Manas Rachh: [WS] Complex scattering makes for simple numerics

Speaker
Manas Rachh, Flatiron Institute

Abstract
Scattering problems involving unbounded interfaces occur frequently in physics and engineering settings. Due to this prevalence, there exist many numerical methods for solving such problems. Unfortunately, the complicated behavior of solutions in the vicinity of infinite interfaces can make it challenging to deriving explicit error bounds for these methods. Many of these methods also require a large computational domain, and so require a large number of discretization points to accurately solve the problem. In this talk, we will present a class of decomposable scattering problems. For this class of problems, the PDE domain can be decomposed into a collection of simple subdomains. The fundamental solutions for these simple regions can then be used to reduce the scattering problem into an integral equation on the interfaces between these subdomains. We demonstrate this procedure for networks of metallic waveguides and if time permits we will discuss its extensions to the leaky case where the bulk radiation poses additional analytical and numerical challenges. Joint work with Charles Epstein, Tristan Goodwill, Jeremy Hoskins, Shidong Jiang, Solomon Quinn and Kosuke Sugita.