A High-Order Nyström Method for Coupled Boundary Integral Equations in Oblique-Incidence Scattering by Impedance Cylinders
It provides a stable, high-accuracy forward solver for electromagnetic scattering problems involving impedance cylinders, which is useful for computational electromagnetics but represents an incremental improvement over existing methods.
The paper develops a high-order Nyström method for solving coupled boundary integral equations arising in oblique-incidence scattering by impedance cylinders, achieving high accuracy and stability in numerical experiments including a manufactured Fourier-Bessel benchmark and plane-wave validation.
We study the numerical solution of electromagnetic scattering by an infinitely long impedance cylinder under oblique incidence. After separation of the axial phase factor, the axial electric and magnetic components satisfy a pair of coupled two-dimensional Helmholtz equations. The Leontovich impedance condition couples these components through tangential derivatives, and the associated boundary integral system contains both logarithmic kernels and principal-value tangential derivative terms. Building on existing coupled integral-equation formulations for oblique-incidence cylinder scattering, we construct a high-order Nystrom implementation based on Kress-type logarithmic kernel decomposition, periodic product quadrature, Fourier differentiation for the tangential derivative contribution, and a block diagonal preconditioner associated with the scalar impedance subproblem. Under uniqueness of the continuous scattering problem and a uniform discrete stability assumption, we formulate a high-order convergence framework for the boundary densities and far-field patterns. Numerical experiments include a manufactured Fourier-Bessel benchmark, a plane-wave circular-cylinder validation, a smooth non-circular boundary test, condition-number and GMRES comparisons, and a variable-impedance scattering-width reduction example in a prescribed backward angular sector. The results indicate that the method provides a stable high-accuracy forward solver for the coupled impedance system, rather than a new physical model.