Study And Application Of Higher-order MoM And Its Fast Algorithm

In the past decades, the method of moments (MoM) has been widely used to solve the electromagnetic radiation and scattering problems. However, the implementation of MoM will lead to a dense system of linear equations in which the memory and computation costs areO(N~2) and O(N~3) , respectively, where N is the number of unknowns. Compared with the traditional small subdomain and lower-order basis functions based MoM, the large subdomain and entire-domain basis functions based MoM will lead to a great reduction of unknowns which can reduce the costs of computer resources. This paper research on the large subdomain and hierarchical basis functions based higher-order MoM and associated fast algorithm and hybrid method, and it also put emphases on the radiation problems of the rectangular waveguide array with edge slots. The main contributions of the dissertation include:1. A hybrid method is proposed to analyze the large array structure efficiently. On one side, entire-domain basis functions are established by the combination of the lower-order basis functions on each array element with which the number of unknowns are reduced to the number array elements. On the other side, the discrete Fourier transform method accelerated forward backward method is introduced to solve the matrix equation efficiently. With the combination of these two methods, the new hybrid method can analyze the scattering of the large finite 2D arrays with both the memory and computation costs only O(N_A) , where N_A is the number of array elements.2. Detail research is done for the hierarchical basis functions based higher-order MoM. The optimized impedance matrix filling method is introduced, and both the relationship between currents expanding order and subdomain size and the influence of the geometry modeling accuracy on the results are analyzed. Meanwhile, the locally corrected Nystr(o|¨)m method which is equivalent to the higher-order MoM is studied. By the comparison of the two methods, a better understanding of the higher-order MoM is provided, and a good foundation is established for the higher-order MoM based fast algorithm and hybrid method.3. In dealing with the difficulties of accelerating the higher-order MoM by AIM, the quadrature points based projecting procedure is proposed. Compared with the existing projecting method, the new method has the advantages of easy accuracy control and less projected grid nodes which can greatly improve the efficiency of projecting the large subdomain defined higher-order basis functions. Meanwhile, a novel improved Gaussian interpolation formula is proposed to increase the interpolation accuracy of the Green’s functions. In other words, with the new interpolation formula and under the same accuracy demand, the grid space can be large which can also improve the efficiency of the implementation of AIM.4. A large subdomain modeling based MoM-PO method is proposed to compute the radiation of the antennas which are mounted on the electrically large platforms. The higher-order basis functions are employed in the MoM region to reduce the number of unknowns, which can save the memory costs of the hybrid method. The Nystr(o|¨)m currents discretization is employed in the PO region, with which the testing functions in the PO region can be constructed easily and the interactions between the two regions can be computed efficiently. Moreover, the locally corrected procedure is introduced to deal with the singular integrals for computing the impedance in overlapped region.5. The higher-order MoM is applied to analyze the rectangular waveguide array with edge slots accurately and efficiently. The equivalent magnetic currents are modeled on the inner surface of the slot cavity to analyze the waveguide interior region efficiently. The equivalent magnetic currents are modeled on the outer surface of the slot cavity to make the surface of waveguide exterior region smooth which can improve the efficiency of analyzing the waveguide exterior structure. Meanwhile, the equivalent electric currents are modeled on the surfaces of both the slot interior region and the waveguide exterior region to accurately analyze the structure of the two regions. Compared with the traditional equivalent magnetic currents based methods which are widely used in dealing with slot structure, the new method considers the structure of the waveguide exterior region more accurately. In solving the integral equations by MoM, the higher-order basis functions are employed to expand all the equivalent currents which can greatly reduce the number of unknowns. Accordingly, the proposed method can analyze the 2D array accurately and efficiently, and it can also make a good preparation for considering the influences of the platform.6. The AIM is introduced to accelerate the higher-order MoM procedure in analyzing the edge slot array. Based on the concept of overlapped domain decomposition method for integral equations, an edge slot near pre-conditioner is proposed to make sure that the iterative method for not quite large arrays is convergent. By employing the combined field integral equation (CFIE) to solve the electric currents in the waveguide exterior area, the convergence of the iterative method is greatly accelerated which can make the AIM valid to analyze large arrays. The projection procedures for all the magnetic and electric currents are also given.