Application of wavelets to scattering problems of inhomogeneous dielectricslabs

In this paper, we apply the discrete wavelet transform (DWT) and the discre te wavelet packet transform (DWPT) with the Daubechies wavelet of order 16 to effectively solve for the electromagnetic scattering from a one-dimensio nal inhomogeneous slab. Methods based on the excitation vector and the [Z] matrix are utilized to sparsify an MoM matrix. As we observed, there are no much high frequency components of the field in the dielectric region, henc e the wavelet coefficients of the small scales components (high frequency c omponents) are very small and negligible. This is different from the case o f two-dimensional scattering from perfect conducting objects. In the excita tion-vector-based method, a modified excitation vector is introduced to ext ract dominant terms and achieve a better compression ratio of the matrix. H owever, a smaller compression ratio and a tiny relative error are not obtai ned simultaneously owing to their deletion of interaction between different scales. Hence, it is inferior to the [Z]-matrix-based methods. For the [Z] -marix-based methods, our numerical results show the column-tree-based DWPT method is a better choice to sparsify the MoM matrix than DWT-based and ot her DWPT-based methods. The cost of a matrix-vector multiplication for the wavelet-domain sparse matrix is reduced by a factor of 10, compared with th at of the original dense matrix.