This paper presents techniques that actively exploit chaotic behavior to accomplish otherwise-impossible control tasks. The state space is mapped by numerical integration at different system parameter values and trajectory segments from several of these maps are automatically combined into a path between the desired system states. A fine-grained search and high computational accuracy are required to locate appropriate trajectory segments, piece them together and cause the system to follow this composite path. The sensitivity of a chaotic system's state-space topology to the parameters of its equations and of its trajectories to the initial conditions make this approach rewarding in spite of its computational demands.

<p> In this day and age, many companies struggle with the maintenance of legacy scientific software systems written in outdated programming languages. These languages use low-level control structures, algorithmic operations and cumbersome syntax that make the true meaning of an algorithm difficult to understand. To make matters worse, the process of reverse engineering the algorithm to specification often involves a considerable amount of manual work which is error-prone and time-consuming.</p> <p> This thesis explores a completely automated method of reverse engineering. We apply this method to FORTRAN77 linear algebra software. This software is transformed to an extension of FORTRAN77, which we call Fortran-M. This language allows for high-level mathematical constructs such as sums, products and vector and matrix operations. To serve as a proof-of-concept for this method, we have developed a tool which uses a combination of pattern matching on the source code's abstract syntax tree to recognise low-level control structures, and symbolic analysis to determine the meaning of loops. Once a pattern has been recognised, or a loop's invariant found, we apply transformations to the syntax tree, thus creating a Fortran-M equivalent.</p> / Thesis / Master of Applied Science (MASc)

Cache-based, general purpose CPUs perform at a small fraction of their maximum floating point performance when executing memory-intensive simulations, such as those required for many scientific computing problems. This is due to the memory bottleneck that is encountered with large arrays that must be stored in dynamic RAM. A system of FPGAs, with a large enough memory bandwidth, and clocked at only hundreds of MHz can outperform a CPU clocked at GHz in terms of floating point performance. An FPGA core designed for a target performance that does not unnecessarily exceed the memory imposed bottleneck can then be distributed, along with multiple memory interfaces, into a scalable architecture that overcomes the bandwidth limitation of a single interface. Interconnected cores can work together to solve a scientific computing problem and exploit a bandwidth that is the sum of the bandwidth available from all of their connected memory interfaces. The implementation demonstrates this concept of scalability with two memory interfaces through the use of available FPGA prototyping platforms. Even though the FPGAs operate at 133 MHz, which is twenty one times slower than an AMD Phenom X4 processor operating at 2.8 GHz, the system of two FPGAs performs eight times slower than the processor for the example problem of SMVM in heat transfer. However, the system is demonstrated to be scalable with a run-time that decreases linearly with respect to the available memory bandwidth. The floating point performance of a single board implementation is 12 GFlops which doubles to 24 GFlops for a two board implementation, for a gather or scatter operation on matrices of varying sizes.

"The complex growth patterns of malignant brain tumors can present challenges in developing accurate models. In particular, the computational costs associated with modeling a realistically sized tumor can be prohibitive. The use of high-performance computing (HPC) and novel mathematical techniques can help to overcome this barrier. This paper presents a parallel implementation of a model for the growth of glioma, a form of brain cancer, and discusses how HPC is being used to take a first step toward realistically sized tumor models. Also, consideration is given to the visualization process involved with large-scale computing. Finally, simulation data is presented with a focus on scaling."

