On the Solution of Elliptic Partial Differential Equations on Regions with Corners, Edges, and Conical Points
Presented By: Kirill Serkh, Yale University
Abstract: The solution of elliptic partial differential equations on regions with non-smooth boundaries (edges, corners, etc.) is a notoriously refractory problem. In this talk, I observe that when the problems are formulated as boundary integral equations of classical potential theory, the solutions (of the integral equations) in the vicinity of corners are representable by series of elementary functions. In addition to being analytically perspicuous, the resulting expressions lend themselves to the construction of accurate and efficient numerical algorithms. The results are illustrated by a number of numerical examples.
Biography: Kirill Serkh received his Ph.D. from Yale University in 2016. He then moved on to become a National Science Foundation Mathematical Sciences Postdoctoral Research Fellow at NYU Courant for two years. His area of research is numerical analysis, with a focus on partial differential equations.
Joint talk with the Departments of Computer Science and Mathematics.