The direct electromagnetic scattering problem by a piecewise constant inhomogeneous cylinder at oblique incidence

Abstract

We consider the solvability of the direct scattering problem of an obliquely incident time-harmonic electromagnetic wave by a piecewise constant inhomogeneous, penetrable and infinitely long cylinder. We prove the existence and uniqueness of the solution using properties of the boundary value operators and the integral equation method. For the numerical solution, we apply a collocation method and we approximate the singular integral operators using quadrature rules. We show convergence of the numerical scheme for the interior and the scattered fields both in the near- and far-field regime.

Figures (5)

• Figure 1: The geometry of the problem and the position of the point sources considered in the first (left) and in the second (right) case of the first example.
• Figure 2: The $L^2-$norm (in semi-logarithmic scale) of the difference between the computed and the exact interior (blue line) and the far-field (red line) of the electric (left) and the magnetic (right) fields. The plots are with respect to $n,$ for the first case of the first example.
• Figure 3: The $L^2-$norm (in semi-logarithmic scale) of the difference between the computed and the exact scattered (blue line) and the interior (red line) electric (left) and the magnetic (right) fields. The plots are with respect to $n,$ for the second case of the first example.
• Figure 4: The norm of the electric (left) and magnetic (right) field, for $\omega =2$ and $\phi = \pi/6.$
• Figure 5: The norm of the electric (left) and magnetic (right) field, for $\omega =2$ and $\phi = \pi/2.$

Theorems & Definitions (8)

• Proposition 1
• Proof 1
• Theorem 1
• Proof 2
• Theorem 2
• Proof 3
• Definition 1: see Wloka
• Theorem 3: see WloRowLaw