Neste trabalho apresentamos a metodologia de orientação ao objeto no desenvolvimentos de uma biblioteca de classes para facilitar o processo de programação numérica paralela. Na implementação dos métodos das classes utilizamos as rotinas do pacote ScaLAPACK, sendo que essas classes oferecem métodos para manipulações matriciais básicas e para a diagonalização de matrizes, onde essas matrizes podem ser reais e complexas, de simples e dupla precisão. Este trabalho apresenta detalhes de implementação e uma análise comparativa de desempenho, a fim de mostrarmos a eficiência e as facilidades de uso da orientação ao objeto no desenvolvimento de programas científicos paralelos. / In this work current vs. voltage (I vs. V) and alternating conductivity (ac) measurements were carried out in poly[(2-methoxy- 5-hexyloxy)-pphenylenevinilene] ? MEH-PPV light-emitting diodes having zinc oxide (ZnO) as transparent anode and Al as metallic cathode. MEH-PPV is a PPV derivative, which emits in the red spectral region; ZnO has a work function similar to that of ITO, but it is less aggressive to the polymer, less expensive and easily processed. The retificated I vs. V curves shows that the direct current depends on the temperature. Moreover, the real and imaginary components of alternating conductivity (ac) present typical behavior of somewhat disordered material: the imaginary component grows as a function of the frequency and the real component was observed to be frequency independent for lower frequencies, and follows a power-law above a certain frequency. The Random Energy Free Barrier model approaches and a resistance in series for the interface phenomenon were developed and adjusted for the ac results. From this experimental-theoretical fitting we obtained important parameters of the devices as well as, quantitative informations about the MEH-PPV transport phenomenon.

Introduced in this paper is the time difference of arrival (TDoA) conic approximation method (TCAM), a technique for passive localization in three dimensions with unknown starting conditions. The TDoA of a mutually detected signal across pairs of detectors is used to calculate the relative angle between the signal source and the center point of the separation between the detectors in the pair. The relative angle is calculated from the TDoA using a mathematical model called the TDoA approximation of the zenith angle (TAZA). The TAZA angle defines the opening angle of a conic region of probability that contains the signal source, produced by each detector pair. The intersecting region of probability is determined from the conic regions of probability and represents the volumetric region with the highest probability of containing the signal source. TCAM was developed and tested using synthetic data in a simulated environment.

A multi-layered periodic structure is investigated for optimal shape design in diffraction gratings. A periodic dielectric material is used as the scattering profile for a planar incident wave. Designing optimal profiles for scattering is a type of inverse problem. The ability to fabricate such materials on the order of the wavelength of the incoming light is key for design strategies. We compute a finite element approximation on a variational setup of the forward problem. On the inverse and optimal design problem, we discuss the stability of the designs and develop computational strategies based on a level-set evolutionary approach.

Neste trabalho apresentamos a metodologia de orientação ao objeto no desenvolvimentos de uma biblioteca de classes para facilitar o processo de programação numérica paralela. Na implementação dos métodos das classes utilizamos as rotinas do pacote ScaLAPACK, sendo que essas classes oferecem métodos para manipulações matriciais básicas e para a diagonalização de matrizes, onde essas matrizes podem ser reais e complexas, de simples e dupla precisão. Este trabalho apresenta detalhes de implementação e uma análise comparativa de desempenho, a fim de mostrarmos a eficiência e as facilidades de uso da orientação ao objeto no desenvolvimento de programas científicos paralelos. / In this work current vs. voltage (I vs. V) and alternating conductivity (ac) measurements were carried out in poly[(2-methoxy- 5-hexyloxy)-pphenylenevinilene] ? MEH-PPV light-emitting diodes having zinc oxide (ZnO) as transparent anode and Al as metallic cathode. MEH-PPV is a PPV derivative, which emits in the red spectral region; ZnO has a work function similar to that of ITO, but it is less aggressive to the polymer, less expensive and easily processed. The retificated I vs. V curves shows that the direct current depends on the temperature. Moreover, the real and imaginary components of alternating conductivity (ac) present typical behavior of somewhat disordered material: the imaginary component grows as a function of the frequency and the real component was observed to be frequency independent for lower frequencies, and follows a power-law above a certain frequency. The Random Energy Free Barrier model approaches and a resistance in series for the interface phenomenon were developed and adjusted for the ac results. From this experimental-theoretical fitting we obtained important parameters of the devices as well as, quantitative informations about the MEH-PPV transport phenomenon.

