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

调查员和他的同事组织了一个研讨会的方法线解决偏微分方程。 主要的主题是常微分方程理论和软件应用于线法（MOL）算法的时间依赖偏微分方程，MOL算法的理论方面，包括误差估计和稳定性的考虑，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，特别是分布式存储器并行处理器，对MOL算法的结构和实现。 该研讨会汇集了新的和有经验的研究人员在数值分析的常微分方程和偏微分方程，讨论他们的MOL研究的相互作用。 特别是，它促进了理论家，MOL软件包的设计者和研究人员之间的合作，应用MOL到大规模的问题，以提高并行实现的目的，并确定影响MOL算法的理论和实践约束。 许多当前非常感兴趣的问题，如全球气候变化或大气或地下水中污染物的行为，都受到各种物理和化学过程的影响。 这些过程可以通过本研讨会中的技术解决的数学模型来模拟。 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，可以同时执行多个任务，有时多达数百个。 因此，它变得可行，以解决更现实的，通常更复杂的，比以前考虑的模型。 本研讨会中讨论的技术所提供的计算速度允许建立全面的模型，为政策决策奠定更坚实的科学基础。 有了这些模型，在实际实施拟议的改变之前，可以有效地预测政策改变（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.