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Os problemas de engenharia atualmente têm aumentado a sua ordem de grandeza, por conta de diversos fatores. A modelagem em ambiente computacional dos mesmos esbarra em limitações, como grandes quantidades de tempo de processamento gastos com diversas simulações da modelagem e a pouca quantidade de memória disponível para alocar propriamente os problemas. A resolução de grandes sistemas de equações lineares, comumente abordado nos problemas atuais de engenharia, necessita da exploração das duas situações mencionadas anteriormente. A subárea computacional que permite explorar a redução do tempo e a possibilidade de alocação na memória de tais problemas é chamada de computação de alto desempenho. O objetivo deste trabalho é ilustrar o uso de softwares de resolução de sistemas de equações lineares, chamados de solvers, projetados para os ambientes computacionais de alto desempenho, testando-os e avaliando-os em um conjunto de matrizes conhecido, bem como abordar os detalhes computacionais envolvidos em tais procedimentos. / Engineering problems today have increased their order of magnitude, due to several factors. Modeling these problems with computers brings up certain limitations, as the amount of processing time needed for several simulations and the lack of available memory to properly allocate them. The resolution of large systems of linear equations, commonly discussed in current engineering problems, needs the exploration of the two situations mentioned above. The subarea that allows exploring the computational time reduction and the possibility of allocating memory in such problems is called high performance computing. The aim of this paper is to illustrate the use of software to solve systems of linear equations, called solvers, designed for high performance computing environments, to test and evaluate them for a set of matrices as well as to address the computational details involved in such procedures.

In the subject of Computational Fluid Dynamics (CFD), there seems to be small number of important progress in the pressure-based methods for several decades. Recent studies on the implicit coupled algorithms for pressure-based methods have brought a new insight. This method seems to provide a huge reduction in the solution times over segregated methods. Fully implicit coupled algorithm for pressure-based methods is very new subject with only few papers in literature. One of the most important work in this area is referenced as [1] in this thesis. Another source of information about the method comes from a commercially available code FLUENT which includes the algorithm as an option for pressure-based solver. However the algorithm in FLUENT does not seem to be a fully implicit with a little information in its manual. In this thesis, a fully implicit coupled pressure-based solver is developed mainly based on the available literature. The developed code is succesfully tested against some test cases.

Os problemas de engenharia atualmente têm aumentado a sua ordem de grandeza, por conta de diversos fatores. A modelagem em ambiente computacional dos mesmos esbarra em limitações, como grandes quantidades de tempo de processamento gastos com diversas simulações da modelagem e a pouca quantidade de memória disponível para alocar propriamente os problemas. A resolução de grandes sistemas de equações lineares, comumente abordado nos problemas atuais de engenharia, necessita da exploração das duas situações mencionadas anteriormente. A subárea computacional que permite explorar a redução do tempo e a possibilidade de alocação na memória de tais problemas é chamada de computação de alto desempenho. O objetivo deste trabalho é ilustrar o uso de softwares de resolução de sistemas de equações lineares, chamados de solvers, projetados para os ambientes computacionais de alto desempenho, testando-os e avaliando-os em um conjunto de matrizes conhecido, bem como abordar os detalhes computacionais envolvidos em tais procedimentos. / Engineering problems today have increased their order of magnitude, due to several factors. Modeling these problems with computers brings up certain limitations, as the amount of processing time needed for several simulations and the lack of available memory to properly allocate them. The resolution of large systems of linear equations, commonly discussed in current engineering problems, needs the exploration of the two situations mentioned above. The subarea that allows exploring the computational time reduction and the possibility of allocating memory in such problems is called high performance computing. The aim of this paper is to illustrate the use of software to solve systems of linear equations, called solvers, designed for high performance computing environments, to test and evaluate them for a set of matrices as well as to address the computational details involved in such procedures.

