### Abstract

Original language | English |
---|---|

Pages (from-to) | 676-719 |

Number of pages | 44 |

Journal | IMA Journal of Applied Mathematics |

Volume | 75 |

Issue number | 5 |

DOIs | |

Publication status | Published - Oct 2010 |

### Fingerprint

### Keywords

- numerical evaluation of the vertex diffracted wave
- the far-field asymptotics
- semi-transparent cone
- functional difference equations
- diffraction

### Cite this

*IMA Journal of Applied Mathematics*,

*75*(5), 676-719. https://doi.org/10.1093/imamat/hxq030

**Scattering of a plane electromagnetic wave by a hollow circular cone with thin semi-transparent walls.** / Lyalinov, M A; Zhu, N Y; Smyshlyaev, Valery P.

Research output: Contribution to journal › Article

*IMA Journal of Applied Mathematics*, vol. 75, no. 5, pp. 676-719. https://doi.org/10.1093/imamat/hxq030

}

TY - JOUR

T1 - Scattering of a plane electromagnetic wave by a hollow circular cone with thin semi-transparent walls

AU - Lyalinov, M A

AU - Zhu, N Y

AU - Smyshlyaev, Valery P

PY - 2010/10

Y1 - 2010/10

N2 - We study electromagnetic plane wave diffraction by a hollow circular cone with thin walls modelled by the so-called impedance-sheet boundary conditions. By means of Kontorovich-Lebedev integral representations for the Debye potentials and a 'partial' separation of variables, the problem is reduced to coupled functional difference (FD) equations for the relevant spectral functions. For a circular cone, the FD equations are then further reduced to integral equations, which are subsequently shown to be Fredholm-type equations via a semi-inversion by use of Dixon's resolvent. We then solve the integral equations numerically using an appropriate quadrature method. Certain useful further integral representations for the solution of 'Watson-Bessel' and Sommerfeld types are developed, which gives a theoretical basis for subsequent calculation of the far-field (high-frequency) asymptotics for the diffracted field. Based on this asymptotics, the radar cross section in the domain, which is free from both the reflected and the surface waves, has been computed numerically.

AB - We study electromagnetic plane wave diffraction by a hollow circular cone with thin walls modelled by the so-called impedance-sheet boundary conditions. By means of Kontorovich-Lebedev integral representations for the Debye potentials and a 'partial' separation of variables, the problem is reduced to coupled functional difference (FD) equations for the relevant spectral functions. For a circular cone, the FD equations are then further reduced to integral equations, which are subsequently shown to be Fredholm-type equations via a semi-inversion by use of Dixon's resolvent. We then solve the integral equations numerically using an appropriate quadrature method. Certain useful further integral representations for the solution of 'Watson-Bessel' and Sommerfeld types are developed, which gives a theoretical basis for subsequent calculation of the far-field (high-frequency) asymptotics for the diffracted field. Based on this asymptotics, the radar cross section in the domain, which is free from both the reflected and the surface waves, has been computed numerically.

KW - numerical evaluation of the vertex diffracted wave

KW - the far-field asymptotics

KW - semi-transparent cone

KW - functional difference equations

KW - diffraction

UR - http://www.scopus.com/inward/record.url?scp=77957724221&partnerID=8YFLogxK

UR - http://dx.doi.org/10.1093/imamat/hxq030

U2 - 10.1093/imamat/hxq030

DO - 10.1093/imamat/hxq030

M3 - Article

VL - 75

SP - 676

EP - 719

JO - IMA Journal of Applied Mathematics

JF - IMA Journal of Applied Mathematics

SN - 0272-4960

IS - 5

ER -