Journal of Integral Equations and Applications

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

Drossos Gintides and Leonidas Mindrinos

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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

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

First available in Project Euclid: 15 April 2016

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35P25: Scattering theory [See also 47A40] 35Q61: Maxwell equations 45B05: Fredholm integral equations 45F15: Systems of singular linear integral equations 78A25: Electromagnetic theory, general

Direct electromagnetic scattering oblique incidence integral equation method hypersingular operator


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.

Export citation


  • F. Cakoni and D. Colton, Qualitative methods in inverse scattering theory, Springer-Verlag, Berlin, 2006.
  • A.C. Cangellaris and R. Lee, Finite element analysis of electromagnetic scattering from inhomogeneous cylinders at oblique incidence, IEEE Trans. Ant. Prop. 39 (1991), 645–650.
  • D. Colton and R. Kress, Integral equation methods in scattering theory, Pure Appl. Math., John Wiley & Sons Inc., New York, 1983.
  • ––––, Inverse acoustic and electromagnetic scattering theory, 2nd edition, Appl. Math. Sci. 93, Springer-Verlag, Berlin, 1998.
  • M. Costabel and E. Stephan, A direct boundary integral equation method for transmission problems, J. Math. Anal. Appl. 106 (1985), 367–413.
  • R. Courant and D. Hilbert, Methods of mathematical physics, volume 2, Wiley-Interscience, New York, 1962.
  • V. Isakov, Inverse problems for partial differential equations, Appl. Math. Sci. 127, Springer, New York, 2006.
  • R. Kittappa and R.E. Kleinman, Acoustic scattering by penetrable homogeneous objects, J. Math. Phys. 16 (1975), 421–432.
  • R.E. Kleinman and P.A. Martin, On single integral equations for the transmission problem of acoustics, SIAM J. Appl. Math. 48 (1988), 307–325.
  • R. Kress, On the numerical solution of a hypersingular integral equation in scattering theory, J. Comp. Appl. Math. 61 (1995), 345–360.
  • ––––, Linear integral equations, 2nd edition, Springer Verlag, Berlin, 1999.
  • ––––, A collocation method for a hypersingular boundary integral equation via trigonometric differentiation, J. Integral Equations Appl. 26 (2014), 197–213.
  • M. Lucido, G. Panariello and F. Schettiho, Scattering by polygonal cross-section dielectric cylinders at oblique incidence, IEEE Trans. Ant. Prop. 58 (2010), 540–551.
  • A.W. Maue, Über die formulierung eines allgemeinen beugungsproblems durch eine integralgleichung, Z. Phys. 126 (1949), 601–618.
  • K.M. Mitzner, Acoustic scattering from an interface between media of greatly different density, J. Math. Phys. 7 (1966), 2053–2060.
  • P. Monk, Finite element methods for maxwell’s equations, Oxford University Press, Oxford, 2003.
  • G. Nakamura and H. Wang, The direct electromagnetic scattering problem from an imperfectly conducting cylinder at oblique incidence, J. Math. Anal. Appl. 397 (2013), 142–155.
  • J.C. Nédélec, Acoustic and electromagnetic equations, Springer-Verlag, New York, 2001.
  • R.G. Rojas, Scattering by an inhomogeneous dielectric/ferrite cylinder of arbitrary cross-section shape-oblique incidence case, IEEE Trans. Ant. Prop. 36 (1988), 238–246.
  • J.L. Tsalamengas, Exponentially converging nyström methods applied to the integral-integrodifferential equations of oblique scattering/ hybrid wave propagation in presence of composite dielectric cylinders of arbitrary cross section, IEEE Trans. Ant. Prop. 55 (2007), 3239–3250.
  • N.L. Tsitsas, E.G. Alivizatos, H.T. Anastassiu and D.I. Kaklamani, Optimization of the method of auxiliary sources $($mas$)$ for oblique incidence scattering by an infinite dielectric cylinder, Electr. Engin. 89 (2007), 353–361.
  • J.R. Wait, Scattering of a plane wave from a circular dielectric cylinder at oblique incidence, Canadian J. Phys. 33 (1955), 189–195.
  • H. Wang and G. Nakamura, The integral equation method for electromagnetic scattering problem at oblique incidence, Appl. Num. Math. 62 (2012), 860–873.
  • J. Yan, R.K. Gordon and A.A. Kishk, Electromagnetic scattering from impedance elliptic cylinders using finite difference method, Electromagnetism 15 (1995), 157–173.
  • H.A. Yousif and A.Z. Elsherbeni, Oblique incidence scattering from two eccentric cylinders, J. Electr. Waves Appl. 11 (1997), 1273–1288.