Investication Of Fast Numerical Methods For Electromagnetic Scattering From Objects

The electromagnetic scattering from objects and influence of radomes on antennas are important research contents in designing of aircrafts and antenna radomes. With the development of the computer technology, the computer simulation has become an important means in design, and opened a new era of computational electromagnetics. The majority of this thesis is concerned with the development of efficient numerical methods to analyze electromagnetic scattering and radiation problems.The electromagnetic scattering from the composite model of objects and randomly rough surface is firstly investigated. For the 2-dimensional scattering problems, a new method that combines the characteristic basis functions (CBFs) and matrix decomposition algorithm (MDA) is proposed to fast analyze the difference field radar cross-section of the object. In this method, the CBFs are used to calculate the induced current on the rough surface, the matrix of nonself-block interactions of the rough surface and the coupling matrix between the object and the rough surface are calculated by the MDA, which reduces the CPU time and memory requirement. For the 3-dimensional scattering problems, the induce current on the object and the rough surface are expressed with the hierarchical basis functions, which allows a larger mesh size compared with the conventional basis functions. The CPU time can be reduced significantly with reasonable order of the basis function and mesh size. The matrix vector product is accelerated with the multilevel fast multipole algorithm (MLFMA).Secondly, a multigrid (MG) preconditioner is proposed based on the near field matrix derived from the MLFMA to accelerate the convergence of the iterative solution. The multigrid model is constructed by recursively dividing every triangular element on the coarse level into 4 small ones. The RWG basis functions defined on the coarse level are expressed with linear combinations of those on the fine level, and the expansion coefficients of which are used to construct the restriction and interpolation operators. To further accelerate the convergence of iterative solution, a set of solenoidal basis functions on the coarse level are constructed additionally, which are also expressed with linear combinations of RWG basis functions on the fine level and adopted to construct the second restriction and interpolation operators. The two sets of coarsening techniques are then combined together to remove the low-frequency components of the iterative error.Thirdly, the monostatic radar cross section (RCS) of the object over a wide-band and wide-angle has been investigated with the fast physical optics (FPO) and the multilevel physical optics (MLPO) method based on the phase compensation and retrieval techniques. In this method, the phase compensated fields at sampling frequencies or angles are firstly calculated and stored. The phase factor is designed to cancel rapid oscillations due to the phase present in the integrand. The phase compensated fields at required frequencies and angles are then obtained efficiently by the interpolation technique, and the required fields are obtained followed by phase retrieval. For the analysis of frequency-angle sweep or angle-angle sweep problems, the phase compensated fields need to be calculated on each level, which form a 2-dimensional matrix. Further investigation shows that this matrix is rank deficient, thus low-rank matrix decomposition method can be used to accelerate the computation. In this paper, the adaptive cross approximation (ACA) is used and good performance is achieved. Further more, the phase compensation and retrieval techniques in the FPO method is extended to the shooting and bouncing ray (SBR) method for wide-band monostatic RCS prediction. Different from the FPO that the integration is implemented over the surface of the object, the integration is implemented over the areas that the ray tubes leave the object in the SBR instead. Hence it is difficult to implement the phase compensation and phase retrieval in the SBR as that in the FPO method directly. In this paper, a coordinate transformation is introduced in the integral equation, which transforms the original ray tubes model into a new one. The FPO technique can then be taken on the revised model for wide band RCS prediction.Finally, the performances of electrically large metal space frame radomes are investigated. Since the radome is electrically large (compared with the wavelength), it is difficult to analyze efficiently with full-wave methods, such as the MLFMA. However, the high frequency methods provide an effective solution means, in which the far fields of the metal space frame and dielectric radome are calculated respectively. For the metal space frame, the induced field ratio (IFR) method is often used to calculate the far fields. However, the frames are replaced by lines in the modeling process and the frames are assumed to be infinite long, which leads to model errors, especially at frames connections. Further more, The IFR method is efficient when the cross section of the frame is circular since the IFR can be obtained with analytical formula. For other cross sections, numerical method is needed to calculate the IFR. In this paper, the physical optics (PO) method is used to calculate the far fields of the metal space frames, which reduces the errors come from modeling. The far fields of the dielectric radome are calculated with the aperture integration-surface integration (AI-SI) method. The Lagrange interpolation technique is used to calculate the transmission coefficients. Further more, the thicknesses of the dielectric radome are optimized with the genetic algorithm.