An accurate boundary value problem solver applied to scattering from cylinders with corners

In this paper we consider the classic problem of scattering of waves
from perfectly conducting cylinders with piecewise smooth
boundaries. The scattering problems are formulated as integral
equations and solved using a Nyström scheme, where the corners of
the cylinders are efficiently handled by a method referred to as
Recursively Compressed Inverse Preconditioning (RCIP). This method
has been very successful in treating static problems in non-smooth
domains and the present paper shows that it works equally well for
the Helmholtz equation. In the numerical examples we focus on
scattering of E- and H-waves from a cylinder with one corner. Even
at a size kd=1000, where k is the wavenumber and $d$ the
diameter, the scheme produces at least 13 digits of accuracy in the
electric and magnetic fields everywhere outside the cylinder.