complicatef time-dependent partial differential equations.

Bibliography: leaves 264-267.

This thesis proposes several new techniques to improve the performance of speciated particle swarms in multimodal environments. We investigate how these algorithms can become more robust and adaptive, easier to use and able to solve a wider variety of optimisation problems. We then develop a technique that uses regression to vastly improve an algorithm's convergence speed without requiring extra evaluations. Speciation techniques play an important role in particle swarms. They allow an algorithm to locate multiple optima, providing the user with a choice of solutions. Speciation also provides diversity preservation, which can be critical for dynamic optimisation. By increasing diversity and tracking multiple peaks simultaneously, speciated algorithms are better able to handle the changes inherent in dynamic environments. Speciation algorithms often require a user to specify a parameter that controls how species form. This is a major drawback since the knowledge may not be available a priori. If the parameter is incorrectly set, the algorithm's performance is likely to be highly degraded. We propose using a time-based measure to control the speciation, allowing the algorithm to define species far more adaptively, using the population's characteristics and behaviour to control membership. Two new techniques presented in this thesis, ANPSO and ESPSO, use time-based convergence measures to define species. These methods are shown to be robust while still providing highly competitive performance. Both algorithms effectively optimised all of our test functions without requiring any tuning. Speciated algorithms are ideally suited to optimising dynamic environments, however the complexity of these environments makes them far more difficult to design algorithms for. To increase an algorithm's performance it is necessary to determine in what ways it should be improved. While all performance metrics allow optimisation techniques to be compared, they cannot show how to improve an algorithm. Until now this has been done largely by trial and error. This is extremely inefficient, in the same way it is inefficient trying to improve a program's speed without profiling it first. This thesis proposes a new metric that exclusively measures convergence speed. We show that an algorithm can be profiled by correlating the performance as measured by multiple metrics. By combining these two techniques, we can obtain far better insight into how best to improve an algorithm. Using this information, we then propose a local convergence enhancement that greatly increases performance by actively estimating the location of an optimum. The enhancement uses regression to fit a surface to the peak, guiding the search by estimating the peak's true location. By incorporating this technique, the algorithm is able to use the information contained within the fitness landscape far more effectively. We show that by combining the regression with an existing speciated algorithm, we are able to vastly improve the algorithm's performance. This technique will greatly enhance the utility of PSO on problems where fitness evaluations are expensive, or that require fast reaction to change.