Parallel and Distributed Integration Algorithms

数值积分在科学和工程的各个领域有许多应用。计算密集的多重积分出现在诸如原子和核物理学、统计学和感官数据分析等领域。本课题设计、分析和开发了一套用于多元数值积分的粗粒度并行分布式算法。主要关注的是在分布式队列管理系统上分层的自适应集成策略。实现的目标是松耦合系统。自适应积分是求解中低维区域积分的主要工具。队列管理将子区域（任务）的插入和删除合并到分布式任务池中，同时在本地队列中保留均衡或近似均衡的负载。它将适应问题以及处理器的类型和松耦合系统中的通信速度。对于低维，将特别注意使用（近）最优度规则和专门用于处理特定积分问题（如奇点或特定权函数）的技术。数论方法将包括高维，不规则区域或不规则函数行为。＊＊＊

9405377 deDoncker Numerical integration has many applications in various areas of science and engineering. Computationally intensive multiple integrals arise in areas such as atomic and nuclear physics, statistics and the analysis of sensory data. This project involves the design, analysis and development of a set of coarse grain parallel and distributed algorithms for multivariate numerical integration. The main focus is on adaptive integration strategies layered over a system for distributed queue management. Implementations are targeted to loosely coupled systems. Adaptive integration is used as the main tool for integrals over regions of low to moderate dimension. The queue management incorporates the insertion and deletion of subregions (tasks) into and from the distributed task pool while retaining balanced or approximately balanced loads in the local queues. It will be adapted to the problem as well as the types of processors and the speed of communications in the loosely coupled system. For low dimensionality special attention will be paid to the use of (near) optimal degree rules and techniques dedicated to the treatment of specific integration problems such as singularities or particular weight functions. Number theoretic methods will be included for high dimensions, irregular regions or erratic function behavior. ***