Multi-Resolution Time-Domain Schemes For Numerical Electromagnetic Calculations

The time-domain methods are the main trend in the development of numericalelectromagnetic calculations. This dissertation introduces a newly proposed method:Multi-Resolution Time-Domain (MRTD), and mainly focuses on the algorithm itself. First of all, the basis of the MRTD method is studied. In Chapter 2, waveletsanalysis and multiresolution analysis, the mathematical basis, are introduced, and thecharacteristics of the wavelets basis functions, including orthonormality, compactsupport, multiresolution and so on, are also introduced. The advantages of theapplications of these functions to the numerical electromagnetic calculations arediscussed. In Chapter 3, the algorithm basis of MRTD: the combination of the waveletsand the method of moments(MoM) is studied. This Chapter shows that the MoM basedMRTD method is the combination of wavelets and MoM using Galerkin sampling.Chapter 4 introduces the applications of the FDTD method. Radiated-transmissionapproach is used to analyze the properties of the ultra-wide band electromagneticpropagation. This Chapter presents the effect of the media on the electromagneticpropagation with different electromagnetic parameters and different configurations, andthe results agree well with those of the measurements. In Chapter 5, the algorithmtheory of the MRTD method is discussed, and the deduce of MRTD is consummatedand the frame of MRTD is constructed. And this Chapter deduces the detailed formulausing Battle-Lemarie wavelets and Harr wavelets, respectively. Finally in Chapter 6, theproblems of boundary conditions and incident wave, as the most valuable problem ofMRTD as a time-domain method, are studied. This Chapter presents the simulationresults of the electromagnetic propagation and its interactions with the dielectric slaband analyse of the graph of the reflection coefficient in frequency. Compared withFDTD results, the numerical results, obtained using the MRTD method, show thedirectness and conciseness of MRTD as a time-domain method and the advantages ingrid enlargement and saving computer resource etc.. The whole frame of thisdissertation follows the idea: Mathematical Basis-- Algorithm Basis-- ExperienceTechnique-- Theory Implementation-- Result Analysis.