In this research, we apply modern high performance computing techniques to solve an engineering problem, structural analysis of grid stiffened panels. An existing engineering code, SPANDO, is studied and modified to execute more efficiently on high performance workstations and parallel computers. Two new SPANDO packages, a modified sequential SPANDO and parallel SPANDO, are developed. In developing the new sequential SPANDO, we use two existing high performance numerical packages: LAPACK and ARPACK to solve our linear algebra problems. Also, a new block-oriented algorithm for computing the matrix-vector multiplication w=A⁻¹Bx is developed. The experimental results show that the new sequential SPANDO can save over 70% of memory size, and is at least 10 times faster than the original SPANDO. In parallel SPANDO, ScaLAPACK and BLACS are used. There are many factors that may affect the performance of parallel SPANDO. The parallel performance and the affects of these factors are discussed in this thesis. / Master of Science

Neste trabalho foi avaliada a utilização da grid computing em aspectos importantes para simulações em Física Computacional. Em particular, para aplicações de diagonalização de matrizes de grande porte. O projeto de código aberto Globus Toolkit foi utilizado para comparar o desempenho da biblioteca paralela de álgebra linear ScaLAPACK em duas versões baseadas na biblioteca de passagem de mensagens, a versão tradicional MPICH e a versão desenvolvida para um ambiente de grid computing MPICH-G2. Várias simulações com diagonalização de matrizes complexas de diversos tamanhos foram realizadas. Para um sistema com uma matriz de tamanho 8000 x 8000 distribuída em 8 processos, nos nós de 64 bits foi alcançado um speedup de 7,71 com o MPICH-G2. Este speedup é muito próximo do ideal que, neste caso, seria igual a 8. Foi constatado também que a arquitetura de 64 bits tem melhor desempenho que a de 32 bits nas simulações executadas para este tipo de aplicação / This work evaluates the use of grid computing in essential issues related to Computational Physics simulations. In particular, for applications with large scale matrix diagonalization. The Globus Toolkit open source project was used to compare the performance of the linear algebra parallel library ScaLAPACK in two different versions based on the message passing library, the traditional version MPICH and its version developed for a grid computing environment MPICH-G2. Several simulations within large scale diagonalization of complex matrix were performed. A 7.71 speedup was reached with the MPICH-G2 for a 8000 x 8000 size matrix distributed in 8 processes on 64 bits nodes. This was very close to the ideal speedup, that would be in this case, 8. It was also evidenced that the 64 bits architecture has better performance than the 32 bits on the performed simulations for this kind of application.

Neste trabalho foi avaliada a utilização da grid computing em aspectos importantes para simulações em Física Computacional. Em particular, para aplicações de diagonalização de matrizes de grande porte. O projeto de código aberto Globus Toolkit foi utilizado para comparar o desempenho da biblioteca paralela de álgebra linear ScaLAPACK em duas versões baseadas na biblioteca de passagem de mensagens, a versão tradicional MPICH e a versão desenvolvida para um ambiente de grid computing MPICH-G2. Várias simulações com diagonalização de matrizes complexas de diversos tamanhos foram realizadas. Para um sistema com uma matriz de tamanho 8000 x 8000 distribuída em 8 processos, nos nós de 64 bits foi alcançado um speedup de 7,71 com o MPICH-G2. Este speedup é muito próximo do ideal que, neste caso, seria igual a 8. Foi constatado também que a arquitetura de 64 bits tem melhor desempenho que a de 32 bits nas simulações executadas para este tipo de aplicação / This work evaluates the use of grid computing in essential issues related to Computational Physics simulations. In particular, for applications with large scale matrix diagonalization. The Globus Toolkit open source project was used to compare the performance of the linear algebra parallel library ScaLAPACK in two different versions based on the message passing library, the traditional version MPICH and its version developed for a grid computing environment MPICH-G2. Several simulations within large scale diagonalization of complex matrix were performed. A 7.71 speedup was reached with the MPICH-G2 for a 8000 x 8000 size matrix distributed in 8 processes on 64 bits nodes. This was very close to the ideal speedup, that would be in this case, 8. It was also evidenced that the 64 bits architecture has better performance than the 32 bits on the performed simulations for this kind of application.

Due to the unpredictability in job arrival times in clusters and widely varying resource requirements, dynamic scheduling of parallel computing resources is necessary to increase system throughput. Dynamically resizable applications provide the flexibility needed for dynamic scheduling. These applications can expand to take advantage of additional free processors, or to meet a Quality of Service (QoS) deadline, or can shrink to accommodate a high priority application, without getting suspended. This thesis is part of a larger effort to define a framework for dynamically resizable parallel applications. This framework includes a scheduler that supports resizing applications, an API to enable applications to interact with the scheduler, and libraries that make resizing viable. This thesis focuses on libraries for efficient resizing of parallel applications—efficient in terms of minimizing the cost of data redistribution, choosing and allocating the right set of additional processors, and focusing on the performance of the application after resizing. We explore the tradeoffs between these goals on both homogeneous and heterogeneous clusters. We focus on structured applications that have 2D data arrays distributed across a 2D processor grid. Our library includes algorithms for processor selection and processor mapping. For homogeneous clusters, processor selection involves selecting the number of processors that needs to be added and processor mapping decides the placement of the new processors in the context of the given topology such that it minimizes the amount of data that is to be redistributed. For heterogeneous clusters, since the processing powers of the processors vary, there is also an additional problem of choosing the right set of processors that needs to be added. We also present results that demonstrate the effectiveness of our approach. / Master of Science

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Dans cette Habilitation à Diriger des Recherches (HDR), nous présentons notre recherche effectuée au cours de ces dernières années dans le domaine du calcul haute-performance. Notre travail a porté essentiellement sur les algorithmes parallèles pour les solveurs d'algèbre linéaire numérique et leur implémentation parallèle dans les bibliothèques logicielles du domaine public. Nous illustrons dans ce manuscrit comment ces calculs peuvent être accélérées en utilisant des algorithmes innovants et être rendus fiables en utilisant des quantités spécifiques de l'analyse d'erreur. Nous expliquons tout d'abord comment les solveurs d'algèbre linéaire numérique peuvent être conçus de façon à exploiter les capacités des calculateurs hétérogènes actuels comprenant des processeurs multicœurs et des GPUs. Nous considérons des algorithmes de factorisation dense pour lesquels nous décrivons la répartition des tâches entre les différentes unités de calcul et son influence en terme de coût des communications. Ces cal- culs peuvent être également rendus plus performants grâce à des algorithmes en précision mixte qui utilisent une précision moindre pour les tâches les plus coûteuses tout en calculant la solution en précision supérieure. Puis nous décrivons notre travail de recherche dans le développement de solveurs d'algèbre linéaire rapides qui utilisent des algorithmes randomisés. La randomisation représente une approche innovante pour accélérer les calculs d'algèbre linéaire et la classe d'algorithmes que nous proposons a l'avantage de réduire la volume de communications dans les factorisations en supprimant complètement la phase de pivotage dans les systèmes linéaires. Les logiciels correspondants on été développés pour architectures multicœurs éventuellement accélérées par des GPUs. Enfin nous proposons des outils qui nous permettent de garantir la qualité de la solution calculée pour les problèmes de moindres carrés sur-déterminés, incluant les moindres carrés totaux. Notre méthode repose sur la dérivation de formules exactes ou d'estimateurs pour le conditionnement de ces problèmes. Nous décrivons les algorithmes et les logiciels qui permettent de calculer ces quantités avec les bibliothèques logicielles parallèles standards. Des pistes de recherche pour les années à venir sont données dans un chapître de conclusion.