Abstract

In this talk I will discuss two contributions to the study of boundary value problems for the Helmholtz equation involving impedance (absorbing) boundary conditions on non-smooth boundaries. The first is an “edge source” representation for the canonical problem of scattering by a right-angled impedance wedge, in which the diffracted field is represented as an integral of secondary sources over the diffracting edge. The second is a well-posedness analysis and boundary element discretization of scattering by a planar impedance screen. The novelty in the latter case is the fact that we make no regularity assumption on the boundary of the screen, so our results are valid for screens with fractal boundaries, such as the Koch snowflake.