Applications Of Wavelet Analysis To Computational Electromagnetics

The Method of Moments(MM) and the finite difference time domain method(FD ID) have been proven to be powerfi.il numerical techniques in electromagnetic field compu- tation. In this thesis, the wavelet MM(WMM) is used to make the moment matrices sparse, so it can be solved quickly with the help of iterative methods. And, a new mul- tiresolution time domain scheme with highly linear dispersion properties based on the Coifman scaling functions is proposed. The emphasis of this thesis is put on the WMM and the emphasis of WMM is put on the digital WMM. The author抯 major contribu- tions are as following. From the matrix theory perspective, a complete and brief digital WMM theory is pro- posed. which is the sum-up of the material available and addition made by author. The construction of wavelet sequences are introduced, the vanishing moments properties of which are proven in digital condition. Also, the construction of wavelet transform ma- trices using wavelet sequences are introduced. The cost of the digital WMM is com- pared with those of the conventional MM. The Mallat algorithm in frequency domain is proposed. The multiresolution analysis of a vector is put forward. The application of digital WMM is studied. The different between wavelet sequences used in two dimension problems and those used in three dimension problems is ana- lyzed and it is shown that the short Haar wavelet is adapted to three dimension problems; The application of orthonormal wavelet transform and dualorthonormal wavelet trans- form in digital WMM are presented and it is found that the dualorthonormal wavelet transform is faster, while the condition number of the moment matrix is unchanged after the orthonorrnal wavelet transform; The different between digital wavelet packet trans- form and digital wavelet transform is discussed and it is found that one can get sparser moment matrices using wavelet packet transform than using wavelet transform. These numerical tests used in above are the RCS computation of different scatters, which show that digital WMM is useful in the RCS computation. Then, the problem about energy leakage arising in the project 揟he EMC of earlywarning plane?is solved with Haar wavelet transform matrix, where the moment matrix is sparified and the equivalent magnetic current is got quickly. This test shows that the WMM is practical. In this thesis, two improvement of digital WMM are proposed. First, the daulor- thonormal wavelet transform is used to make the matrix arising in the MOM solution of magnetic field integral equation sparse, then the induced current is get using submatrix 5 iterative method. It is shown that the execution time is more effectively reduced than the method based on the MM hybird physical optics current. Second, a precondition method which is related to the sparity of the moment matrix in digital WMM is proposed. This method is very effective in accelerating computing compared to the method available. Coifiimn intervallic scaling functions are used as basis and testing functions in the MM solution of electric field integral equation. The number of numerical integral is reduced with the help of the vanishing moments of Coiflnan scaling functions. Two methods of vanishing moment approximating are proposed for integral equations with different kernel. Finally, a new method of multiresolution time-domain analysis is proposed, which is...