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日至28日在佐治亚州亚特兰大市格鲁吉亚理工学院举行的“数学和工程中的多面体元素方法”会议。本次会议将促进目前正在研究偏微分方程数值近似解的多面体离散化方法的许多数学和工程社区之间的交流。 各种不同的多面体元素的方法已被设计成近似的解决方案相同类型的现代工程问题，但需要一个研讨会式的环境，以促进社区范围内的理解每种技术的比较优势，并制定一套最佳实践的实施。 赠款资金将用于支持博士的出席。研究人员和研究生，重点是支持最近的博士学位。受助人和研究人员谁是代表性不足的群体在这个迅速发展的研究领域的成员。 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至关重要。关于单纯形和立方网格的离散化解决方案已经研究了几十年，从而对相关的数学和计算工程挑战有了清晰的理解。 最近，一直存在对关于相对于通用多面体网格（通常为2D中的凸多边形网格或3D中的凸多面体网格）的离散化的等效研究主体的期望和需要。 适用于多面体网格的方法包括虚元法、弱伽辽金法、拟有限差分法、广义重心坐标法和相容离散算子法。 这些方法已被应用到扩散建模，斯托克斯流，弹性，麦克斯韦方程，本征值问题，和其他建模问题。 许多方法和实现只是在过去几年中才开发出来的，在该领域产生了一些开放的问题。 本次会议将帮助研究界从理论和实践的角度确定这一领域最重要的成果和最迫切的需求。

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.