La simulation des systèmes multicorps avec une dynamique non régulière trouve ses applications dans différents domaines comme l'aéronautique, l'automobile, le ferroviaire, la robotique, la réalité virtuelle et même l'industrie horlogère. Ces industries ont de plus en plus d'exigences sur la rapidité ainsi que la précision des méthodes utilisées pour calculer la dynamique. Par conséquent, la recherche dans le domaine de la mécanique non régulière est très active et a pour objectif constant de proposer des algorithmes plus robustes et plus rapides pour calculer la dynamique ainsi que de développer de meilleurs modèles pour le contact avec ou sans frottement. Les méthodes proposées doivent en plus bien gérer les sauts dans la vitesse et l'accélération des systèmes, ces sauts résultent de phénomènes tels que l'impact et le frottement. Dans ce manuscrit, quelques méthodes d'intégration d'équations différentielles algébriques d'index 3, 2 et 1 sont testées sur plusieurs mécanismes industriels avec contraintes unilatérales et bilatérales. Ces méthodes sont ensuite comparées sur la base de la satisfaction des contraintes bilatérales, de l'efficacité numérique et de leur capacité à gérer une dynamique raide. Cette étude a aussi permis d'apporter une réponse claire sur le choix de la méthode d'intégration pour un système mécanique connaissant ses caractéristiques (nombre de contacts, présence de contraintes bilatérales, dynamique raide...). La deuxième partie de ce travail traite certains problèmes qui sont fréquemment rencontrés dans la simulation des systèmes multicorps, notamment: le phénomène d'accumulation des impacts, la résolution du frottement, ainsi que la gestion des sauts qui peuvent être provoqués par la présence de singularités géométriques. Calculer la dynamique dans ces cas est particulièrement difficile dans le cadre des schémas event-driven. La solution proposée est un schéma d'intégration mixte "event-driven/time-stepping" dont le but est d'utiliser les avantages de chacune des familles d'intégration (event-driven et time-stepping). Notre algorithme est ensuite testé sur de nombreux exemples. / The applications of the nonsmooth multibody systems field cover several fields including aeronautics, automotive, robotics, railway, virtual reality and watch industry to cite a few. These industrial applications have ever more stringent requirements on both accuracy and speed of the numerical methods used for the computation of the dynamics. As a consequence, the research in the nonsmooth mechanics domain is very active, to provide better integration methods for the resolution of the equations of motions and to develop better models for the contact problems with and without friction. Since the nonsmooth mechanics framework allows for jumps in the velocity and in the acceleration of the mechanical systems, the resulting algorithms have to handle such non-smoothness. In this PhD, several numerical schemes for the resolution of index-3, index-2 and index-1 DAEs are compared on industrial benchmarks with bilateral and unilateral constraints. The aim is to improve the efficiency of the Ansys Rigid Body solver which is based on an event-driven integration strategy. Points of comparison include the enforcement of the bilateral constraints, time efficiency and handling the stiff dynamics. This study also aimed at having a clear idea on the choice of the most suitable integration method for a given mechanical system knowing its characteristics (number of contacts, presence of bilateral constraints, stiff dynamics...). The second part discusses several issues that frequently occur in the simulation of multibody systems, namely, the problem of accumulation of impacts, the resolution of friction and handling the jumps resulting from the presence of some geometrical singularities. Dealing with such issues is very difficult, especially in the framework of event-driven schemes. In order to handle these problems, a mixed event-driven/time-stepping scheme is developed which takes advantage of both integration families (event-driven and time-stepping). Several examples are used to validate our methodology.