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<p>Electromagnetic forward modeling and inversion methods have extensive applications in geophysical exploration, and large-scale controlled-source electromagnetic method has recently drawed lots of attention. However, to obtain a rigorous and efficient forward solver for this large-scale three-dimensional problem is difficult, since it usually requires to solve for a large number of unknowns from a system of equations describing the complicate scattering behavior of electromagnetic waves that happened within inhomogeneous media. As for the development of an efficient inversion solver, because of the nonlinear, non-unique and ill-posed properties of the problem, it is also a very challenging task. </p><p>In the first part of this dissertation, a fast three-dimensional nonlinear reconstruction method is proposed for controlled-source electromagnetic method. The borehole-to-surface and airborne electromagnetic survey methods are investigated using synthetic data. In this work, it is assumed that there is only electric contrast between the inhomogeneous object and the layered background medium, for the reason that the electric contrast is much more dominant than magnetic contrast in most cases of the earth formation. Therefore, only the EFIE is needed to solve. While the forward scattering problem is solved by the stabilized bi-conjugate gradient FFT (BCGS-FFT) method to give a rigorous and efficient modeling, the Bore iterative method along with the multiplicative regularization technique is used in the inversion through frequency hopping. In the inversion, to speed up the expensive computation of the sensitivity matrix relating every receiver station to every unknown element, a fast field evaluation (FFE) technique is proposed using the symmetry property of the layered medium Green's function combined with a database strategy. The conjugate-gradient method is then applied to minimize the cost function after each iteration. Due to the benefits of using 3D FFT acceleration, the proposed FFE technique as well as the recursive matrix method combined with an interpolation technique to evaluate the LMGF, the developed inversion solver is highly efficient, and requires very low computation time and memory. Numerical experiments for both 3D forward modeling and conductivity inversion are presented to show the accuracy and efficiency of the method. </p><p>Some recent research on artificial nanoparticles have demonstrated the improved performance in geophysical imaging using magnetodielectric materials with enhanced electric and magnetic contrasts. This gives a promising perspective to the future geophysical exploration by infusing well-designed artificial magnetodielectric materials into the subsurface objects, so that a significantly improved imaging can be achieved. As a preparation for this promising application, the second part of the dissertation presents an efficient method to solve the scattering problem of magnetodielectric materials with general anisotropy that are embedded in layered media. In this work, the volume integral equation is chosen as the target equation to solve, since it solves for fields in inhomogeneous media with less number of unknowns than the finite element method. However, for complicated materials as magnetodielectric materials with general anisotropy, it is a very challenging task, because it requires to simultaneously solve the electric field integral equation (EFIE) and magnetic field integral equation (MFIE). Besides that, the numerous evaluation of the layered medium Green's function (LMGF) for the stratified background formation adds on the difficulty and complexity of the problem. To my knowledge, there is no existing fast solver for the similar problem. In this dissertation, using the mixed order stabilized biconjugate-gradient fast Fourier transform (mixed-order BCGS-FFT) method, a fast forward modeling method is developed to solve this challenging problem. Several numerical examples are performed to validate the accuracy and efficiency of the proposed method.</p><p> </p><p>Besides the above mentioned two topics, one-dimensional inversion method is presented in the third part to determine the tilted triaxial conductivity tensor in a dipping layered formation using triaxial induction measurements. The tilted triaxial conductivity tensor is described by three conductivity components and three Euler angles. Based on my knowledge, due to the highly nonlinear and ill-posed nature of the inverse problem, this study serves as the first work that investigates on the subject. There are six principal coordinate systems that can give the same conductivity tensor. Permutation is performed to eliminate the ambiguity of inversion results caused by the ambiguity of the principal coordinate system. Three new Euler angles after permutation for each layer can be found by solving a nonlinear equation. Numerical experiments are conducted on synthetic models to study the feasibility of determining triaxially anisotropic conductivity tensor from triaxial induction data. This project is accomplished during my internship in the Houston Formation Evaluation Integration Center (HFE) at Schlumberger, a world-leading oilfield service company.</p> / Dissertation

In this thesis we consider two research problems, namely, (i) language constructs for modelling stochastic programming (SP) problems and (ii) solution methods for processing instances of different classes of SP problems. We first describe a new design of an SP modelling system which provides greater extensibility and reuse. We implement this enhanced system and develop solver connections. We also investigate in detail the following important classes of SP problems: singlestage SP with risk constraints, two-stage linear and stochastic integer programming problems. We report improvements to solution methods for single-stage problems with second-order stochastic dominance constraints and two-stage SP problems. In both cases we use the level method as a regularisation mechanism. We also develop novel heuristic methods for stochastic integer programming based on variable neighbourhood search. We describe an algorithmic framework for implementing decomposition methods such as the L-shaped method within our SP solver system. Based on this framework we implement a number of established solution algorithms as well as a new regularisation method for stochastic linear programming. We compare the performance of these methods and their scale-up properties on an extensive set of benchmark problems. We also implement several solution methods for stochastic integer programming and report a computational study comparing their performance. The three solution methods, (a) processing of a single-stage problem with second-order stochastic dominance constraints, (b) regularisation by the level method for two-stage SP and (c) method for solving integer SP problems, are novel approaches and each of these makes a contribution to knowledge.

