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Numerical simulation of electromagnetic wave scattering from very rough, Gaussian, surfaces

Devayya, Robert Hanz; (1993) Numerical simulation of electromagnetic wave scattering from very rough, Gaussian, surfaces. Doctoral thesis (Ph.D), UCL (University College London). Green open access

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Abstract

A numerical investigation into electromagnetic wave scattering from perfectly-conducting, two-dimensional, Gaussian, rough surfaces is conducted. The rough surfaces considered have a root-mean-square surface height and a correlation-length of the same order, and of the order of the incident wavelength. These surfaces are beyond the range of application of existing scattering theories. The scattering problem is solved by determining the solution of the magnetic-field-integral-equation. The convergence and the rate of convergence of two iterative methods applied to the numerical solution of the magnetic-field-integral-equation are investigated; the Neumann expansion, which has been used to formally represent the solution of the rough surface scattering problem; and the conjugate-gradient method, an iterative method of solving matrix equations whose convergence is in theory sure. However, applied to the solution of scattering from very rough surfaces, both methods have been found to diverge. Presented in this thesis is a step-by-step procedure for identifying divergent Neumann expansions, and a numerically robust conjugate-gradient method that has been successfully applied to the solution of the scattering problem. This study provides a comparative investigation of vertical and horizontal polarization wave scattering. Results are presented for both the field in the vicinity of the surface boundary, and the average value of the power scattered from an ensemble of rough surface realizations. A procedure is presented for obtaining from the solution of the magnetic-field-integral-equation, two explicit corrections to the Kirchhoff method. In the high-frequency limit one of the corrections accounts for shadowing, and the other accounts for multiple-reflections at the randomly rough, surface boundary. The significance of the two corrections at lower frequencies is investiagted. It is concluded that at lower frequencies the former correction accounts for the partial-shadowing and diffraction of the incident and scattered waves, and the latter correction accounts for the illumination of the surface by waves scattered from other parts of the surface.

Type: Thesis (Doctoral)
Qualification: Ph.D
Title: Numerical simulation of electromagnetic wave scattering from very rough, Gaussian, surfaces
Open access status: An open access version is available from UCL Discovery
Language: English
Additional information: Thesis digitised by ProQuest.
Keywords: Applied sciences
URI: https://discovery.ucl.ac.uk/id/eprint/10099782
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