Dans le contexte de l'analyse numérique en calcul de structures, la génération de maillages conformes sur des modèles à géométrie complexe conduit à des tailles de modèles importantes, et amène à imaginer de nouvelles approches éléments finis. Le temps de génération d'un maillage est directement lié à la complexité de la géométrie, augmentant ainsi considérablement le temps de calcul global. Les processeurs graphiques (GPU) offrent de nouvelles opportunités pour le calcul en temps réel. L'architecture grille des GPU a été utilisée afin d'implémenter une méthode éléments finis sur maillage cartésien. Ce maillage est particulièrement adapté à la parallélisation souhaitée par les processeurs graphiques et permet un gain de temps important par rapport à un maillage conforme à la géométrie. Les formulations de la méthode des éléments finis ainsi que de la méthode des éléments finis étendue ont été reprises afin d'être adaptées à notre méthode. La méthode des éléments finis étendus permet de prendre en compte la géométrie et les interfaces à travers un choix adéquat de fonctions d'enrichissement. Cette méthode discrétise par exemple sans mailler explicitement les fissures, et évite surtout de remailler au cours de leur propagation. Des adaptations de cette méthode sont faites afin de ne pas avoir besoin d'un maillage conforme à la géométrie. La géométrie est définie implicitement par une fonction surfaces de niveau, ce qui permet une bonne approximation de la géométrie et des conditions aux limites sans pour autant s'appuyer sur un maillage conforme. La géométrie est représentée par une fonction surfaces de niveau que nous appelons la densité. La densité est supérieure à 0.5 à l'intérieur du domaine de calcul et inférieure à 0.5 à l'extérieur. Cette fonction densité, définie par ses valeurs aux points noeuds du maillage, est interpolée à l'intérieur de chaque élément. Une méthode d'intégration adaptée à cette représentation géométrique est proposée. En effet, certains éléments sont coupés par la fonction surfaces de niveau et l'intégration de la matrice de raideur ne doit se faire que sur la partie pleine de l'élément. La méthode de quadrature de Gauss qui permet d'intégrer des polynômes de manière exacte n'est plus adaptée. Nous proposons d'utiliser une méthode de quadrature avec des points d'intégration répartis sur une grille régulière et dense. L'intégration peut s'avérer coûteuse en temps de calcul, c'est pour cette raison que nous proposons une technique d'apprentissage donnant la matrice élémentaire de rigidité en fonction des valeurs de la fonction surfaces de niveau aux sommets de l'élément considéré. Cette méthode d'apprentissage permet de grandes améliorations du temps de calcul des matrices élémentaires. Les résultats obtenus après analyse par la méthode des éléments finis standard ou par la méthode des éléments finis sur maillage cartésien ont une taille qui peut croître énormément selon la complexité des modèles, ainsi que la précision des schémas de résolution. Dans un contexte de programmation sur processeurs graphiques, où la mémoire est limitée, il est intéressant d'arriver à compresser ces données. Nous nous sommes intéressés à la compression des modèles et des résultats éléments finis par la transformée en ondelettes. La compression mise en place aidera aussi pour les problèmes de stockage en réduisant la taille des fichiers générés, et pour la visualisation des données. / Generating a conformal mesh on complex geometries leads to important model size of structural finite element simulations. The meshing time is directly linked to the geometry complexity and can contribute significantly to the total turnaround time. Graphics processing units (GPUs) are highly parallel programmable processors, delivering real performance gains on computationally complex, large problems. GPUs are used to implement a new finite element method on a Cartesian mesh. A Cartesian mesh is well adapted to the parallelism needed by GPUs and reduces the meshing time to almost zero. The novel method relies on the finite element method and the extended finite element formulation. The extended finite element method was introduced in the field of fracture mechanics. It consists in enriching the basis functions to take care of the geometry and the interface. This method doesn't need a conformal mesh to represent cracks and avoids refining during their propagation. Our method is based on the extended finite element method, with a geometry implicitly defined, wich allows for a good approximation of the geometry and boundary conditions without a conformal mesh.To represent the model on a Cartesian grid, we use a level set representing a density. This density is greater than 0.5 inside the domain and less than 0.5 outside. It takes 0.5 on the boundary. A new integration technique is proposed, adapted to the geometrical representation. For the element cut by the levet set, only the part full of material has to be integrated. The Gauss quadrature is no longer adapted. We introduce a quadrature method with integration points on a cartesian dense grid.In order to reduce the computational effort, a learning approach is then considered to form the elementary stiffness matrices as function of density values on the vertices of the elements. This learning method reduces the stiffness matrices time computation. Results obtained after analysis by finite element method or the novel finite element method can have important storage size, dependant of the model complexity and the resolution scheme exactitude. Due to the limited direct memory of graphics processing units, the data results are compressed. We compress the model and the element finite results with a wavelet transform. The compression will help for storage issue and also for data visualization.