scholarly journals Rigorous Solution to Plane Wave Scattering by an Arbitrary-Shaped Particle Embedded into a Cylindrical Cell of Similar Material

2009 ◽  
Vol 2009 ◽  
pp. 1-6 ◽  
Author(s):  
Constantine A. Valagiannopoulos
Keyword(s):  
Plane Wave ◽  
Electromagnetic Scattering ◽  
Hypergeometric Functions ◽  
Integral Formula ◽  
Scattering Problem ◽  
Double Series ◽  
Infinite Cylinder ◽  
Shaped Particle ◽  
Plane Wave Scattering ◽  
Good Agreement

An infinite cylinder of arbitrary shape is embedded into a circular one, and the whole structure is illuminated by a plane wave. The electromagnetic scattering problem is solved rigorously under the condition that the materials of the two cylinders possess similar characteristics. The solution is based on a linear Taylor expansion of the scattering integral formula which can be useful in a variety of different configurations. For the specific structure, its own far field response is given in the form of a double series incorporating hypergeometric functions. The results are in good agreement with those obtained via eigenfunction expansion. Several numerical examples concerning various shape patterns are examined and discussed.

scholarly journals Electromagnetic Scattering from Surfaces with Curved Wedges Using the Method of Auxiliary Sources (MAS)

2020 ◽  
Vol 10 (7) ◽  
pp. 2309 ◽  
Author(s):  
Vissarion G. Iatropoulos ◽  
Minodora-Tatiani Anastasiadou ◽  
Hristos T. Anastassiu
Keyword(s):  
Plane Wave ◽  
Electromagnetic Scattering ◽  
Wave Scattering ◽  
Transverse Magnetic ◽  
Numerical Results ◽  
Circular Arcs ◽  
Artificial Surface ◽  
Method Of Auxiliary Sources ◽  
Plane Wave Scattering ◽  
Auxiliary Source

The method of auxiliary sources (MAS) is utilized in the analysis of Transverse Magnetic (TM) plane wave scattering from infinite, conducting, or dielectric cylinders, including curved wedges. The latter are defined as intersections of circular arcs. The artificial surface, including the auxiliary sources, is shaped in various patterns to study the effect of its form on the MAS accuracy. In juxtaposition with the standard, conformal shape, several deformations are tested, where the auxiliary sources are forced to approach the tip of the wedge. It is shown that such a procedure significantly improves the accuracy of the numerical results. Comparisons of schemes are presented, and the optimal auxiliary source location is proposed.

scholarly journals Electromagnetic diffraction and scattering of a complex-source beam by a semi-infinite circular cone

2013 ◽  
Vol 11 ◽  
pp. 31-36 ◽  
Author(s):  
H. Brüns ◽  
L. Klinkenbusch
Keyword(s):  
Plane Wave ◽  
Electromagnetic Scattering ◽  
Scattering Problem ◽  
Multipole Expansion ◽  
Circular Cone ◽  
Plane Wave Incident ◽  
Complex Source ◽  
Full Plane ◽  
Complex Valued ◽  
Electromagnetic Diffraction

Abstract. A complex-source beam (CSB) is used to investigate the electromagnetic scattering and diffraction by the tip of a perfectly conducting semi-infinite circular cone. The boundary value problem is defined by assigning a complex-valued source coordinate in the spherical-multipole expansion of the field due to a Hertzian dipole in the presence of the PEC circular cone. Since the incident CSB field can be interpreted as a localized plane wave illuminating the tip, the classical exact tip scattering problem can be analysed by an eigenfunction expansion without having the convergence problems in case of a full plane wave incident field. The numerical evaluation includes corresponding near- and far-fields.

