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The dissertation focuses on one of the major research needs in the area of adaptive /intelligent/smart structures, the development and application of finite element analysis and genetic algorithms for optimal design of large-scale adaptive structures. We first review some basic concepts in finite element method and genetic algorithms, along with the research on smart structures. Then we propose a solution methodology for solving a critical problem in the design of a next generation of large-scale adaptive structures -- optimal placements of a large number of actuators to control thermal deformations. After briefly reviewing the three most frequently used general approaches to derive a finite element formulation, the dissertation presents techniques associated with general shell finite element analysis using flat triangular laminated composite elements. The element used here has three nodes and eighteen degrees of freedom and is obtained by combining a triangular membrane element and a triangular plate bending element. The element includes the coupling effect between membrane deformation and bending deformation. The membrane element is derived from the linear strain triangular element using Cook's transformation. The discrete Kirchhoff triangular (DKT) element is used as the plate bending element. For completeness, a complete derivation of the DKT is presented. Geometrically nonlinear finite element formulation is derived for the analysis of adaptive structures under the combined thermal and electrical loads. Next, we solve the optimization problems of placing a large number of piezoelectric actuators to control thermal distortions in a large mirror in the presence of four different thermal loads. We then extend this to a multi-objective optimization problem of determining only one set of piezoelectric actuator locations that can be used to control the deformation in the same mirror under the action of any one of the four thermal loads. A series of genetic algorithms, GA Version 1, 2 and 3, were developed to find the optimal locations of piezoelectric actuators from the order of 10<SUP>21</SUP> ~ 10<SUP>56</SUP> candidate placements. Introducing a variable population approach, we improve the flexibility of selection operation in genetic algorithms. Incorporating mutation and hill climbing into micro-genetic algorithms, we are able to develop a more efficient genetic algorithm. Through extensive numerical experiments, we find that the design search space for the optimal placements of a large number of actuators is highly multi-modal and that the most distinct nature of genetic algorithms is their robustness. They give results that are random but with only a slight variability. The genetic algorithms can be used to get adequate solution using a limited number of evaluations. To get the highest quality solution, multiple runs including different random seed generators are necessary. The investigation time can be significantly reduced using a very coarse grain parallel computing. Overall, the methodology of using finite element analysis and genetic algorithm optimization provides a robust solution approach for the challenging problem of optimal placements of a large number of actuators in the design of next generation of adaptive structures. / Ph. D.

A procedure for generating a customized weight function for wing bending material weight of a High Speed Civil Transport (HSCT) is described. The weight function is based on HSCT configuration parameters. A response surface methodology is used to fit a quadratic polynomial to data gathered from a large number of structural optimizations. To reduce the time of performing a large number of structural optimizations, coarse-grained parallelization with a master-slave processor assignment on an Intel Paragon computer is used. The results of the structural optimization are noisy. Noise reduction in the structural optimization results is discussed. It is shown that the response surface filters out this noise. A statistical design of experiments technique is used to minimize the number of required structural optimizations and to maintain accuracy. Simple analysis techniques are used to find regions of the design space where reasonable HSCT designs could occur, thus customizing the weight function to the design requirements of the HSCT, while the response surface itself is created employing detailed analysis methods. Analysis of variance is used to reduce the number of polynomial terms in the response surface model function. Linear and constant corrections based on a small number of high fidelity results are employed to improve the accuracy of the response surface model. Configuration optimization of the HSCT employing a customized weight function is compared to the configuration optimization of the HSCT with a general weight function. / Ph. D.

