Scalable Parallel Algorithms for Partial Differential Equations

偏微分方程组的可伸缩并行算法摘要偏微分方程组的可伸缩算法在计算科学和工程中起着关键作用。随着当今超级计算机中处理器数量的快速增长，可伸缩性成为算法设计中最重要的问题之一。在过去的几年里，这一领域的研究取得了巨大的进展。这次会议汇集了来自世界各地的这一领域的专家，讨论了可伸缩算法的最新发展，并向年轻的研究人员介绍了这一令人兴奋的研究领域。会议还支持研究生的参与，并为他们提供了一个向广大观众展示他们的研究和向专家学习的独特机会。主要重点是区域分解方法，这些方法包括到目前为止在大规模并行分布式分层存储计算机上进行大规模模拟的最常见的可扩展范例。在区域分解中，一个大的问题被归结为一组较小的问题，每个问题在计算上比未分解的问题更容易求解，并且大多数或全部可以独立和并发地解决。通常，需要对较小问题的集合进行迭代，而区域分解算法的大部分理论兴趣在于确保所需的迭代次数非常少。事实上，最好的区域分解方法与它们的近亲多重网格方法具有相同的性质，即总的计算量与输入数据的大小成线性比例，或者所需的迭代次数与单个子域的自由度数至多是对数。在这种情况下，其工作要求与输入数据的大小呈线性关系的算法被称为最优算法。最优域分解算法现在对科学和工程中出现的许多重要问题都是已知的，但肯定不是所有的。目前对区域分解算法的大部分研究兴趣在于扩展已知最优算法的问题的类别。域分解算法可以根据反映在数学运算符中的物理系统的属性、可用处理器的数量，甚至特定的体系结构参数，例如高速缓存大小和存储器带宽与浮点处理速率的比率来定制。

Scalable Parallel Algorithms for Partial Differential EquationsAbstractScalable algorithms for partial differential equations play a key role in Computational Science and Engineering. As the number of processors in today's supercomputers grows rapidly, scalability becomes one of the most important issues in algorithm design. Tremendous progress has been made in this research area in the past few years. The conference brings together experts in this field from all over the world to discuss the latest development of scalable algorithms, and to introduce junior researchers to this exciting research field. The conference also supports the participation of graduate students and provides them with a unique opportunity for exposing their research to a large audience and for learning from experts.The primary focus is on domain decomposition METHODS which COMPRISE by far the most common scalable paradigm for large-scale simulation on massively parallel distributed, hierarchical memory computers. In domain decomposition, a large problem is reduced to a collection of smaller problems, each of which is easier to solve computationally than the un-decomposed problem, and most or all of which can be solved independently and concurrently. Typically, it is necessary to iterate over the collection of smaller problems, and much of the theoretical interest in domain decomposition algorithms lies in ensuring that the number of iterations required is very small. Indeed, the best domain decomposition methods share with their cousins, multigrid methods, the property that the total computational work is linearly proportional to the size of the input data, or that the number of iterations required is at most logarithmic in the number of degrees of freedom of individual subdomains. Algorithms whose work requirements are linear in the size of the input data in this context are said to be optimal. Optimal domain decomposition algorithms are now known for many, but certainly not all, important classes of problems that arise in science and engineering. Much of the current research interest in domain decomposition algorithms lies in extending the classes of problems for which optimal algorithms are known. Domain decomposition algorithms can be tailored to the properties of the physical system as reflected in the mathematical operators, the number of processors available, and even to specific architectural parameters, such as cache size and the ratio of memory bandwidth to floating point processing rate.