Application Of Wavelet And Multiresolution Time Domain (MRTD) On Electromagnetic Scattering

This dissertation is concerned with the improved algorithm of wavelet functions in the scattering problems—Wavelet MoM fast algorithm and Multiresolution Time Domain (MRTD), whose basis principle is the wavelet-Galerkin time domain (WGTD). They are developed based on the MoM and FDTD method. The conception of scaling function and mother wavelet function are presented after Multiresolution Analysis (MRA) of wavelet function, and illustrate the decomposition and reconstruction of Mallat and explicate the principle of MRA by use of Haar wavelet.To avoid the integration of wavelet functions, the discrete wavelet MoM method is used in the paper, that is, impendence matrix approximation at high level is calculated using MoM method, which was obtained with pulse base and dirac-δtesting. We use Daubechies'wavelet of order 6 and Coifleit wavelet of order 4 to sparsify matrix upon transforming it into the standard matrix through FWT. After the sparse matrix is created by setting threshold, the row-indexed sparse storage technique is used to accelerate multiplying operations matrix with vector in Bi-CGSTAB iterative solver. Scattering of electromagnetic waves from a two-dimensional groove in an infinite conducting plane is studied numerically using the hybrid method of PO and wavelet MoM. At last, we compute the scattering and composition scattering of random rough surface using wavelet MoM method, and the results show the advantages of computational efficiency of this algorithm.FDTD is a powerful numerical technique in electromagnetic field computation; however to restrain its numerical dispersion, fineness cells are required, which takes more computer resources and longer computing time. To circumvent this, we make a professional research on MRTD based Daubechies'scaling function with two vanishing moment. An interface between FDTD and MRTD method is presented and MRTD method is successfully applied in the EM scattering problems. MRTD method can enlarged cells size to reduce memory without sacrifice accuracy, so it has better computational efficiency. Compared with FDTD, MRTD has less phase error and so its numerical dispersion is less with the same cells size. It is well known that the effect between circumstance and object is very complicated but has an important role in EM scattering. The EM scattering of target, which is in lossy half space, is computed by MRTD method. We construct the fractal model of clustered particles and then analysis its scattering characteristic using MRTD method. Through parameter setting, plasma is equivalent to Debye dispersive media. The Auxiliary Differential Equations (ADEs) is a flexible method in dispersive media for FDTD method, we combine its procedure with MRTD method and compute the scattering of Debye dispersive media and plasma correctly. The validity and accuracy of MRTD method for dispersive media are proved through obtained results.