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In the past decade we have witnessed an abrupt shift to parallel computing subsequent to the increasing demand for performance and functionality that can no longer be satisfied by conventional paradigms. As a consequence, the abstraction gab between the applications and the underlying hardware increased, triggering both industry and academia in several research directions. This thesis project aims at analyzing some of these directions in order to offer a solution for bridging the abstraction gap between the description of a problem at a functional level and the implementation on a heterogeneous parallel platform using ForSyDe – a formal design methodology. This report treats applications employing data-parallel and time-parallel computation, regards nvidia CUDA-enabled GPGPUs as the main backend platform. The report proposes a heuristic transformation-and-refinement process based on analysis methods and design decisions to automate and aid in a correct-by-design backend code synthesis. Its purpose is to identify potential data parallelism and time parallelism in a high-level system. Furthermore, based on a basic platform model, the algorithm load-balances and maps the execution onto the best computation resources in an automated design flow. This design flow will be embedded into an already existing tool, f2cc (ForSyDe-to-CUDA C) and tested for correctness on an industrial-scale image processing application aimed at monitoring inkjet print-heads reliability.

In a heterogeneous mobile ad hoc network (MANET), assorted devices with different computation and communication capabilities co-exist. In this thesis, we consider the case when the nodes of a MANET have various degrees of mobility and range, and the communication links are asymmetric. Many routing protocols for ad hoc networks routinely assume that all communication links are symmetric, if node A can hear node B and node B can also hear node A. Most current MAC layer protocols are unable to exploit the asymmetric links present in a network, thus leading to an inefficient overall bandwidth utilization, or, in the worst case, to lack of connectivity. To exploit the asymmetric links, the protocols must deal with the asymmetry of the path from a source node to a destination node which affects either the delivery of the original packets, or the paths taken by acknowledgments, or both. Furthermore, the problem of hidden nodes requires a more careful analysis in the case of asymmetric links. MAC layer and routing protocols for ad hoc networks with asymmetric links require a rigorous performance analysis. Analytical models are usually unable to provide even approximate solutions to questions such as end-to-end delay, packet loss ratio, throughput, etc. Traditional simulation techniques for large-scale wireless networks require vast amounts of storage and computing cycles rarely available on single computing systems. In our search for an effective solution to study the performance of wireless networks we investigate the time-parallel simulation. Time-parallel simulation has received significant attention in the past. The advantages, as well as, the theoretical and practical limitations of time-parallel simulation have been extensively researched for many applications when the complexity of the models involved severely limits the applicability of analytical studies and is unfeasible with traditional simulation techniques. Our goal is to study the behavior of large systems consisting of possibly thousands of nodes over extended periods of time and obtain results efficiently, and time-parallel simulation enables us to achieve this objective. We conclude that MAC layer and routing protocols capable of using asymmetric links are more complex than traditional ones, but can improve the connectivity, and provide better performance. We are confident that approximate results for various performance metrics of wireless networks obtained using time-parallel simulation are sufficiently accurate and able to provide the necessary insight into the inner workings of the protocols.

Les méthodes de décomposition de domaine en espace ont prouvé leur utilité dans le cadre des architectures parallèles. Pour les problèmes d’évolution en temps, il est nécessaire d’introduire une dimension supplémentaire de parallélisme dans la direction du temps. Ceci peut alors être couplé avec des méthodes de type optimisé Schwarz waveform relaxation. Nous nous intéressons dans cette thèse aux méthodes directes de décomposition en temps. Nous en étudions particulièrement deux. Dans une première partie nous étudions la méthode de produit tensoriel, introduite par R. E. Lynch, J. R. Rice, et D. H. Thomas in 1963. Nous proposons une méthode d’optimisation des pas de temps, basée sur une étude d’erreur en variable de Fourier en temps. Nous menons cette étude sur les schémas d’Euler et de Newmark pour la discrétisation en temps de l’équation de la chaleur. Nous présentons ensuite des tests numériques établissant la validité de cette approche. Dans la seconde partie, nous étudions les méthodes dites de Bloc, introduites par Amodio et Brugnano en 1997. Nous comparons diverses implémentations de la méthode, basées sur différentes approximations de l’exponentielle de matrice. Nous traitons l’équation de la chaleur et l’équation des ondes, et montrons par une étude numérique bidimensionnelle la puissance de la méthode. / Domain decomposition methods in space applied to Partial Differential Equations (PDEs) expanded considerably thanks to their effectiveness (memory costs, calculation costs, better local conditioned problems) and this related to the development of massively parallel machines. Domain decomposition in space-time brings an extra dimension to this optimization. In this work, we study two different direct time-parallel methods for the resolution of Partial Differential Equations. The first part of this work is devoted to the Tensor-product space-time method introduced by R.E. Lynch, J. R. Rice, and D. H. Thomas in 1963. We analyze it in depth for Euler and Crank-Nicolson schemes in time applied to the heat equation. The method needs all time steps to be different, while accuracy is optimal when they are all equal (in the Euler case). Furthermore, when they are close to each other, the condition number of the linear problems involved becomes very big. We thus give for each scheme an algorithm to compute optimal time steps, and present numerical evidences of the quality of the method. The second part of this work deals with the numerical implementation of the Block method of Amodio and Brugnano presented in 1997 to solve the heat equation with Euler and Crank- Nicolson time schemes and the elasticity equation with Euler and Gear time schemes. Our implementation shows how the method is accurate and scalable.

