Functional Analysis and Applications Seminar 

30/03/2012, 15:00 — 16:00 — Room P3.10, Mathematics Building
Frank-Olme Speck, Instituto Superior Técnico

Diffraction from a three-quarter-plane using an abstract Babinet principle

The modelling of diffraction of time-harmonic electromagnetic or acoustic waves from obstacles and screens leads to boundary value problems for the three-dimensional Helmholtz equation with Dirichlet, Neumann or other conditions on the boundary. A prominent example is the problem of diffraction from a quarter-plane in $\mathbb{R}^3$, which admits an explicit solution. In this paper the Dirichlet and Neumann problems for the three-quarter-plane are solved by an algebraic trick: the matricial coupling of operators associated to "dual" boundary value problems, a kind of abstract Babinet principle.