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Abstract. This paper describes how the specific access structure of the Brusselator equation, a typical example for ordinary differential equations (ODEs) derived by the method of lines, can be exploited to obtain scalable distributed-memory implementations of explicit Runge-Kutta (RK) solvers. These implementations need less communication and therefore achieve better speed-ups than general explicit RK implementations. Particularly, we consider implementations based on a pipelining computation scheme leading to an improved locality behavior.

SUMMARYSince a static work distribution does not allow for satisfactory speed-ups of parallel irregular algorithms, there is a need for a dynamic distribution of work and data that can be adapted to the runtime behavior of the algorithm. Task pools are data structures which can distribute tasks dynamically to different processors where each task specifies computations to be performed and provides the data for these computations. This paper discusses the characteristics of task-based algorithms and describes the implementation of selected types of task pools for shared-memory multiprocessors. Several task pools have been implemented in C with POSIX threads and in Java. The task pools differ in the data structures to store the tasks, the mechanism to achieve load balance, and the memory manager used to store the tasks. Runtime experiments have been performed on three different shared-memory systems using a synthetic algorithm, the hierarchical radiosity method, and a volume rendering algorithm.

The estimation and evaluation of the energy consumption of computers is becoming an important issue. In this article, we address the question how the energy consumption for computations can be captured by an analytical energy consumption model. In particular, we address the possibility to reduce the energy consumption by dynamic frequency scaling and model this energy reduction in the context of task execution models. We demonstrate the use of the model by simulating task executions and their energy consumption.

A task-based execution provides a universal approach to dynamic load balancing for irregular applications. Tasks are arbitrary units of work that are created dynamically at runtime and that are stored in a parallel data structure, the task pool, until they are scheduled onto a processor for execution. In this paper, we evaluate the performance of different task pool implementations for shared-memory computer systems using several realistic applications. We consider task pools with different data structures, different load balancing strategies and a specialized memory management. In particular, we use synchronization operations based on hardware support that is available on many modern microprocessors. We show that the resulting task pool implementations lead to a much better performance than implementations using Pthreads library calls for synchronization. The applications considered are parallel quicksort, volume rendering, ray tracing, and hierarchical radiosity. The target machines are an IBM p690 server and a SunFire 6800.

SUMMARYBecause of environmental and monetary concerns, it is increasingly important to reduce the energy consumption in all areas, including parallel and high performance computing. In this article, we propose an approach to reduce the energy consumption needed for the execution of a set of tasks computed in parallel in a fork-join fashion. The approach consists of an analytical model for the energy consumption of a parallel computation in fork-join form on dynamic voltage frequency scaling processors, a theoretical specification of an energy-optimal frequency-scaled state, and the energy minimization by computing optimal scaling factors. For larger numbers of tasks, the approach is extended by scheduling algorithms, which exploit the analytical result and aim at a reduction of the energy. Energy measurements of a complex numerical method and the SPEC CPU2006 benchmarks as well as simulations for a large number of randomly generated tasks illustrate and validate the energy modeling, the minimization, and the scheduling results.

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