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

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 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 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.

19 pages, 3 figures

References in corpus (2)

• Quadrature by Expansion: A New Method for the Evaluation of Layer Potentials
• High-order accurate Nystrom discretization of integral equations with weakly singular kernels on smooth curves in the plane

Cited by in corpus (4)

• An explicit kernel-split panel-based Nyström scheme for integral equations on axially symmetric surfaces
• Determination of normalized magnetic eigenfields in microwave cavities
• Variants of an explicit kernel-split panel-based Nyström discretization scheme for Helmholtz boundary value problems
• A novel integral equation for scattering by locally rough surfaces and application to the inverse problem: the Neumann case