Eric Aubanel

Scheduling of tasks in the parareal algorithm

Parallelization of partial differential equations (PDEs) by time decomposition has attracted much interest, mainly due to its potential to enable very long time simulations beyond what is possible using spatial domain decomposition. However, there has only been limited performance analysis of the parareal algorithm in the literature, ignoring the efficient scheduling of tasks. This paper presents a detailed study of the scheduling of tasks in the parareal algorithm that achieves significantly better efficiency than the usual algorithm. Two algorithms are proposed, one which uses a manager-worker paradigm with overlap of sequential and parallel phases, and a second that is completely distributed. Experiments were conducted with the 2D heat equation. It was found that the rate of convergence decreases as the number of processors increases, in the case of strong scaling (fixed time interval). However, for weak scaling results the rate of convergence was unaffected by the number of processors. The results of this paper suggest that the parareal algorithm is a promising approach to solving long time evolution problems, particularly when the goal is simulation of longer times using more processors. It also exhibits characteristics that make it particularly suitable for execution on heterogeneous computational grids, such as low communication overhead and easy accommodation of different processor and network speeds.

PaGrid: A Mesh Partitioner for Computational Grids

Computational Grids are emerging as a new infrastructure for high performance computing. Since the resources in a Grid can be heterogeneous and distributed, mesh-based applications require a mesh partitioner that considers both processor and network heterogeneity. We have developed a heterogeneous mesh partitioner, called PaGrid. PaGrid uses a multilevel graph partitioning approach, augmented by execution time load balancing in the final uncoarsening phase. We show that minimization of total communication cost (e.g., as used by JOSTLE) can lead to significant load being placed on processors connected by slow links, which results in higher application execution times. Therefore, PaGrid balances the estimated execution time of the application across processors. PaGrid performance is compared with two existing mesh partitioners, METIS 4.0 and JOSTLE 3.0, for mapping several application meshes to two models of heterogeneous computational Grids. PaGrid is found to produce significantly better partitions than JOSTLE and slightly better partitions than METIS in most cases, in terms of estimated application execution time averaged over a large number of runs with different random number seeds.

Orbital alignment and electron control in photodissociation products by two-color laser interference

Time-dependent coupled equations are used to illustrate the laser control of the spatial orientation of diatomic photodissociation products and the concomitant orbital alignment of the electrons in the atomic fragments along the dissociation orientation. Such asymmetrical photodissociation and its control can be achieved by symmetry-breaking interference between two multiphoton pathways which produce isoenergy states of different symmetry. Conditions for this new laser control scenario are obtained for the simultaneous photodissociation of the 1 1Πu and 1 1Πg states of Cl2 by a two-color laser multiphoton absorption with subpicosecond pulses.

Experimental analysis of heuristics for the bottleneck traveling salesman problem

In this paper we develop efficient heuristic algorithms to solve the bottleneck traveling salesman problem (BTSP). Results of extensive computational experiments are reported. Our heuristics produced optimal solutions for all the test problems considered from TSPLIB, JM-instances, National TSP instances, and VLSI TSP instances in very reasonable running time. We also conducted experiments with specially constructed ‘hard’ instances of the BTSP that produced optimal solutions for all but seven problems. Some fast construction heuristics are also discussed. Our algorithms could easily be modified to solve related problems such as the maximum scatter TSP and testing hamiltonicity of a graph.

Proceedings. 19th IEEE International Parallel and Distributed Processing Symposium

HIPS-HPGC 2005 is a full-day workshop, focusing on high-performance grid computing and high-level parallel programming models. The papers deal with component models and service-based systems for grids, emphasizing on experiences with existing systems. Also the papers report on the state of the art of grid applications, both for academic and industrial problems

Electron control in photodissociation by two-color multiphoton processes☆

Numerical solutions of coupled time-dependent Schrodinger equations for multiphoton excitation of the Cl2 molecule are used to illustrate the principle of electron control in photodissociation. Thus using a symmetry breaking laser-induced interference between two multiphoton pathways which produce isoenergy states of different symmetry, we have shown that it is possible to separate atomic fragments with different electron configurations. Laser alignment by rotational pumping at high intensity enhances the separation of the products. Temperature effects are shown to destroy the asymmetry or anisotropies in the angular distributions which are essential to the separation of the distinct photofragments.

Pulse-shape effects and laser-induced avoided crossings in photodissociation

Abstract In a dressed state representation, laser-induced avoided crossings occur between field—molecule electronic surfaces giving rise to stable laser-induced resonances. It is shown that such states can be used to interpret short-pulse (subpicosecond and picosecond) induced molecular photodissociation. Time-dependent numerical calculations of photodissociation probabilities in H + 2 are used to illustrate pulse-shape effects on photodissociation. It is found that stable (long-lived) laser-induced resonances produce many kinetic energy peaks in photofragmentation, and are sensitive to pulse shapes. Short-lived resonances are insensitive to pulse details. At high intensities, nonadiabatic effects due to pulse-shape variation dominate.

Mesh partitioners for computational grids: a comparison

Computational grids are emerging as a new infrastructure for high performance computing. Since the resources in a grid can be heterogeneous and distributed, mesh-based applications may require a mesh partitioner that considers both processor and network heterogeneity. We have developed a heterogeneous mesh partitioner, called PaGrid. PaGrid uses a multilevel graph partitioning approach, augmented by execution time load balancing in the final uncoarsening phase. We propose that estimated execution time of the application is a better metric for the performance of a mesh partitioner than communication cost. The main objective of this paper is to compare the performance of PaGrid with two existing mesh partitioners, METIS 4.0 and Jostle 3.0, for mapping applications to a heterogeneous computational grid. We have found that PaGrid produces comparable or better partitions than Jostle. Although the performance of METIS is worse, in terms of total communication cost, than PaGrid and Jostle, it is comparable to them in terms of the estimated execution time of the application.

The impact of heterogeneous multi-core clusters on graph partitioning: an empirical study

The advent of multi-core architectures provides an opportunity for accelerating parallelism in mesh-based applications. This multi-core environment, however, imposes challenges not addressed by conventional graph-partitioning techniques that are originally designed for distributed-memory uniprocessors. As the first step to exploit the multi-core platform, this paper presents experimental evaluation to understand partitioning performance on small-scaled heterogeneous multi-core clusters. With results and analyses gathered, we propose a hierarchical framework for resource-aware graph partitioning on heterogeneous multi-core clusters. Preliminary evaluation demonstrates the potential of the framework and motivates directions for incorporating application requirements into graph partitioning.

Incorporating Latency in Heterogeneous Graph Partitioning

Parallel applications based on irregular meshes make use of mesh partitioners for efficient execution. Some mesh partitioners can map a mesh to a heterogeneous computational platform, where processor and network performance may vary. Such partitioners generally model the computational platform as a weighted graph, where the weight of a vertex gives relative processor performance, and the weight of a link indicates the relative transmission rate of the link between two processors. However, the performance of a network link is typically characterized by two parameters, bandwidth and latency, which cannot be captured in a single weight. We show that taking into account the network heterogeneity of a computational resource can significantly improve the quality of a domain decomposition obtained using graph partitioning. Furthermore, we show that taking into account bandwidth and latency of the network links is significantly better than just considering the former. This work is presented as an extension to the PaGridpartitioner, and includes a model for estimated execution time, which is used as a cost function by the partitioner but could also be used for performance prediction by application-oriented schedulers.