Thesis (MScEng)--Stellenbosch University, 2011. / ENGLISH ABSTRACT: Modern-day processors are not getting any faster. Due to the power consumption limit of frequency scaling, parallel processing is increasingly being used to decrease computation time. In this thesis, several parallel paradigms are used to improve the performance of commonly serial SAO programs. Four novelties are discussed: First, replacing double precision solvers with single precision solvers. This is attempted in order to take advantage of the anticipated factor 2 speed increase that single precision computations have over that of double precision computations. However, single precision routines present unpredictable performance characteristics and struggle to converge to required accuracies, which is unfavourable for optimization solvers. Second, QP and dual are statements pitted against one another in a parallel environment. This is done because it is not always easy to see which is best a priori. Therefore both are started in parallel and the competing threads are cancelled as soon as one returns a valid point. Parallel QP vs. dual statements prove to be very attractive, converging within the minimum number of outer iterations. The most appropriate solver is selected as the problem properties change during the iteration steps. Thread cancellation poses problems caused by threads having to wait to arrive at appropriate checkpoints, thus su ering from unnecessarily long wait times because of struggling competing routines. Third, multiple global searches are started in parallel on a shared memory system. Problems see a speed increase of nearly 4x for all problems. Dynamically scheduled threads alleviate the need for set thread amounts, as in message passing implementations. Lastly, the replacement of existing matrix-vector multiplication routines with optimized BLAS routines, especially BLAS routines targeted at GPGPU technologies (graphics processing units), proves to be superior when solving large matrix-vector products in an iterative environment. These problems scale well within the hardware capabilities and speedups of up to 36x are recorded. / AFRIKAANSE OPSOMMING: Hedendaagse verwerkers word nie vinniger nie as gevolg van kragverbruikingslimiet soos die verwerkerfrekwensie op-skaal. Parallelle prosesseering word dus meer dikwels gebruik om berekeningstyd te laat daal. Verskeie parallelle paradigmas word gebruik om die prestasie van algemeen sekwensiële optimeringsprogramme te verbeter. Vier ontwikkelinge word bespreek: Eerste, is die vervanging van dubbel presisie roetines met enkel presisie roetines. Dit poog om voordeel te trek uit die faktor 2 spoed verbetering wat enkele presisie berekeninge het oor dubbel presisie berekeninge. Enkele presisie roetines is onvoorspelbaar en sukkel in meeste gevalle om die korrekte akkuraatheid te vind. Tweedens word QP teen duale algoritmes in ’n parallel omgewing gebruik. Omdat dit nie altyd voor die tyd maklik is om te sien watter een die beste gaan presteer nie, word almal in parallel begin en die mededingers word dan gekanselleer sodra een terugkeer met ’n geldige KKT punt. Parallele QP teen duale algoritmes blyk om baie aantreklik te wees. Konvergensie gebeur in alle gevalle binne die minimum aantal iterasies. Die mees geskikte algoritme word op elke iterasie gebruik soos die probleem eienskappe verander gedurende die iterasie stappe. “Thread” kanseleering hou probleme in en word veroorsaak deur “threads” wat moet wag om die kontrolepunte te bereik, dus ly die beste roetines onnodig as gevolg van meededinger roetines was sukkel. Derdens, verskeie globale optimerings word in parallel op ’n “shared memory” stelsel begin. Probleme bekom ’n spoed verhoging van byna vier maal vir alle probleme. Dinamiese geskeduleerde “threads” verlig die behoefte aan voorafbepaalde “threads” soos gebruik word in die “message passing” implementerings. Laastens is die vervanging van die bestaande matriks-vektor vermenigvuldiging roetines met geoptimeerde BLAS roetines, veral BLAS roetines wat gerig is op GPGPU tegnologië. Die GPU roetines bewys om superieur te wees wanneer die oplossing van groot matrix-vektor produkte in ’n iteratiewe omgewing gebruik word. Hierdie probleme skaal ook goed binne die hardeware se vermoëns, vir die grootste probleme wat getoets word, word ’n versnelling van 36 maal bereik.

This thesis develops efficient modeling frameworks via a Partial Differential Equation (PDE) approach for multi-factor financial derivatives, with emphasis on three-factor models, and studies highly efficient implementations of the numerical methods on novel high-performance computer architectures, with particular focus on Graphics Processing Units (GPUs) and multi-GPU platforms/clusters of GPUs. Two important classes of multi-factor financial instruments are considered: cross-currency/foreign exchange (FX) interest rate derivatives and multi-asset options. For cross-currency interest rate derivatives, the focus of the thesis is on Power Reverse Dual Currency (PRDC) swaps with three of the most popular exotic features, namely Bermudan cancelability, knockout, and FX Target Redemption. The modeling of PRDC swaps using one-factor Gaussian models for the domestic and foreign interest short rates, and a one-factor skew model for the spot FX rate results in a time-dependent parabolic PDE in three space dimensions. Our proposed PDE pricing framework is based on partitioning the pricing problem into several independent pricing subproblems over each time period of the swap's tenor structure, with possible communication at the end of the time period. Each of these subproblems requires a solution of the model PDE. We then develop a highly efficient GPU-based parallelization of the Alternating Direction Implicit (ADI) timestepping methods for solving the model PDE. To further handle the substantially increased computational requirements due to the exotic features, we extend the pricing procedures to multi-GPU platforms/clusters of GPUs to solve each of these independent subproblems on a separate GPU. Numerical results indicate that the proposed GPU-based parallel numerical methods are highly efficient and provide significant increase in performance over CPU-based methods when pricing PRDC swaps. An analysis of the impact of the FX volatility skew on the price of PRDC swaps is provided. In the second part of the thesis, we develop efficient pricing algorithms for multi-asset options under the Black-Scholes-Merton framework, with strong emphasis on multi-asset American options. Our proposed pricing approach is built upon a combination of (i) a discrete penalty approach for the linear complementarity problem arising due to the free boundary and (ii) a GPU-based parallel ADI Approximate Factorization technique for the solution of the linear algebraic system arising from each penalty iteration. A timestep size selector implemented efficiently on GPUs is used to further increase the efficiency of the methods. We demonstrate the efficiency and accuracy of the proposed GPU-based parallel numerical methods by pricing American options written on three assets.

<p>U radu je predstavljeno istraživanje vezano za poboljšanje performansi rada velikih nadzorno-upravljačkih sistema poput DMS-a. Ovaj cilj je postignut koordinacijom izvršavanja tokova aktivnosti, što podrazumeva efikasnu raspodelu zadataka na računarske resurse. U te svrhe razvijeni su i testirani različiti algoritmi. Ovakav pristup je obezbedio veći stepen iskorišćenja računarskih resursa, što je rezultiralo boljim performansama.</p> / <p>Thе paper presents an approach how to improve performance of larger scale distributed utility management system such as DMS. This goal is accomplished by using an intelligent workflow management. Workflows are divided into the atomic tasks which are scheduled to computing resources for execution. For these purposes various scheduling algorithms are developed and thoroughly tested. This approach has provided greater utilization of computing resources which further have resulted in better performance.</p>