Nyström method with edge condition for electromagnetic scattering by 2D open structures

A Nyström method with edge condition (EC) is developed for electromagnetic scattering by two-dimensional (2D) open structures. Since EC correctly describes the edge behavior of currents on the scatterers, the use of it in Nyström method can dramatically coarsen the discretization near the edges. In the implementation of the scheme, we derive the closed-form expressions for the singular or near-singular integrations of Hankel functions multiplied by the polynomials with or without EC. This allows us to control the numerical errors efficiently by approximating the Hankel functions with more series terms and selecting higher-order polynomials to represent the currents in the local correction. The numerical results illustrate that the solutions with the use of EC converge much faster than without the use of EC. Also, EC is more essential in TM polarization than in TE polarization due to the singular behavior of current near edges.