Abstract: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.
From: Haochen Liu [view email]
[v1]
Sun, 14 Jun 2026 05:55:36 UTC (24 KB)
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