DMS Colloquium: Dr. Youngjoon Hong

Speaker: Dr. Youngjoon Hong, University of Illinois at Chicago

Title: How to handle a small parameter in numerical computations

Abstract: Especially since high-speed computers have become readily available, there has been enormous effort to develop discrete numerical methods to approximate continuous solutions of partial differential equations. One of the more difficult situations that can arise is when small parameters other than those appearing in the discretization are involved. Such singular or boundary perturbation problems arise all too frequently in practice. To achieve accurate numerical approximations in this situation can be daunting, as it is often computationally prohibitive to take the discretization small compared to the already existing small parameters in the problem.

The talk will focus on some recently developed techniques coming from certain physical models featuring small parameters. The ideas will be explained in the context of concrete examples arising in fluid dynamics, optics and electromagnetism. These will include singularly perturbed convection dominated equations and electromagnetic scattering problems in a periodic multiply layered grating structure.