This study presented a substructure based parallel linear solution framework for the static analysis of linear structural engineering problems having multiple loading conditions. The framework was composed of two separate programs designed to work on PC Clusters having the Windows operating system. The first program was responsible for creating the optimum substructures for the parallel solution and first partitioned the structure in such a way that the number of substructures was equal to the number of processors. Then, the estimated condensation time imbalance of the initial substructures was adjusted by iteratively transferring nodes from the substructures with slower estimated condensation times to the substructures with faster estimated condensation times. Once the final substructures were created, the second program started the solution. Each processor assembled its substructures stiffness matrix and condensed it to the interface with other substructures. The interface problem was solved by a parallel variable band solver. After computing the interface unknowns, each processor calculated the internal displacements and element stresses or forces. Examples which illustrate the applicability and efficiency of this approach were also presented. In these examples, the number of processors was varied from one to twelve to demonstrate the performance of the overall solution framework.

Cette thèse traite du problème de la redistribution dynamique parallèle efficace de la charge pour les problèmes numériques de très grande taille. Nous présentons tout d'abord un état de l'art des algorithmes permettant de résoudre les problèmes du partitionnement, du repartitionnement, du placement statique et du re-placement. Notre première contribution vise à étudier, dans un cadre séquentiel, les caractéristiques algorithmiques souhaitables pour les méthodes parallèles de repartitionnement. Nous y présentons notre contribution à la conception d'un schéma multi-niveaux k-aire pour le calcul sequentiel de repartitionnements. La partie la plus exigeante de cette adaptation concerne la phase d'expansion. L'une de nos contributions majeures a été de nous inspirer des méthodes d'influence afin d'adapter un algorithme de raffinement par diffusion au problème du repartitionnement.Notre deuxième contribution porte sur la mise en oeuvre de ces méthodes sur machines parallèles. L'adaptation du schéma multi-niveaux parallèle a nécessité une évolution des algorithmes et des structures de données mises en oeuvre pour le partitionnement. Ce travail est accompagné d'une analyse expérimentale, qui est rendue possible grâce à la mise en oeuvre des algorithmes considérés au sein de la bibliothèque Scotch. / This thesis concerns efficient parallel dynamic load balancing for large scale numerical problems. First, we present a state of the art of the algorithms used to solve the partitioning, repartitioning, mapping and remapping problems. Our first contribution, in the context of sequential processing, is to define the desirable features that parallel repartitioning tools need to possess. We present our contribution to the conception of a k-way multilevel framework for sequential repartitioning. The most challenging part of this work regards the uncoarsening phase. One of our main contributions is the adaptation of influence methods to a global diffusion-based heuristic for the repartitioning problem. Our second contribution is the parallelization of these methods. The adaptation of the aforementioned algorithms required some modification of the algorithms and data structure used by existing parallel partitioning routines. This work is backed by a thorough experimental analysis, which is made possible thanks to the implementation of our algorithms into the Scotch library.

L'équilibrage de charge est une étape importante conditionnant les performances des applications parallèles. Dans le cas où la charge varie au cours de la simulation, il est important de redistribuer régulièrement la charge entre les différents processeurs. Dans ce contexte, il peut s'avérer pertinent d'adapter le nombre de processeurs au cours d'une simulation afin d'obtenir une meilleure efficacité, ou de continuer l'exécution quand toute la mémoire des ressources courantes est utilisée. Contrairement au cas où le nombre de processeurs ne varie pas, le rééquilibrage dynamique avec un nombre variable de processeurs est un problème peu étudié que nous abordons ici.Cette thèse propose différentes méthodes basées sur le repartitionnement de graphe pour rééquilibrer la charge tout en changeant le nombre de processeurs. Nous appelons ce problème « repartitionnement M x N ». Ces méthodes se décomposent en deux grandes étapes. Dans un premier temps, nous étudions la phase de migration et nous construisons une « bonne » matrice de migration minimisant plusieurs critères objectifs comme le volume total de migration et le nombre total de messages échangés. Puis, dans un second temps, nous utilisons des heuristiques de partitionnement de graphe pour calculer une nouvelle distribution optimisant la migration en s'appuyant sur les résultats de l'étape précédente. En outre, nous proposons un algorithme de partitionnement k-aire direct permettant d'améliorer le partitionnement biaisé. Finalement, nous validons cette thèse par une étude expérimentale en comparant nos méthodes aux partitionneursactuels. / Load balancing is an important step conditioning the performance of parallel programs. If the workload varies drastically during the simulation, the load must be redistributed regularly among the processors. Dynamic load balancing is a well studied subject but most studies are limited to an initially fixed number of processors. Adjusting the number of processors at runtime allows to preserve the parallel code efficiency or to keep running the simulation when the memory of the current resources is exceeded.In this thesis, we propose some methods based on graph repartitioning in order to rebalance the load while changing the number of processors. We call this problem \M x N repartitioning". These methods are split in two main steps. Firstly, we study the migration phase and we build a \good" migration matrix minimizing several metrics like the migration volume or the number of exchanged messages. Secondly, we use graph partitioning heuristics to compute a new distribution optimizing the migration according to the previous step results. Besides, we propose a direct k-way partitioning algorithm that allows us to improve our biased partitioning. Finally, an experimental study validates our algorithms against state-of-the-art partitioning tools.

This thesis describes the development a new swarm-enhanced sampling methodology and its application to the exploration of biologically relevant molecules. First, the development of a new multi-dimensional swarm-enhanced sampling molecular dynamics (msesMD) approach is detailed. Relative to the original swarm-enhanced sampling molecular dynamics (sesMD) methodology, the msesMD method demonstrates improved parameter transferability, resulting in more extensive sampling when scaling to larger systems such as alanine heptapeptide. The implementation and optimisation of the swarm-enhanced sampling algorithms in the AMBER software suite are also described. Through the use of the newer pmemd molecular dynamics (MD) engine and asynchronous MPI routines, speedups of up to three times the original sesMD implementation were achieved. The msesMD method is then applied to the investigation of carbohydrates, first looking at rare conformational changes in Lewis oligosaccharides. Validating against multi-microsecond unbiased MD trajectories and other enhanced sampling methods, the msesMD simulations identified rare conformational changes leading to the adoption of non-canonical unstacked core trisaccharide structures. Next, the use of msesMD as a tool to probe pyranose ring pucker events is explored. Evaluating against four benchmark monosaccharide systems, msesMD simulations accurately recover puckering details not easily obtained via multi-microsecond unbiased MD. This was followed by an exploration of the impact of ring substituents on conformation in glycosaminoglycan monosaccharides: through msesMD simulations, the influence of specific sulfation patterns were explored, finding that in some cases, such as 4-O-sulfation in N-acetyl-galactosamine, large changes in the relative stability of ring conformers can arise. Finally, the msesMD method was coupled with a thermodynamic integration scheme and used to evaluate solvation free energies for small molecule systems. Comparing against independent trajectory TI simulations, it was found that although the correct solvation free energies were obtained, the msesMD based method did not offer an advantage over unbiased MD for these small molecule systems. However, interesting discrepancies in free energy estimates arising from the use of hydrogen mass repartitioning were found.