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

TL;DR

This paper introduces a highly accurate boundary value problem solver for wave scattering from cylinders with corners, utilizing the RCIP method to achieve exceptional precision even at high frequencies.

Contribution

It demonstrates that the RCIP method, successful in static problems, effectively solves Helmholtz scattering problems with corners at high frequencies, providing extremely accurate results.

Findings

Achieves at least 13 digits of accuracy at high frequencies (kd=1000).

Effectively handles corners in scattering problems using RCIP.

Validates the method's applicability to Helmholtz equations in non-smooth domains.

Abstract

In this paper we consider the classic problems of scattering of waves from perfectly conducting cylinders with piecewise smooth boundaries. The scattering problems are formulated as integral equations and solved using a Nystr\"om 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 specialize to 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.