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

该奖项支持参加2015年10月26-28日在乔治亚理工学院举行的“数学与工程中的多边形元素方法”会议。本次会议将促进目前研究偏微分方程数值逼近解的多边形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素方法来近似解决相同类型的现代工程问题，但是需要一个工作间式的环境来促进对每种技术的比较优势的社区范围的理解，并开发一套关于实现的最佳实践。赠款资金将用于支持博士研究员和研究生的出席，重点是支持最近的博士获得者和研究人员，他们是这个快速发展的研究领域中代表性不足的群体的成员。关于会议的更多信息可在http://www.poems15.gatech.edu.Robust上获得，偏微分方程解的数值近似的有效方法对于许多物理现象的表征和量化是必不可少的。关于简单网格和立方体网格的离散化解决方案已经研究了几十年，导致对相关数学和计算工程挑战的清晰理解。最近，对于一般多边形网格（通常是二维的凸多边形网格或三维的凸多面体网格）的离散化，人们都渴望并需要进行等效的研究。适用于多面网格的方法包括虚元法、弱伽辽金法、拟有限差分法、广义质心坐标法和兼容离散算子法。这些方法已经应用于扩散建模、斯托克斯流、弹性、麦克斯韦方程组、特征值问题和其他建模问题。许多方法和实现是在过去几年才开发出来的，这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结果和最迫切的需求。

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.