| Wavelet analysis is an international forward research field in recent years. It not only contains abundant mathematical theories, but also is a powerful method and tool in engineering—it bring new ideas to many fields. The theory of wavelet analysis has been successfully applied to solving partial differential equations, and some preliminary results on wavelet multilevel inversion were also given. In this paper, based on these works, wavelet analysis and Regularization-Gauss-Newton method are applied to the inverse simulations for Maxwell equations. The algorithms are further studied, and the new methods are given.In the second chapter, the basic theory of wavelet analysis is introduced in detail. It gives"Daub4"for decomposition of source and electromagnetism field, and brings two-dimensional decomposition construction algorithms.In the third chapter, it not only introduces the discrete method of Maxwell equation including Yee difference form, but also gives discrete equation and elaboration of stability condition and chromatic dispersion problem. There are Mur condition that is often used on absorbing condition, and ultra absorption's precision is higher but it's computation quantity is large. At last we give absorbing boundary condition in consuming medium.In the last chapter, wavelet multilevel method is designed for the two-dimensional wave equation inversion. The source function and electromagnetism field function are decomposed in different scales. Fully utilizing the connection between different scales, the iteration of inversion begins at a large scale, and then repeat at small scales, at each scale, we use Regularization-Gauss-Newton iteration method. At last we obtain the optimal solution of the original nonlinear optimization problem. The results of numerical simulations indicate that wavelet multilevel inversion is stable, has the ability of anti-noise, and can overcome the problem of local minimum. It is a global optimization inversion method.
|
PDF Full Text Request