Parallelization of direct algorithms using multisplitting methods in grid environments

The goal of this paper is to introduce a new approach to the building of efficient distributed linear system solvers. The starting point of the results of this paper lies in the fact that the parallelization of direct algorithms requires frequent synchronizations in order to obtain the solution for a linear problem. In a grid computing environment, communication times are significant and the bandwidth is variable, therefore frequent synchronizations slow down performances. Thus it is desirable to reduce the number of synchronizations in a parallel direct algorithm. Inspired from multisplitting techniques, the method we present consists in solving several linear problems obtained by splitting the original one. Each linear system is solved independently on a cluster by using the direct method. This paper uses the theoretical results of \cite{BMR97} in order to build coarse grained algorithms designed for solving linear systems in the grid computing context

A bibliography on parallel and vector numerical algorithms

This is a bibliography of numerical methods. It also includes a number of other references on machine architecture, programming language, and other topics of interest to scientific computing. Certain conference proceedings and anthologies which have been published in book form are listed also

Parallel and Multistep Simulation of Power System Transients

RÉSUMÉ La simulation des régimes transitoires électromagnétiques (EMT) est devenue indispensable aux ingénieurs dans de nombreuses études des réseaux électriques. L’approche EMT a une nature de large bande et est applicable aux études des transitoires lents (électromécaniques) et rapides (électromagnétiques). Cependant, la complexité des réseaux électriques modernes qui ne cesse de s’accroître, particulièrement des réseaux avec des interconnexions HVDC et des éoliennes, augmente considérablement le temps de résolution dans les études des transitoires électromagnétiques qui exigent la résolution précise des systèmes d’équations différentielles et algébriques avec un pas de calcul pré-déterminé. En tant que sujet de recherche, la réduction du temps de résolution des grands réseaux électriques complexes a donc attiré beaucoup d’attention et d’intérêt. Cette thèse a pour objectif de proposer de nouvelles méthodes numériques qui sont efficaces, flexibles et précises pour la simulation des régimes transitoires électromagnétiques des réseaux électriques. Dans un premier temps, une approche parallèle et à pas multiples basée sur la norme Functional Mock-up Interface (FMI) pour la simulation transitoire des réseaux électriques avec systèmes de contrôle complexes est développée. La forme de co-simulation de la norme FMI dont l’objectif est de faciliter l’échange de données entre des modèles développés avec différents logiciels est implémentée dans EMTP. Tout en profitant de cette implémentation, les différents systèmes de contrôle complexes peuvent être découplés du réseau principal en mémoire et résolus de façon indépendante sur des processeurs séparés. Ils communiquent avec le réseau principal à travers une interface de co-simulation pendant une simulation. Cette méthodologie non seulement réduit la charge de calcul total sur un seul processeur, mais elle permet aussi de simuler les systèmes de contrôle découplés de façon parallèle et à pas multiples. Deux modes de co-simulation sont proposés dans la première étape du développement, qui sont les modes asynchrone et synchrone. Dans le mode asynchrone, tous les systèmes de contrôle découplés (esclaves) sont simulés en parallèle avec le réseau principal (maître) en utilisant un seul pas de calcul tandis que le mode synchrone permet une simulation séquentielle en utilisant différents pas de calcul dans le maître et les esclaves. La communication entre le maître et les esclaves est réalisée et coordonnée par des fonctions qui implémentent le primitif de synchronisation de bas niveau sémaphore.----------ABSTRACT The simulation of electromagnetic transients (EMT) has become indispensable to utility engineers in a multitude of studies in power systems. The EMT approach is of wideband nature and applicable to both slower electromechanical as well as faster electromagnetic transients. However, the ever-growing complexity of modern-day power systems, especially those with HVDC interconnections and wind generations, considerably increases computational time in EMT studies which require the accurate solution of usually large sets of differential and algebraic equations (DAEs) with a pre-determinded time-step. Therefore, computing time reduction for solving complex, practical and large-scale power system networks has become a hot research topic. This thesis proposes new fast, flexible and accurate numerical methods for the simulation of power system electromagnetic transients. As a first step in this thesis, a parallel and multistep approach based on the Functional Mock-up Interface (FMI) standard for power system EMT simulations with complex control systems is developed. The co-simulation form of the FMI standard, a tool independent interface standard aiming to facilitate data exchange between dynamic models developed in different simulation environments, is implemented in EMTP. Taking advantage of the compatibility established between the FMI standard and EMTP, various computationally demanding control systems can be decoupled from the power network in memory, solved independently on separate processors, and communicate with the power network through a co-simulation interface during a simulation. This not only reduces the total computation burden on a single processor, but also allows parallel and multistep simulation for the decoupled control systems. Following a master-slave co-simulation scheme (with the master representing the power network and the slaves denoting the decoupled control systems), two co-simulation modes, which are respectively the asynchronous and synchronous modes, are proposed in the first stage of the development. In the asynchronous mode, all decoupled subsystems are simulated in parallel with a single numerical integration time-step whereas the synchronous mode allows the use of different numerical time-steps in a sequential co-simulation environment. The communication between master and slaves is coordinated by functions employing the low-level synchronization primitive semaphore

Resilience for Asynchronous Iterative Methods for Sparse Linear Systems

Large scale simulations are used in a variety of application areas in science and engineering to help forward the progress of innovation. Many spend the vast majority of their computational time attempting to solve large systems of linear equations; typically arising from discretizations of partial differential equations that are used to mathematically model various phenomena. The algorithms used to solve these problems are typically iterative in nature, and making efficient use of computational time on High Performance Computing (HPC) clusters involves constantly improving these iterative algorithms. Future HPC platforms are expected to encounter three main problem areas: scalability of code, reliability of hardware, and energy efficiency of the platform. The HPC resources that are expected to run the large programs are planned to consist of billions of processing units that come from more traditional multicore processors as well as a variety of different hardware accelerators. This growth in parallelism leads to the presence of all three problems. Previously, work on algorithm development has focused primarily on creating fault tolerance mechanisms for traditional iterative solvers. Recent work has begun to revisit using asynchronous methods for solving large scale applications, and this dissertation presents research into fault tolerance for fine-grained methods that are asynchronous in nature. Classical convergence results for asynchronous methods are revisited and modified to account for the possible occurrence of a fault, and a variety of techniques for recovery from the effects of a fault are proposed. Examples of how these techniques can be used are shown for various algorithms, including an analysis of a fine-grained algorithm for computing incomplete factorizations. Lastly, numerous modeling and simulation tools for the further construction of iterative algorithms for HPC applications are developed, including numerical models for simulating faults and a simulation framework that can be used to extrapolate the performance of algorithms towards future HPC systems

Efficient Solvers for the Phase-Field Crystal Equation: Development and Analysis of a Block-Preconditioner

A preconditioner to improve the convergence properties of Krylov subspace solvers is derived and analyzed in this work. This method is adapted to linear systems arising from a finite-element discretization of a phase-field crystal equation