Research On Fast Hybrid Algorithm Based On Integral Equation Method

The future wars will be the confrontation of technology, covering land, sea, air, space, that can be all-round and multi-level war. Thus the design technology of radar system has ever-increasing demands. In the design technology of radar system, the research on analysis of electromagnetic scattering of large complex targets and radiation of complex antennas mounted on complex platforms has gained much attention.Being associated with the National Natural Science Fund and a number of research projects, this dissertation mainly focuses on integral equation fast Fourier transform and the hybrid method research based on the electric field integral equation, and combines this algorithm with the technique of frequency sweep to realize the fast analysis of broadband electromagnetic system. The major contributions in this paper are summarized as follows:1) The method of moments(Mo M) based on electric field integral equation(EFIE), magnetic field integral equation(MFIE) and combined field integral equation(CFIE) is studied in detail. The computational accuracy, applicable area, advantages and disadvantages of these three surface integral equations are deeply analyzed. It is well known that the computing resources are usually insufficient when Mo M is used to solve electrically large problems. To alleviate this difficulty, describes three methods which are based on fast Fourier transform(FFT) accelerate the matrix-vector multiplication: sparse matrix-canonical grid, pre-correction fast Fourier transform, adaptive integral method.2) The integral equation-fast Fourier transform(IE-FFT) is studied and the algorithm processes are presented: Green’s function interpolation, Lagrange polynomial interpolation, store the sparse matrices in compressed format, FFT accelerate the matrix-vector multiplication, the storage and computation of IE-FFT. Then the IE-FFT based on MFIE and CFIE is studied in detail.3) Two modified IE-FFT algorithms are introduced in detail. The modified single-level fast Fourier transform(FFT) algorithm which is based on the sub-domain FFT acceleration is introduced the concept of the empty groups. The empty grid of theregular Cartesian grid is abandoned, the storage of the Cartesian grid from the global grid into the non-empty grid. To optimize the interpolation process, a novel Gauss interpolation operator in the IE-FFT algorithm. At the same precision, the grid distance of the Gaussian interpolation process can be greater than the Lagrange interpolation process. The IE-FFT algorithm can optimize accuracy of the grid distance.4) The principle, formulation and process of the asymptotic waveform evaluation and the best uniform rational approximation are introduced in detail. Furthermore, in conjunction with the integral equation methods(included Mo M and IE-FFT, etc.) to fast analyze electromagnetic problems in both wide-band frequency and angular domains. Finally, numerical examples analyze advantages and disadvantages of memory requirements, computational accuracy and solution time.5) The method of moments and physical optics(PO) hybrid principle, formulation and process are studied. An efficient hybrid analysis that combines integral equations with physical optics approximation is proposed, which further extends the hybrid algorithm. The modified single-level Fast Fourier Transform(FFT) algorithm based on combined field integral equation(CFIE), simplifying the process of near-field correction, and abandon empty grid of the regular Cartesian grid. The modified integral equation-physical optics(IE-PO) hybrid formulation with the best uniform approximation, is applied to analyzing wide-band properties. Finally, the relative root mean square(RMS) RCS error of this algorithm is given.6) The principle, formulation and process of EI-MoM-PO and EI-IE-PO hybrid formulation are studied in detail. The method proposed in this paper provides a possible way to avoid the calculation and storage of two coupling matrix and the interaction impedance matrix. Compared with the conventional Mo M-PO method, the proposed method can greatly reduce the memory requirements and improve the computational efficiency. The proposed method combined with the best uniform approximation, is applied to analyzing wide-band properties.