The fast and accurate solution of large size sparse systems of linear equations is at the heart of numerical applications from a very broad range of domains including structural mechanics, fluid dynamics, geophysics, medical imaging, chemistry. Among the most commonly used techniques, direct methods, based on the factorization of the system matrix, are generally appreciated for their numerical robustness and ease of use. These advantages, however, come at the price of a considerable operations count and memory footprint. The work presented in this thesis is concerned with improving the scalability of sparse direct solvers, intended as the ability to solve problems of larger and larger size. More precisely, our work aims at developing solvers which are scalable in performance, memory consumption and complexity. We address performance scalability, that is the ability to reduce the execution time as more computational resources are available, introducing algorithms that improve parallelism by reducing communications and synchronizations. We discuss the use of novel parallel programming paradigms and tools to achieve their implementation in an efficient and portable way on modern, heterogeneous supercomputers. We present methods that make sparse direct solvers memory-scalable, that is, capable of taking advantage of parallelism without increasing the overall memory footprint. Finally we show how it is possible to use data sparsity to achieve an asymptotic reduction of the cost of such methods. The presented algorithms have been implemented in the freely distributed MUMPS and qr_mumps solver packages and their effectiveness assessed on reallife problems from academic and industrial applications.

https://hal.archives-ouvertes.fr/tel-01913033/document

Scalability of parallel sparse direct solvers: methods, memory and performance

Les methodes iteratives de Krylov sont utilisees sur les plate-formes de Calcul Haute Performance (CHP) pour resoudre les grands systemes lineaires issus des domaines de la science et de l’ingenierie. Avec l’augmentation du nombre de cœurs et de l’heterogeneite des superordinateurs, le temps consacre a la communication et synchronisation globales nuit gravement aux leurs performances paralleles. La programmation tend a etre distribuee et parallele. Le developpement d’algorithmes devrait prendre en compte les principes: 1) parallelisme avec multi-granularite; 2) memoire hierarchique; 3) minimisation de la communication globale; 4) promotion de l’asynchronicite; 5) proposition de strategies d’ordonnancement et de moteurs de gestion pour gerer les trafics et la tolerance aux pannes. En reponse a ces objectifs, nous presentons un paradigme de programmation multi-niveaux distribues et paralleles pour les methodes de Krylov sur les plates-formes de CHP. La premiere partie porte sur la mise en œuvre d’un generateur de matrices avec des valeurs propres prescrites pour la reference des methodes iteratives. Dans la deuxieme partie, nous etudions les performances numeriques et paralleles de la methode iterative proposee. Son implementation avec un moteur de gestion peut gerer la communication, la tolerance aux pannes et la reutilisabilite. Dans la troisieme partie, un schema de reglage automatique est introduit pour la selection intelligente de ses parametres lors de l’execution. Enfin, nous etudions la possibilite d’implementer ce paradigme dans un environnement d’execution de flux de travail.

Contribution à l’émergence de nouvelles méthodes parallèles et réparties intelligentes utilisant un paradigme de programmation multi-niveaux pour le calcul extrême

The Japanese-french project FP3C targets the post-petascale and the next generation of exascale systems. Its goal is to study the software technologies, languages and programming models to achieve the performance promised by post-petascale computing. The project consortium regroups some of the HPC key players in Japan and in France: * Universities of Kyoto, Tokyo and Tsukuba, Tokyo Institute of Technology, Japanese- French Laboratory on Informatics * CEA Saclay, CNRS (IRIT and PRISM), INRIA (Bordeaux, Rennes and Saclay), with a strong connection with RIKEN AICS at Kobe in Japan. The ability to efficiently program and exploit these future high performance systems is considered as a strategical issue by all research national agencies worldwide. The exascale computers are expected to a large-scale highly hierarchical architecture with many-core processsors possibly mixed with accelerators with up to millions of cores and threads. As a consequence, existing operating and runtime systems, languages, programming paradigms and parallel algorithms would have, at best, to be adapted, and may become often obsolete. Exploiting these ultra large-scale parallelsystems will require runtime systems allowing the management of huge amount of distributed data, minimizing the energy consumption, and exhibiting fault resilient properties. In addition to these features, accelerating technology, based on GPGPU and many-core processors, are also crucial issues for post-petascale computing systems. Efficient exploitation (programing, execution) of large scale systems is an important challenge. The hierarchical nature of these architecture and the scalability issues (parallelization at different level: intra / inter computational nodes composed of many core processors and/or accelerators) complexifies the algorithm design. Existing programming framework and runtime systems together with new approaches should be examined, experimented andevaluated. Benchmarks and libraries adapted to the post-petascale systems will have to be proposed. The FP3C project aims at defining a framework for high performance computing on the road to exascale. We cover most of the issues related to the emergence of post- petascale computing: from high level languages to efficient exploitation of the underlying architecture at the runtime level or using specific extensions for accelerators. Our approach is illustrated with experiments on a set of numerical codes (including numerical libraries) that can be seen as a benchmark. One of the goal of the project is to proceed to experiments on some of the most recent computers available in Europe (e.g. CURIE Computer at TGCC/France) and in Japan (e.g. K Computer at Kobe).

/pdf/towards-exascale-with-the-anr-jst-japanese-french-project-wsuw4qblkt.pdf

Towards exascale with the ANR-JST japanese-french project FP3C (Framework and Programming for Post- Petascale Computing)

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Towards exascale with the ANR-JST japanese-french project FP3C (Framework and Programming for Post- Petascale Computing)