Diffusion par des surfaces rugueuses: approximations faibles pentes Marc Saillard LSEET UMR 6133...
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Transcript of Diffusion par des surfaces rugueuses: approximations faibles pentes Marc Saillard LSEET UMR 6133...
Diffusion par des surfaces rugueuses: approximations faibles pentes
Marc Saillard
LSEET
UMR 6133 CNRS-Université du Sud Toulon-Var
BP 132, 83957 La Garde cedex, France
Outline
Boundary integral formalism
Approximate scattering theories
• Kirchhoff approximation
• Small perturbation theory
• Two-scale model
• Small Slope Approximation
• IEM
• Small Slope Integral Equation
Conclusion
Comparison of MoM with
Kirchhoff approx. (KA),
Small Perturbation Method (SPM)
1st order Small Slope Approx. (SSA)Comparison of MoM (solid line) with 1st order SSA (dashed line)
n = 1.6 r.m.s height 0.17 - correlation length
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Numerical examples: Gaussian spectrum
Band limited [k/30,4k] power-law spectrum (K-4); h = /5; s = 0.1; khs = 1/8
Numerical examples: power-law spectrum
Horizontal distance d
distance R
Slope s Height h = sd
22211 dsdsdR
dszd'rr
Validity : khs<<1.
dd
RRrr
π4ikexp
π4ikexp',G
Matrices associated to integral operators are 2D Toeplitz
Storage : 2N instead of N2 Product : 2Nlog2N instead of N2
Small slope integral equation (Meecham – Lysanov)
1st order
Conclusion
• Domain of validity that covers both that of SSA1 and of the
tangent plane approximation (as SSA2 or OEM)
• No assumption on the surface statistics
• The accuracy can be estimated
• Very low computational cost
• It provides an estimation of the cross-polarized component in
the plane of incidence
• It is an alternative to statistical approximate methods
but requires Monte-Carlo process