On a superalgebraically converging, numerically stable solving strategy for electromagnetic scattering by impedance cylinders

We review guidelines to obtain fast and accurate solutions-based on integral equations-of the Helmholtz equation with mixed boundary values in two dimensions, a crucial issue when modeling electromagnetic phenomena in complex photonic media. We solve the electric- and magnetic-field integral equations (EFIE and MFIE) to treat scattering of electromagnetic waves from transverse magnetic (TM)- and transverse electric (TE)-excited impedance cylinders represented with smoothly parameterized cross-section contours. We show that it is possible to obtain superalgebraic convergence with accurate calculations of the kernels of the integral equations whose singularities vary from weak to hypersingular. These Fredholm equations of the second kind are subject to stable discretization procedures. However, for various values of impedance, numerical stability can be maintained only via analytical regularization. Finally, we provide numerical results that support our conclusions.