The notion that a universally effective problem solver may still exist, and is simply waiting to be found, is slowly being abandoned in the light of a growing body of work reporting on the narrow applicability of individual heuristics. As the formalism of the constraint satisfaction problem remains a popular choice for the representation of problems to be solved algorithmically, there exists an ongoing need for new algorithms to effciently handle the disparate range of problems that have been posed in this representation. Given the costs associated with manually applying human algorithm development and problem solving expertise, methods that can automatically adapt to the particular features of a specific class of problem have begun to attract more attention. Whilst a number of authors have developed adaptive systems, the field, and particularly with respect to their application to constraint satisfaction problems, has seen only limited discussion as to what features are desirable for an adaptive constraint system. This may well have been a limiting factor with previous implementations, which have exhibited only subsets of the five features identified in this work as important to the utility of an adaptive constraint satisfaction system. Whether an adaptive system exhibits these features depends on both the chosen represen-tation and the method of adaptation. In this thesis, a three-part representation for constraint algorithms is introduced, which defines an algorithm in terms of contention, preference and selection functions. An adaptive system based on genetic programming is presented that adapts constraint algorithms described using the mentioned three-part representation. This is believed to be the first use of standard genetic programming for learning constraint algo-rithms. Finally, to further demonstrate the efficacy of this adaptive system, its performance in learning specialised algorithms for hard, real-world problem instances is thoroughly evaluated. These instances include random as well as structured instances from known-hard benchmark distributions, industrial problems (specifically, SAT-translated planning and cryptographic problems) as well as over-constrained problem instances. The outcome of this evaluation is a set of new algorithms - valuable in their own right - specifically tailored to these problem classes. Partial results of this work have appeared in the following publications: [1] Stuart Bain, John Thornton, and Abdul Sattar (2004) Evolving algorithms for constraint satisfaction. In Proc. of the 2004 Congress on Evolutionary Computation, pages 265-272. [2] Stuart Bain, John Thornton, and Abdul Sattar (2004) Methods of automatic algorithm generation. In Proc. of the 9th Pacific Rim Conference on AI, pages 144-153. [3] Stuart Bain, John Thornton, and Abdul Sattar. (2005) A comparison of evolutionary methods for the discovery of local search heuristics. In Australian Conference on Artificial Intelligence: AI'05, pages 1068-1074. [4] Stuart Bain, John Thornton, and Abdul Sattar (2005) Evolving variable-ordering heuristics for constrained optimisation. In Principles and Practice of Constraint Programming: CP'05, pages 732-736.

As the circuit size increases in modern electronics, the design process becomes more complicated. Even though the hardware design process is divided into multiple phases, many of the divided problems are still extremely time consuming to solve. One of these NP-hard problems is the routing problem. As electronics step into the deep submicron era, optimizing the routing becomes increasingly important. One of the methods to solve global routing is to formulate the problem as an integer programming (IP) problem. This formulation can then be relaxed into a linear programming problem and solved using interior point method. This thesis investigates two new approaches to optimize the speed of solving global routing using Karmarkar’s interior point method, as well as the effect of combining various optimizations with these new approaches. The first proposed approach is to utilize solution stability as the interior point loop converges, and attempt to remove solutions that have already stabilized. This approach reduces the problem size and allows subsequent interior point iterations to proceed faster. The second proposed approach is to solve the inner linear system (projection step) in interior point method in parallel. Experimental results show that for large routing problems, the performance of the solver is improved by the optimization approaches. The problem reduction stage allows for great speedup in the interior point iterations, without affecting the quality of the solution significantly. Furthermore, the timing required to solve inner linear system in the interior point method is improved by solving the problem in parallel. With these optimizations, solving the routing problem using the IP formation becomes increasingly more efficient. By solving an efficient parallel IP formation rather than a traditional sequential approach, more efficient optimal solutions which incorporate multiple conflicting objectives can be achieved.