Diffusion par des surfaces rugueuses: approximations faibles pentes Marc Saillard LSEET UMR 6133...

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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 [email protected]

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

[email protected]

Outline

Boundary integral formalism

Approximate scattering theories

• Kirchhoff approximation

• Small perturbation theory

• Two-scale model

• Small Slope Approximation

• IEM

• Small Slope Integral Equation

Conclusion

Integral representation of fields

Perfect conductor

Scattering matrix

Approximate scattering theories

Kirchhoff approximation

Small perturbation theory

Small height limit of KA

Two-scale model (KA + SPM)

Small slope approximation

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

IEM

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

Band limited [k/30,4k] power-law spectrum (K-4); khs = 1/8Gaussian spectrum ; khs = 1/4

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