Pipelining the Fast Multipole Method over a Runtime System

Fast Multipole Methods (FMM) are a fundamental operation for the simulation of many physical problems. The high performance design of such methods usually requires to carefully tune the algorithm for both the targeted physics and the hardware. In this paper, we propose a new approach that achieves high performance across architectures. Our method consists of expressing the FMM algorithm as a task flow and employing a state-of-the-art runtime system, StarPU, in order to process the tasks on the different processing units. We carefully design the task flow, the mathematical operators, their Central Processing Unit (CPU) and Graphics Processing Unit (GPU) implementations, as well as scheduling schemes. We compute potentials and forces of 200 million particles in 48.7 seconds on a homogeneous 160 cores SGI Altix UV 100 and of 38 million particles in 13.34 seconds on a heterogeneous 12 cores Intel Nehalem processor enhanced with 3 Nvidia M2090 Fermi GPUs.Comment: No. RR-7981 (2012

Task-based FMM for heterogeneous architectures

International audienceHigh performance fast multipole method is crucial for the numerical simulation of many physical problems. In a previous study, we have shown that task-based fast multipole method provides the flexibility required to process a wide spectrum of particle distributions efficiently on multicore architectures. In this paper, we now show how such an approach can be extended to fully exploit heterogeneous platforms. For that, we design highly tuned graphics processing unit (GPU) versions of the two dominant operators P2P and M2L) as well as a scheduling strategy that dynamically decides which proportion of subsequent tasks is processed on regular CPU cores and on GPU accelerators. We assess our method with the StarPU runtime system for executing the resulting task flow on an Intel X5650 Nehalem multicore processor possibly enhanced with one, two, or three Nvidia Fermi M2070 or M2090 GPUs (Santa Clara, CA, USA). A detailed experimental study on two 30 million particle distributions (a cube and an ellipsoid) shows that the resulting software consistently achieves high performance across architectures

Task-based FMM for heterogeneous architectures

High performance \FMM is crucial for the numerical simulation of many physical problems. In a previous study~\cite{Agullo2013}, we have shown that task-based \FMM provides the flexibility required to process a wide spectrum of particle distributions efficiently on multicore architectures. In this paper, we now show how such an approach can be extended to fully exploit heterogeneous platforms. For that, we design highly tuned GPU versions of the two dominant operators (P2P and M2L) as well as a scheduling strategy that dynamically decides which proportion of subsequent tasks are processed on regular CPU cores and on GPU accelerators. We assess our method with the StarPU runtime system for executing the resulting task flow on an Intel X5650 Nehalem multicore processor possibly enhanced with one, two or three Nvidia Fermi M2070 or M2090 GPUs. A detailed experimental study on two 30 million particle distributions (a cube and an ellipsoid) shows that the resulting software consistently achieves high performance across architectures.Développer une méthode des Multipôles Rapide (FMM) à haute performance est cruciale pour des simulations numériques dans beaucoup de problèmes physiques. Dans une étude précédente~\cite{Agullo2013}, nous avons montré que l'utilisation d'un paradigme à base de tâches fournit la flexibilité nécessaire pour traiter efficacement un large spectre de distributions de particules sur des architectures homogènes. Dans ce document, nous montrons maintenant comment une telle approche peut être étendue pour exploiter toutes les unités de calculs (CPU et GPU) des machines hétérogènes. Pour cela, nous présentons une version optimisée pour GPU des deux opérateurs dominants (P2P et M2L) de la FMM ainsi qu'une stratégie d'ordonnancement qui décide dynamiquement quelle proportion de tâches est traitée par les cœurs CPU et par des accélérateurs GPU. Nous évaluons notre méthode avec le moteur d'exécution StarPU pour exécuter le flot de tâches résultant sur un processeur Intel X5650 Nehalem augmenté avec un, deux ou trois Nvidia Fermi M2070 ou M2090. Une étude expérimentale détaillée sur deux distributions de 30 millions de particules (un cube et un ellipsoïde) montre que nous obtenons des résultats performants sur cette architecture

Scalable Parallel Delaunay Image-to-Mesh Conversion for Shared and Distributed Memory Architectures

Mesh generation is an essential component for many engineering applications. The ability to generate meshes in parallel is critical for the scalability of the entire Finite Element Method (FEM) pipeline. However, parallel mesh generation applications belong to the broader class of adaptive and irregular problems, and are among the most complex, challenging, and labor intensive to develop and maintain. In this thesis, we summarize several years of the progress that we made in a novel framework for highly scalable and guaranteed quality mesh generation for finite element analysis in three dimensions. We studied and developed parallel mesh generation algorithms on both shared and distributed memory architectures. In this thesis we present a novel two-level parallel tetrahedral mesh generation framework capable of delivering and sustaining close to 6000 of concurrent work units (cores). We achieve this by leveraging concurrency at two different granularity levels by using a hybrid message passing and multi-threaded execution model which is suitable to the hierarchy of the hardware architecture of the distributed memory clusters. An end-user productivity and scalability study was performed on up to 6000 cores, and indicated very good end-user productivity with about 300 million tets per second and about 3600 weak scaling speedup. Both of these results suggest that: compared to the best previous algorithm, we have seen an improvement of more than 7000 times in performance, measured in terms of speed (elements per second) by using about 180 times more CPUs, for geometries that are by many orders of magnitude more complex