## Journal of Integral Equations and Applications

### The direct scattering problem of obliquely incident electromagnetic waves by a penetrable homogeneous cylinder

#### Abstract

In this paper we consider the direct scattering problem of obliquely incident time-harmonic electromagnetic plane waves by an infinitely long dielectric cylinder. We assume that the cylinder and the outer medium are homogeneous and isotropic. From the symmetry of the problem, Maxwell's equations are reduced to a system of two 2D Helmholtz equations in the cylinder and two 2D Helmholtz equations in the exterior domain where the fields are coupled on the boundary. We prove uniqueness and existence of this differential system by formulating an equivalent system of integral equations using the direct method. We transform this system into a Fredholm type system of boundary integral equations in a Sobolev space setting. To handle the hypersingular operators we take advantage of Maue's formula. Applying a collocation method we derive an efficient numerical scheme and provide accurate numerical results using as test cases transmission problems corresponding to analytic fields derived from fundamental solutions.

#### Article information

Source
J. Integral Equations Applications Volume 28, Number 1 (2016), 91-122.

Dates
First available in Project Euclid: 15 April 2016

https://projecteuclid.org/euclid.jiea/1460727506

Digital Object Identifier
doi:10.1216/JIE-2016-28-1-91

Mathematical Reviews number (MathSciNet)
MR3488156

Zentralblatt MATH identifier
1358.35182

#### Citation

Gintides, Drossos; Mindrinos, Leonidas. The direct scattering problem of obliquely incident electromagnetic waves by a penetrable homogeneous cylinder. J. Integral Equations Applications 28 (2016), no. 1, 91--122. doi:10.1216/JIE-2016-28-1-91. https://projecteuclid.org/euclid.jiea/1460727506

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