Comparison of Two Convergent Numerical Methods for Solving the Problem of Wave-Scattering by a Dielectric Rod with a Conformal Strip of Graphene

We consider the scattering of an H-polarized plane wave by an infinite circularly curved graphene strip of arbitrary angular width, placed at the dielectric rod. Our analysis is based on the two types of analytical methods. The first is a hypersingular integral equation for the current induced on the strip. Discretization of this equation is carried out by the Nystrom-type method that has a guaranteed convergence. The second is the method of analytical regularization (MAR), which uses explicit inversion of the static part of the problem. We perform numerical experiments demonstrating how the rate of convergence depends on truncation number and interpolation order. We compare these two methods and their errors as a function of frequency.