Three dimensional wave scattering by arrays of elliptical and circular cylinders

A solution to the two-dimensional scattering properties of a conducting elliptic cylinder coated with a confocal homogeneous anisotropic elliptical shell is obtained. The transmitted field of the anisotropic shell is expressed as an integral equation based on waves with different wave numbers and different directions of propagation. The waves in all directions are represented as the eigenfunction expansion in elliptic coordinates in terms of Mathieu functions. In order to solve the nonorthogonality properties of Mathieu functions, Galerkin's method is applied and a matrix is required for the computation of unknown expansion coefficients of the scattered and transmitted fields. Only the transverse magnetic (TM) polarization is presented, while the transverse electric (TE) polarization can be obtained in the same way. Some numerical results are presented in graphical forms. The result is in agreement with that available as expected when a coated elliptic cylinder degenerates to the coated circular one.

Two-Dimensional Scattering by a Conducting Elliptic Cylinder Coated With a Homogeneous Anisotropic Shell

This lecture presents a modern approach for the computation of Mathieu functions. These functions find application in boundary value analysis such as electromagnetic scattering from elliptic cylinders and flat strips, as well as the analogous acoustic and optical problems, and many other applications in science and engineering. The authors review the traditional approach used for these functions, show its limitations, and provide an alternative "tuned" approach enabling improved accuracy and convergence. The performance of this approach is investigated for a wide range of parameters and machine precision. Examples from electromagnetic scattering are provided for illustration and to show the convergence of the typical series that employ Mathieu functions for boundary value analysis.

Accurate Computation of Mathieu Functions

The hydrodynamic scattering problem by arrays of elliptical truncated cylinders subjected to regular waves is investigated. Linear potential theory is employed that is based on the assumption of inviscid/incompressible fluid and irrotational flow. Effort is made to provide an analytical solution of the associated hydrodynamic boundary value problem. The solution is based on the semi-analytical formulation of the diffraction potentials and the application of the so-called Mathieu functions addition theorem. The latter is decomposed into even and odd Mathieu functions whereas it considers arbitrary angular orientations of the semi-major axes of the bodies. It was also extended to account for negative Mathieu parameters which correspond to the infinite real roots of the transcendental equation. The details of the interaction phenomena are investigated with the aid of the transfer functions of the exciting forces on two-body configurations. Indicative results for the free surface elevation around the bodies are also provided.

The hydrodynamics of arrays of truncated elliptical cylinders

Wavefield Scattering By a 2-D Near-surface Elliptic Anomaly

The scattering of a plane electromagnetic wave by a perfectly conducting elliptic cylinder is investigated theoretically. The calculations are based upon the expansion of the scattered wave functions in terms of Mathieu functions. Both E- and H-polarized waves are considered. Numerical results, in particular for the scattering cross-section, are presented for cylinders the cross-sectional dimensions of which are up to many wavelengths (e.g. distance between the focal lines up to 20 wavelengths).

H. J. van Schaik

Papers

Diffraction of a plane electromagnetic wave by a perfectly conducting elliptic cylinder