Electromagnetic Research On Scattering Of Dielectric Targets And Radiation Of Antenna On Platform

Radar has a rapid development in the Second World War and today becomes a typical case which represents the advanced level of the military industry of a country. The design of Radar system is closely related to the prediction of electromagnetic scattering characteristics of targets and the analysis of radiation performance of antennas as the system front end. The electromagnetic computational method is the foundation of the prediction of electromagnetic scattering characteristics of targets whose final requirement is the accurate and fast calculation of targets of complex shape and electrically large size. On the other hand, one of the difficulties of the analysis of antenna radiation performance is the computation of effect of complex platform on antenna.Being associated with the above background and predicted projects of national defense, this dissertation mainly focuses on the Method of Moments (MoM) and its fast algorithm regarding with the dielectric targets in electromagnetic algorithms. The fast computation of wideband scattering property of dielectric targets is realized with the frequency sweeping technique. In addition, relative research on the radiation performance of antenna mounted on platform is conducted. The major contribution of this dissertation can be summarized as the following six aspects:1. The MoM of electric field integral equation is studied in detail. The mathematical principle of MoM is introduced and the electric field integral equation is established according to the boundary condition of perfect electric conductor. The feature of RWG basis function, the Galerkin testing procedure and the Gauss Quadrature are emphatically discussed. Detailed formula deduction originated from the singularity problem is implemented.2. The MoM based on the PMCHWT equations and volume integral equation (VIE) is investigated. To begin with the equivalently external and internal problem concerning with the scattering model of homogeneous dielectric targets, the formation of the PMCHWT equations is described. The MoM is utilized to solve the PMCHWT equations. The symmetrical property of impedance sub-matrices and the corresponding singularity problem are discussed. The SWG basis function and its characteristics based on tetrahedral mesh are presented. The VIE which is suitable for general dielectric targets is resolved by the MoM while the formulae related to the singularity problem are deduced. Further study on MoM for dielectric-metal mixed target is conducted.3. In the Integral Equation-Fast Fourier Transform (IE-FFT), the construction of the uniform Cartesian grids and the interpolation technique of Green’s function in free space by the Lagrange Polynomials are introduced. The three-layered Toeplitz property of the discrete Green’s function matrix is displayed visually and the principle of the three-layered Toeplitz matrix and vector product accelerated by FFT is completely explained. To the problem of large memory requirement of the MoM and high computational complexity of the solution of matrix equation, the IE-FFT based on the PMCHWT equations is studied while two possible schemes of the FFT acceleration are compared, which reduces the memory requirement and the computational complexity to O(N1.5) and O(N1.5 log N), respectively. Likewise, the IE-FFT based on the VIE is investigated, which decreases the memory requirement and the computational complexity to O(N) and O(N log N), respectively.4. The VIE-MoM in combination with the asymptotic waveform evaluation (AWE) and the best uniform rational approximation (BURA), respectively, is applied to the fast prediction of wideband electromagnetic scattering property of dielectric targets. The first one implements a Taylor series expansion of the impedance matrix, excitation vector and unknown vector of the matrix equation at the given frequency. The coefficients of the Taylor series of the unknown vector are solved by the merger of similar polynomial item regarding with frequency. The Pade approximation of the unknown vector is employed to further extend the bandwidth. The second algorithm chooses the Chebyshev nodes within the whole bandwidth, calculates the equivalent volume current density at the corresponding wavenumber and improves the computational accuracy by the Maehly approximation. For the analysis of wideband scattering property of homogeneous targets, the hybrid method that combines the PMCHWT-IE-FFT with BURA is proposed which shortens the solution time of the electric and magnetic currents by FFT during the BURA procedure.5. To the problem of higher computational complexity of the modified impedance matrix, the IE-FFT-PO which unites the MoM-PO and IE-FFT is proposed. First of all, the modified impedance matrix is decomposed into the product of the mutual interaction impedance matrix and the coupling matrix between the MoM region and the PO region. Then the elements of the self-interaction impedance matrix, the mutual interaction impedance matrix and the coupling impedance matrix are sparsely stored while three matrix vector products accelerated by FFT in every step of the iterative solution are performed.6. For the radiation problem of antennas on platform, the technique of partitioning of the MoM region based on the MoM-PO is proposed which classifies each antenna with its vicinity as one MoM region and treats the rest area as the PO region. The method considers the mutual interaction between each MoM region and PO region and further accounts for the self-interaction among the MoM regions. Compared with the conventional MoM-PO, the proposed technique leads to significant decrease of the number of modified impedance elements, which cuts down the modification time of the self-interaction impedance matrix. Profiting from the thought of iterative MoM-PO, the Multi-IMoM-PO is proposed which further reduces the analysis time of radiation problem of multi-antenna mounted on platform compared with the Multi-MoM-PO.