Mathematical Sciences: Workshop on the Method of Lines for Time-Dependent Problems

研究者和他的同事们组织了一个关于求解偏微分方程的直线方法的研讨会。主要的主题是常微分方程理论和应用于时变偏微分方程的线法（MOL）算法中的软件，MOL算法的理论方面，包括误差估计和稳定性考虑，MOL软件的设计和开发，MOL软件的科学和工程应用，以及现代计算机体系结构的影响，特别是分布式内存并行处理器。MOL算法的结构与实现。研讨会汇集了常微分方程和偏微分方程数值分析的新研究人员和经验丰富的研究人员，讨论他们MOL研究的相互作用。特别是，它促进了理论家、MOL软件包设计者和将MOL应用于大规模问题的研究人员之间的协作，旨在改进并行实现，并确定影响MOL算法的理论和实践约束。当前许多重要的问题，如全球气候变化或大气中污染物在地下水中的行为，都受到各种物理和化学过程的影响。这些过程可以通过数学模型来模拟。作为研究这些模型的工具，参加研讨会的研究人员正在开发先进的计算技术，用于涉及并行处理的高性能计算系统。在这种类型的计算机上，几个任务，有时多达几百个，可以同时执行。因此，解决比以前考虑的更现实、通常更复杂的模型变得可行。本次研讨会中讨论的技术所提供的计算速度使全面的模型能够为政策决策奠定更坚实的科学基础。有了这样的模型，就可以在提议的变化实际实施之前有效地预测政策变化（例如排放标准）的短期和长期影响。

The investigator and his colleagues organize a workshop on the method of lines for solving partial differential equations. Major themes are ordinary differential equation theory and software as applied in method of lines (MOL) algorithms for time-dependent partial differential equations, theoretical aspectsof MOL algorithms including error estimation and stability considerations, the design and development of MOL software, scientific and engineering applications of MOL software, and the impact of modern computer architectures, particularly distributed memory parallel processors, on the structuring and implementation of MOL algorithms. The workshop brings together both new and experienced researchers in the numerical analysis of ordinary and partial differential equations to discuss the interaction of their MOL research. In particular, it facilitates collaboration among theoreticians, designers of MOL software packages, and researchers applying the MOL to large scale problems, with the aim of improving parallel implementations, and identifying theoretical and practical constraints impacting MOL algorithms. Many issues of considerable current interest, such as global climate change or the behavior of contaminants in the atmosphereor in groundwater, are influenced by a variety of physical and chemical processes. These processes can be simulated by mathematical models solved by techniques in this workshop. As tools in the study of these models, researchers participating in the workshop are developing advanced computational techniques for use on high performance computing systems involving parallel processing. On a computer of this type, several tasks, sometimes as many as several hundred, can be executed simultaneously. As a consequence, it becomes feasible to solve more realistic, and usually more complex, models than those previously considered. The computational speed afforded by techniques discussed in this workshop permits comprehensive models that can lay a firmer scientific foundation for policy decisions. With such models, the short-and long-term effects of a change in policy, for example in emission standards, can be effectively predicted before a proposed change is actually implemented.