Electromagnetic scattering by a dielectric sphere partially buriedin an infinte plane

2002 ◽  
Vol 80 (9) ◽  
pp. 979-986
Author(s):  
A -K Hamid ◽  
M Hamid
Keyword(s):  
Plane Wave ◽  
Electromagnetic Scattering ◽  
Plane Electromagnetic Wave ◽  
Ground Plane ◽  
Scattering Problem ◽  
Dielectric Constants ◽  
Angle Of Incidence ◽  
Spherical Scatterer ◽  
Incident Plane ◽  
The Given

An analytical solution of the scattering problem of a plane electromagnetic wave scattered by a dielectric spherical scatterer residing or partially buried in an infinite perfectly conducting ground plane is formulated in conjunction with the method of images. With imaging, the geometry is replaced by two touching or overlapping dielectric spheres in the absence of the ground plane, but with the given incident plane wave and its plane-wave image to satisfy the boundary conditions on the ground plane in the original problem. Numerical results are presented for the normalized scattering cross section at an arbitrary height from the ground plane, at any specific angle of incidence, and different relative dielectric constants. PACS Nos.: 41.10H, 41.90

scholarly journals A sharp relative-error bound for the Helmholtz h-FEM at high frequency

2021 ◽  
Author(s):  
D. Lafontaine ◽  
E. A. Spence ◽  
J. Wunsch
Keyword(s):  
Plane Wave ◽  
Relative Error ◽  
High Frequency ◽  
Wave Scattering ◽  
Scattering Problem ◽  
Practical Applications ◽  
Polynomial Degree ◽  
Fixed Order ◽  
Explicit Bounds ◽  
Plane Wave Scattering

AbstractFor the h-finite-element method (h-FEM) applied to the Helmholtz equation, the question of how quickly the meshwidth h must decrease with the frequency k to maintain accuracy as k increases has been studied since the mid 80’s. Nevertheless, there still do not exist in the literature any k-explicit bounds on the relative error of the FEM solution (the measure of the FEM error most often used in practical applications), apart from in one dimension. The main result of this paper is the sharp result that, for the lowest fixed-order conforming FEM (with polynomial degree, p, equal to one), the condition “$$h^2 k^3$$ h 2 k 3 sufficiently small" is sufficient for the relative error of the FEM solution in 2 or 3 dimensions to be controllably small (independent of k) for scattering of a plane wave by a nontrapping obstacle and/or a nontrapping inhomogeneous medium. We also prove relative-error bounds on the FEM solution for arbitrary fixed-order methods applied to scattering by a nontrapping obstacle, but these bounds are not sharp for $$p\ge 2$$ p ≥ 2 . A key ingredient in our proofs is a result describing the oscillatory behaviour of the solution of the plane-wave scattering problem, which we prove using semiclassical defect measures.

scholarly journals Electromagnetic Scattering at the Waveguide Step between Equilateral Triangular Waveguides

2016 ◽  
Vol 2016 ◽  
pp. 1-16 ◽  
Author(s):  
Ana Morán-López ◽  
Juan Córcoles ◽  
Jorge A. Ruiz-Cruz ◽  
José R. Montejo-Garai ◽  
Jesús M. Rebollar
Keyword(s):  
Plane Wave ◽  
Electromagnetic Scattering ◽  
Communication Systems ◽  
Scattering Problem ◽  
Mathematical Formulation ◽  
Building Blocks ◽  
Analysis And Design ◽  
Mode Spectrum ◽  
Analytic Expressions ◽  
Commercial Software Package

The analysis of the electromagnetic scattering at discontinuities between equilateral triangular waveguides is studied. The complete electromagnetic solution is derived using analytical closed form expressions for the mode spectrum of the equilateral waveguide. The mathematical formulation of the electromagnetic scattering problem is based on the quasi-analytical Mode-Matching method. This method benefits from the electromagnetic field division into symmetries as well as from the plane wave formulation presented for the expressions involved. The unification of the surface integrals used in the method thanks to the plane wave formulation is revealed, leading to expressions that are very well suited for its implementation in an electromagnetic analysis and design code. The obtained results for some cases of interest (building blocks for microwave components for communication systems) are verified using other numerical methods included in a commercial software package, showing the potential of the presented approach based on quasi-analytic expressions.

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