Polytopal Element Methods in Mathematics and Engineering; October 26 - 28, 2015; Atlanta, GA

数学和工程中的多面元方法；

• 批准号: 1542183
• 负责人: Chunmei Wang
• 金额: $ 2.5万
• 依托单位: Georgia Tech Research Corporation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-09-01 至 2016-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1542183&HistoricalAwards=false
• 关键词: Polytopal; Element; Methods; Mathematics; Engineering

This award supports participation in the conference "Polytopal Element Methods in Mathematics and Engineering," held October 26-28, 2015, at the Georgia Institute of Technology, Atlanta, GA. This conference will promote communication among the many mathematical and engineering communities currently researching polytopal discretization methods for the numerical approximation of solutions of partial differential equations. A variety of distinct polytopal element methods have been designed to approximate solutions of the same types of modern engineering problems, but a workshop-type environment is required to foster a community-wide understanding of the comparative advantages of each technique and to develop a set of best practices regarding implementation. The grant funds will be used to support the attendance of Ph.D. researchers and graduate students, with emphasis on supporting recent Ph.D. recipients and researchers who are members of under-represented groups in this rapidly developing research area. More information on the conference is available at http://www.poems15.gatech.edu.Robust and efficient methodologies for the numerical approximation of the solutions of partial differential equations are essential for the characterization and quantification of many physical phenomena. Discretization of solutions with respect to simplicial and cubical meshes has been studied for decades, resulting in a clear understanding of both the relevant mathematics and computational engineering challenges. Recently, there has been both a desire and need for an equivalent body of research regarding discretization with respect to generic polytopal meshes, typically a mesh of convex polygons in 2D or a mesh of convex polyhedra in 3D. Methodologies accommodating polytopal meshes include virtual element, weak Galerkin, mimetic finite difference, generalized barycentric coordinate, and compatible discrete operator methods. These methods have been applied to diffusion modeling, Stokes flow, elasticity, Maxwell's equations, eigenvalue problems, and other modeling problems. Many of the approaches and implementations have only been developed in the past few years, generating a number of open questions in the field. This conference will help the research community identify the most important results and most pressing needs in this area from both theoretical and practical standpoints.

该奖项支持参加 2015 年 10 月 26 日至 28 日在佐治亚州亚特兰大佐治亚理工学院举行的“数学和工程中的多面元方法”会议。本次会议将促进目前正在研究偏微分方程解数值逼近的多面离散化方法的许多数学和工程界之间的交流。 已经设计了各种不同的多面元方法来近似解决相同类型的现代工程问题，但是需要一个研讨会式的环境来促进整个社区对每种技术的比较优势的理解，并开发一套有关实施的最佳实践。 赠款资金将用于支持攻读博士学位。研究人员和研究生，重点是支持最近的博士学位。在这个快速发展的研究领域中属于代表性不足群体的接受者和研究人员。 有关会议的更多信息，请访问 http://www.poems15.gatech.edu。 偏微分方程解的数值近似的稳健且高效的方法对于许多物理现象的表征和量化至关重要。单纯网格和立方网格解的离散化已经研究了数十年，从而使人们对相关数学和计算工程挑战有了清晰的理解。 最近，对于关于通用多面体网格（通常是 2D 凸多边形网格或 3D 凸多面体网格）的离散化的等效研究主体存在期望和需要。 适应多面网格的方法包括虚拟元素、弱伽辽金、模拟有限差分、广义重心坐标和兼容的离散算子方法。 这些方法已应用于扩散建模、斯托克斯流、弹性、麦克斯韦方程、特征值问题和其他建模问题。 许多方法和实施是在过去几年才开发出来的，在该领域产生了许多悬而未决的问题。 本次会议将帮助研究界从理论和实践的角度确定该领域最重要的成果和最迫切的需求。