This study is concerned with the numerical solution of certain stochastic models of chemical reactions. Such descriptions have been shown to be useful tools when studying biochemical processes inside living cells where classical deterministic rate equations fail to reproduce actual behavior. The main contribution of this thesis lies in its theoretical and practical investigation of different methods for obtaining numerical solutions to such descriptions. In a preliminary study, a simple but often quite effective approach to the moment closure problem is examined. A more advanced program is then developed for obtaining a consistent representation of the high dimensional probability density of the solution. The proposed method gains efficiency by utilizing a rapidly converging representation of certain functions defined over the semi-infinite integer lattice. Another contribution of this study, where the focus instead is on the spatially distributed case, is a suggestion for how to obtain a consistent stochastic reaction-diffusion model over an unstructured grid. Here it is also shown how to efficiently collect samples from the resulting model by making use of a hybrid method. In a final study, a time-parallel stochastic simulation algorithm is suggested and analyzed. Efficiency is here achieved by moving parts of the solution phase into the deterministic regime given that a parallel architecture is available. Necessary background material is developed in three chapters in this summary. An introductory chapter on an accessible level motivates the purpose of considering stochastic models in applied physics. In a second chapter the actual stochastic models considered are developed in a multi-faceted way. Finally, the current state-of-the-art in numerical solution methods is summarized and commented upon.

Une large classe de méthodes numériques possède une propriété d’échelonnabilité connue comme étant la loi d’Amdahl. Elle constitue l’inconvénient majeur limitatif du calcul parallèle, en ce sens qu’elle établit une borne supérieure sur le nombre d’unités de traitement parallèles qui peuvent être utilisées pour accélérer un calcul. Des activités de recherche sont donc largement conduites à la fois sur les plans mathématiques et informatiques, pour repousser cette limite afin d’être en mesure de tirer le maximum des machines parallèles. Les méthodes de décomposition de domaine introduisent une approche naturelle et optimale pour résoudre de larges problèmes numériques de façon distribuée. Elles consistent en la division du domaine géométrique sur lequel une équation est définie, puis le traitement itératif de chaque sous-domaine, séparément, tout en assurant la continuité de la solution et de sa dérivée sur leur interface de jointure. Dans le présent travail, nous étudions la suppression de la limite d’accélération en appliquant des itérations asynchrones dans différents cadres de décomposition, à la fois de domaines spatiaux et temporels. Nous couvrons plusieurs aspects du développement d’algorithmes asynchrones, de l’analyse théorique de convergence à la mise en oeuvre effective. Nous aboutissons ainsi à des méthodes asynchrones efficaces pour la décomposition de domaine, ainsi qu’à une nouvelle bibliothèque de communication pour l’expérimentation asynchrone rapide d’applications scientifiques existantes. / An important class of numerical methods features a scalability property well known as the Amdahl’s law, which constitutes the main limiting drawback of parallel computing, as it establishes an upper bound on the number of parallel processing units that can be used to speed a computation up. Extensive research activities are therefore conducted on both mathematical and computer science aspects to increase this bound, in order to be able to squeeze the most out of parallel machines. Domain decomposition methods introduce a natural and optimal approach to solve large numerical problems in a distributed way. They consist in dividing the geometrical domain on which an equation is defined, then iteratively processing each sub-domain separately, while ensuring the continuity of the solution and of its derivative across the junction interface between them. In the present work, we investigate the removal of the scalability bound by the application of the asynchronous iterations theory in various decomposition frameworks, both for space and time domains. We cover various aspects of the development of asynchronous iterative algorithms, from theoretical convergence analysis to effective parallel implementation. Efficient asynchronous domain decomposition methods are thus successfully designed, as well as a new communication library for the quick asynchronous experimentation of existing scientific applications.