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

Georgia Tech Research Corporation, Atlanta GA

Investigators

Abstract

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.