L. Nannen:

"Tranparent boundary conditions";

Keynote Lecture: Summer School 2020 »Computational Photonics«, Karlsruhe (invited); 2020-09-21 - 2020-09-25.

The propagation of acoustic, electromagnetic or elastic waves is often described by wave equations in unbounded domains. Since standard finite element methods are restricted to bounded domains, they cannot be used directly for a numerical simulation of such problems. One remedy is to combine standard finite element methods for a bounded subdomain with specialized methods for a most simple but unbounded so called exterior domain. These methods for the exterior domain can be interpreted as transparent boundary conditions for the artificial interface between the bounded and the unbounded domain.

In this lecture, we first introduce radiation conditions, which control the behavior of waves if the local coordinate increases to infinity. These conditions take the role of a boundary condition at infinity. They should guarantee unique solvability of the problems as well as that a solution is of physical relevance. The basic radiation condition enforces a positive energy flux towards infinity. We will replace this radiation condition by somehow equivalent ones, which are better suited for a numerical discretization.

Created from the Publication Database of the Vienna University of Technology.