Fractal rough surface scattering boundary element method and parameter inversion
|Keywords||Fractal rough surface Scattering BEM Finite element Inverse problem Inversion|
Rough surface scattering problem has an extremely wide range of applications , such as radar waves through water and land surface scattering , and non-destructive exploration of natural and artificial body surface of the product , etc. Also , there are many ways to solve non- smooth surface scattering issues such as the KAM (Kirchhoff Approximation Method), SPM (SmallPerturbation Method) two-scale method , Rayleigh method of fractal geometry discussed the self-similar fractal structure of distribution , and taking into account the random rough surface and a wide range of small-scale non- ordered sequence characteristics, tend to be more close to the actual rough surface . fractal function with only a small number of parameters, we can describe complex objects , so this paper rough surface fractal curve represents the finite element method and boundary element method is a numerical solution of partial differential equations important ways. finite element method in rough surface scattering calculations are already many applications, and boundary element method and finite element method has obvious advantages in the actual boundary element method calculation can be calculated directly (?) u / (?) n, and the finite element method must be used instead of difference quotients (?) u / (?) n, because of the difference quotient instability , might give the final calculation result large errors. using the boundary element method fractal rough surface scattering problems have a greater advantage . article also discusses the inversion of the fractal parameters , in order to avoid the determination of the fractal dimension of difficulty , using minimal objective function method to invert the fractal parameters. single parameter inverse problem is the inversion of dimension D, totaling forget D = 1.1, ..., 1.9 which nine sets of results are discussed as well as the maximum error and the average error iteration steps , also discussed η, n, z0, L, d aliquots shape parameters on the anti- little impact on the results of speech . finally discusses observations with small perturbations on the inversion results. article also discusses single-parameter inverse problem was also discussed on the basis of the use of multi-parameter inversion algorithm ( direct search method that does not containing derivative information ) inversion fractal parameters D and b. calculate multiple results , discuss the maximum error and mean error , also discussed the n, z0, L aliquots shaped parameter changes have little effect on the inversion results . Finally If the observations are discussed with small perturbations on the inversion results.