A Study On The Multiresolution Time-domain Method And Its Applications To Electromagnetic Scattering Problems

With the rapid development of stealth technology, wideband and ultra-wideband radar, thetheoretical analysis and research on wideband electromagnetic scattering characteristics of radar targetsare demanded urgently. By means of simple time-frequency transformation, the time-domain numericalmethods can obtain wideband information of targets and then achieve more profound and intuitionisticcomprehension about physical quantity and phenomenon, therefore have aroused great attention. As anew full-wave time-domain numerical method, the multiresolution time-domain (MRTD) scheme canapply lower sampling rate in space under the circumstance of remaining relatively less phase error dueto a good linear dispersion property. Its sampling rate can reach Nyquist sampling limit theoretically, i.e.two sampling points per shortest wavelength. So the MRTD scheme can hugely save computerresources, reduce computational time and then enhance computational efficiency. For electrically largetargets, especially, the MRTD scheme has more obvious advantage in computation.The main researches and contributions of the thesis are summarized as follows:1. The MRTD schemes based on Daubechies scaling functions (Daubechies-MRTD) andbiorthogonal Cohen-Daubechies-Feauveau scaling and wavelet functions (CDF-MRTD) are studiedtheoretically. The iterative equations of the electromagnetic fields are derived in detail.2. The time stability and the space numerical dispersion property of the MRTD only based onscaling functions (S-MRTD) are dedailed analyzed. Analysis results show that the numerical dispersionproperties of the MRTD schemes are obvious better than those of the conventional finite-differncetime-domain (FDTD) method. But the time stability condition, i.e. Courant condition, of MRTDscheme is more rigorous than that of the conventional FDTD method, which explains that the MRTDscheme trades time for space in computing.3. The connecting boundary condition aiming at the application of S-MRTD is studied. TakingDaubechies-S-MRTD as the example, the connecting boundary conditions under the two-dimensional(2D) TM polarized and three-demensional (3D) conditions are deduced in detail. And the complete"modified iterative equations" of the connecting boundary conditions under the2D TM polarized and3D conditions, which is general for all of the S-MRTD schems, are presented first.4. The application of the MRTD scheme to electromagnetic scattering is investigated, whichincludes the anisotropic perfectly matched layer (APML) absorbing boundary condition andnear-to-far-field extrapolation method under the circumstances of time-harmonic and transient field, etc. And the numerical tests of electromagnetic scattering computed by the Daubechies-S-MRTD andCDF-S-MRTD schemes are carried out. Numerical results show that the connecting boundary conditionand the APML absorbing boundary condition investigated in this thesis are effective, and thecomputational efficiency of the two schemes are better than that of the conventional FDTD method.5. According to the multi-region decomposition technology of Daubechies-S-MRTD, a conformalMRTD (CMRTD) scheme based on Daubechies scaling functions used to the perfectly electricconductor (PEC) targets is proposed by combining the Daubechies-S-MRTD scheme with the locallyconformal FDTD (CFDTD) algorithm used to PEC targets. The numerical results of theelectromagnetic scattering computation of PEC targets demonstrate that the proposed CMRTD schemecan effectively reduce the staircase error of Yee's leapfrog meshing and improve the computationalaccuracy obviously. The proposed CMRTD scheme can also be used in the CDF-S-MRTD scheme.6. Based on locally conformal technology and the concept of effective dielectric constant (EDC),two CMRTD schemes based on Daubechies scaling functions used to dielectric targets, namely, thescaling functions integral CMRTD (SFI-CMRTD) and multi-region CMRTD (MR-CMRTD) scheme,are proposed and studied. The numerical results of the electromagnetic scattering computation ofdielectric targets show that both of the two schemes can solve the ineffectivity caused by thediscontinuous surface in dielectric case and the staircase error of Yee's leapfrog meshing, and also canimprove computational accuracy obviously. Moreover, the MR-CMRTD scheme has bettercomputational efficiency than the SFI-CMRTD scheme, and has more advantage when analyzingelectrically large dielectric targets.