CBMS Conference: Algorithms for solving elliptic PDEs on modern computers---fast direct solvers, randomized methods, and high order discretizations,

CBMS 会议：在现代计算机上求解椭圆偏微分方程的算法——快速直接求解器、随机方法和高阶离散化，

• 批准号: 1347163
• 负责人: Alexander Barnett
• 金额: $ 3.8万
• 依托单位: Dartmouth College
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-03-01 至 2015-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1347163&HistoricalAwards=false
• 关键词: CBMS; Conference; Algorithms; solving; elliptic

The award supports an NSF/CBMS regional conference that will be held at Dartmouth College in June of 2014 on the topic of so called "fast methods" for numerically solving linear partial differential equations (PDEs). This field of research has recently seen very rapid progress, and the purpose of the conference is to introduce recent results to junior researchers, and to engage them with current research. In particular, the conference will describe (1) new "direct" (as opposed to "iterative") solvers that in a single sweep construct an approximate solution to the equation under consideration, (2) new randomized methods for accelerating certain linear algebraic computations, and (3) the interplay between direct solvers and high-order discretization techniques that allow the solution of PDEs to ten digits of accuracy or more, even on complicated geometries.The broader motivation for the research to be discussed during the conference is the growing importance of computational simulations of physical phenomena in science and engineering. The ability to perform rapid virtual experiments rather than real (expensive) ones is a key driver of technological progress. While more powerful computers are important, development of efficient numerical algorithms that run well on modern hardware is equally crucial. The CBMS conference supported will disseminate knowledge about newly developed powerful algorithms that are designed from the ground up to minimize communication, which is emerging as the most important computational bottleneck. The conference will in addition to traditional lectures also give participants an opportunity for hands-on computational experimentation using tutorial style software. The lectures will be recorded and will be posted online along with the lecture slides, and the tutorial software. A monograph will be produced to create an integrated set of resources that will maximize the impact and reach of the conference. This project will be jointly supported by the Infrastructure Program and the Computational Mathematics Program within the Division of Mathematical Sciences.

该奖项支持NSF/CBMS区域会议，该会议将于2014年6月在达特茅斯学院举行，其主题称为“快速方法”，用于求解线性偏微分方程（PDES）。该研究领域最近取得了非常迅速的进步，会议的目的是向初级研究人员介绍最新结果，并参与当前的研究。 In particular, the conference will describe (1) new "direct" (as opposed to "iterative") solvers that in a single sweep construct an approximate solution to the equation under consideration, (2) new randomized methods for accelerating certain linear algebraic computations, and (3) the interplay between direct solvers and high-order discretization techniques that allow the solution of PDEs to ten digits of accuracy or more, even on complicated几何形状。会议期间要讨论的研究的更广泛的动机是对科学和工程中物理现象的计算模拟的重要性越来越重要。执行快速虚拟实验而不是真实（昂贵）的能力是技术进步的关键驱动力。尽管更强大的计算机很重要，但在现代硬件上运行良好的有效数值算法的开发同样至关重要。支持的CBMS会议将传播有关新开发的强大算法的知识，这些算法是从头开始设计的，以最大程度地减少通信，这正在成为最重要的计算瓶颈。会议除传统讲座外还将为参与者提供使用教程样式软件进行动手计算实验的机会。演讲将记录下来，并将与演讲幻灯片和教程软件一起在线发布。将制作专着，以创建一组集成的资源，以最大程度地发挥会议的影响和影响力。 该项目将由数学科学部门内的基础架构计划和计算数学计划共同支持。