Research On Domain Decomposition Method Based On The Hybridization Of High Frequency And Low Frequency Methods

The researches on the problems of antennas mounted on the electrically large platforms, electromagnetic compatibility, large antenna array and the details on the platform affecting the antenna have received much attention in the modern antenna applications. When solving these problems, the existing numerical methods are facing severe challenges. The properties of multi-scale and large number of unknowns in the problems will result in the high computational costs. In some applications, under the condition of keeping the accuracy, it is necessary for antenna designs to improve the efficiency and reduce the computational costs.After researching the equivalence principle algorithm(EPA) deeply, the combinations of equivalence principle algorithm and other numerical methods are studied thoroughly in this thesis. The combinations are based on the idea of the domain decomposition method, improve the computational efficiency of the equivalence principle algorithm and also keep the accuracy. The researches in this thesis focus on the following contents:1. The theory of the equivalence principle algorithmIn this thesis, the theorem of Huygens is studied firstly. Then the process of using EPA and the operators used in EPA are introduced. In EPA, the object with complex structures or high permittivity is enclosed by an equivalence surface. The equivalence operator can calculate the interactions between the equivalence surface and the object in the surface. The function of the equivalence operator is to translate the unknowns on the object to the equivalence surface. The mutual couplings among the different equivalence surfaces are computed by the translation operator. The density of unknowns on the equivalence surface is much smaller than that on the object inside and the meshes on the surface is more equally distributed than those on the object. Therefore this method is more suitable for solving the multi-scale problems. The equivalence operator varies as the object enclosed by the equivalence surface changes. If the object is metallic, the surface integral equation will be used to calculate the equivalence operator. If the object consists of metal and dielectric, the volume-surface integral equation will be utilized. The equivalence operators based on the two integral equations are introduced.2. The excitation for radiation problems and antenna design based on EPAUnlike the scattering problems, the excitations in the radiation problems are more complicated on modeling and being evaluated. The calculation of the excitation is related to the accuracy of the numerical method. In this thesis, several ways of modeling the excitation are given, and the equivalence operator for the radiation problems is introduced. Furthermore, the feasibility of EPA for solving the practical applications is demonstrated by the comparisons on simulated and measured results of two antennas designed.3. Hybridization of EPA and physical optics for the problems of antenna mounted on the electrically large platform.To the many existing numerical methods it is difficult to solve the problems on antennas mounted on the electrically large platform for the properties of multi-scale and large number of unknowns. The multi-scale property will make the condition number of the impedance matrix become worse. This will result in the slow convergence of the iterative method. Therefore, in this thesis, EPA is combined with physical optics(EPA-PO). The currents around the antenna are computed by EPA, and currents on the platform are estimated by PO. This method can keep the precision and improve the efficiency of EPA when solving the problem of antenna mounted on the electrically large platform. Besides, in many practical applications, the antennas are connected with the platform. In order to avoid the currents flowing from the antenna to the platform being cut by the equivalence surface, the transition region is introduced to keep the continuity of currents in EPA-PO. However, the existance of the transition region will make the convergence of iterative solver slower than before. In this thesis, one preconditioning is introduced to speed up the convergence of EPA-PO in this case.4. The high efficient estimation of large periodic antenna arrayDesigning the large periodic antenna array will spend lots of computational resource if normal numerical methods are used. If the structure of the antenna is complex, the computational efficiency will reduce further. Periodic method of moments(PMM) is a typical way which utilizes the periodicity of the array. In this method, method of moments and the periodic Green’s function are combined. However, the periodic Green’s function is series. Evaluating of the series is slow, especially the array is two-dimensional. The most time consuming procedure in PMM is calculating the periodic Green’s function series. If the number of unknowns becomes fewer, the times calculating the series will be fewer, and the elapsed time will become shorter correspondingly. Based on this idea, the periodic equivalence principle algorithm(PEPA) is introduced in this thesis. In this method, EPA which can reduce the number of unknowns is combined with the periodic Green’s function. The efficiency of PMM is improved. This method can also research the arrays with same periodicity but different antenna elements efficiently. Besides, PEPA can accelerated by the touched equivalence surfaces.5. The high efficient computation of large finite periodic antenna array based on the hybrid of high frequency and low frequency methods.PEPA is based on the hypothesis that currents on the each element are identical and the edge effect is ignored. This will result in errors. In order to avoid the errors, the research contains two aspects. Firstly, the technique on extracting the active element pattern of sub arrays based on EPA is introduced. In this method, the sub arrays are calculated by EPA and the far-field radiation pattern is derived by the field of sub arrays. Secondly, one kind of hybridization based on domain decomposition method is discussed. In this method, the array is divided into two parts, the center part and edge part. The center part and the edge part of the array are calculated by PEPA and EPA respectively. Compared to PEPA, although the efficiency is sacrificed, the accuracy is improved. The two methods are practical in applications. Furthermore, in order to meet the requirement of solving the problem on antenna array mounted on the platform, the hybridization of PEPA, EPA and PO are involved. This method makes the domain decomposition method based on the high frequency and low frequency methods more practical.The researches presented in this thesis cover the topics of the domain decomposition method based on the high frequency and low frequency methods in different practical applications. By reducing the computational costs and improving the efficiency, it provideds us a new solution for simulation of the problems about antennas mounted on the electrically large platform.