Translator Disclaimer
2016 The direct scattering problem of obliquely incident electromagnetic waves by a penetrable homogeneous cylinder
Drossos Gintides, Leonidas Mindrinos
J. Integral Equations Applications 28(1): 91-122 (2016). DOI: 10.1216/JIE-2016-28-1-91

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.

Citation

Download Citation

Drossos Gintides. Leonidas Mindrinos. "The direct scattering problem of obliquely incident electromagnetic waves by a penetrable homogeneous cylinder." J. Integral Equations Applications 28 (1) 91 - 122, 2016. https://doi.org/10.1216/JIE-2016-28-1-91

Information

Published: 2016
First available in Project Euclid: 15 April 2016

zbMATH: 1358.35182
MathSciNet: MR3488156
Digital Object Identifier: 10.1216/JIE-2016-28-1-91

Subjects:
Primary: 35P25, 35Q61, 45B05, 45F15, 78A25

Rights: Copyright © 2016 Rocky Mountain Mathematics Consortium

JOURNAL ARTICLE
32 PAGES


SHARE
Vol.28 • No. 1 • 2016
Back to Top