Application of beam simulation to scattering at low grazing angles: 1. Methodology and validation

Abstract

Numerical simulations of rough surface scattering at near‐grazing incidence require very large surfaces (≳500λ). Conventional methods of exact solutions require the inversion of a very large matrix, which can exceed the memory and speed capabilities of even modern supercomputers. The beam simulation method proposed by Saillard and Maystre circumvents this problem by decomposing the large incident beam into narrower subbeams and then synthesizing the large beam by coherent superposition. The radius of these narrower subbeams is determined by the local interaction distance on the surface, which is found to increase with incidence angle, ultimately forcing a single beam in the limit of strict grazing incidence. This paper demonstrates that this technique gives essentially the same results as can be obtained by the method of moments and can handle surfaces as large as 1000λ for grazing incidence angle as low as 10°.

Forward-backward method for scattering from imperfect conductors

“…Accordingly, we approximate the integral on the right-hand side of (8) by (14) where (15) and (16) for a flat surface and . The above approximation in (14) is more accurate than a previously published "impedance boundary condition" approximation [6], which further approximates the integrals in (15) and (16) by taking (17) (18) The accuracy of the approximations in (14) is discussed in Section V where it is shown to be good.…”

Analysis of Electromagnetic Interaction with Ships on the Ocean Surface

“…The bound in the resolvability criterion discussed by Ngo and Rino [36] also becomes significant at low grazing angles. The recommendation for the 3-D vector case is to start over and simply use the spectrum given by (13) which has the additional April 24, 2000 DRAFT benefit of being given in closed form.…”

“…However, using the following argument we arrive at a condition for the validity of (28) that is similar to the one given in the 2-D case [36], [34], [35], in particular the dependence on (f -6i) 2 near grazing carries over to 3-D: The radius of convergence of the full Taylor series (27) is limited to k -k ip because of the branch point of the square root function. Thus…”

Scattering of electromagnetic waves from two-dimensional perfectly conducting random rough surfaces – study with the curvilinear coordinate method

“…This is a weak point of the C method. Moreover, numerical simulations of rough surface scattering at near-grazing incidence requires very large surfaces [33,34]. The C-method in the present form isn't suitable to analyse this particular scattering problem.…”

“…As α decreases, approximations (34) become more accurate. Finally, from substituting Equation (34) into Equations (32) to (33) and applying the point matching method at discrete values (α s ; β t ), we obtain two sets of coupled first-order differential equations relating coefficientsψ(α s , β t , z ) andψ (α s , β t , z ) to each other.…”