Research On The Integrative Electromagnetic Modelling And High Efficient Algorithms For Objects Located In A Half Space

Composite electromagnetic scattering form objects residing in an inhomogeneous environment can be commonly found in practical engineering applications. A halfspace scenario is a very typical inhomogeneous environment that have to be considered in the integrated electromagnetic modeling of objects and the earth/sea-air background.This dissertation studies the key techniques and fast solutions of integral equations for scattering and radiation problems in a half space.In the first, the electromagnetic waves generated by a point source located in a general half space are decoupled in the spectrum domain into TEand TMterms which are governed by transmission line equations(TLEs). As a result, the solution of complicated half-space Green’s functions is converted to the solution of much simpler TLEs.By imposing the continuous boundary conditions for each term at the infinite interface of the two half spaces, the field-type Green’s functions are expressed analytically, and are transformed into space domain by 2-D inverse Fourier transformation. The potential type Green’s functions, which are less singular, have also been deduced in this dissertation. Specially, the field-type Green’s functions when the source is located above a perfect-electrically-conducting(PEC) half space are given in closed form. After that, the singularity of the half-space Green’s functions is discussed.In view of efficient evaluation of the half-space Green’s function, the properties and physical meanings of Sommerfeld integrations(SIs) are analyzed and summarized.Various efficient methods for evaluating SIs are systematically researched, which can be classified into three types: direct numerical calculation and its optimizations, discrete complex image method(DCIM), and asymptotic approximation methods for large parameters. The optimizations for direct numerical calculation include extracting the asymptotic term, the branch point singular term and optimizing the SI path(SIP). The asymptotic approximation methods include reciprocal method, leading order approximation(LOA)and the revised weighted real image method. In order to reduce the time of numerically computing the Green’s function in the matrix filling stage, a tabulation and interpolation technique is introduced.Based on the efficient evaluation methods of Green’s functions, the method of moments(Mo M) is applied to solve the half-space surface integral equation(SIE). The numerical solution and critical techniques have been stated in detail. A set of wellconditioned SIE is firstly proposed according the equivalence principle. Then, the RWG basis functions, curvilinear RWG basis functions and Roof-top basis functions are introduced to expand the equivalent currents on the surface of the objects. After that, the integral equations are discretized into linear matrix equations with Galerkin’s method. An efficient matrix-filling strategy is adopted to avoid the repetitive computation of Green’s functions. The singularity of the Green’s functions is treated by adding and subtracting a singular term for RWG basis functions and Duffy transform method for CRWG and Roof-top basis functions. The excitation vector of the matrix system is discussed for scattering and radiation problems. Finally, methods of solving the linear matrix system are summarized. Numerical examples validate the accuracy of the codes developed based on the aforementioned techniques.The adaptive cross approximation(ACA) algorithm is adopted in this dissertation to reduce the computational complexity and the memory storage requirement in half-space Mo M. Due to its pure algebraic nature, the ACA algorithm does not depend on the integral kernel, which makes it very suitable for half-space problems involving complicated Green’s functions. As the object is naturally separated into two parts by the interface of the half space, two different mesh densities are required due to the contrast of the two background materials. Therefore, two multilevel tree structures are set up individually in the two regions. When the source and field points are in the same region, the implementation is similar to the free-space case. However, when considering the mutual coupling of the two regions, difficulties arise since the two trees are independent and the numbers of levels are, in general, different. In this case, a z-dependent grouping strategy including three clustering methods is proposed to redefine the well-separated interactions. Several numerical examples are demonstrated to validate the proposed schemes.In order to further enhance the efficiency for solving electrical large objects above or below the half-space interface, multilevel fast multipole algorithm(MLFMA) has been successfully implemented in this dissertation. The near field interactions are evaluated by traditional Mo M and the Green’s functions are rigorously computed without approximation. The far couplings are split into direct terms and reflected terms. The direct terms can be treated as that in free space MLFMA framework. While, the reflected terms can be approximated by the revised weighted-real-image method and also implemented via MLFMA. When the objects get very close to the interface, the phenomenon that the real image method deteriorates is observed and physical explanations are given. After that,a novel hybrid method of ACA and MLFMA is proposed to efficiently analyze the electromagnetic scattering from arbitrarily shaped, PEC bodies that are very close to or even penetrate the interface of a half space. The performance of the developed programmes is examined via several numerical examples。Finally, a recently developed higher-order basis function based on curvilinear triangular patches is extended to half-space applications and investigated carefully from different aspects. This high-order method reduces the degrees of freedom and especially the number of field-source interactions to a minimum level, which result in an extreme high efficient analysis of half-space electromagnetic scattering problems. Due to the flexibility of order selection, a uniform mesh guarantees the modeling accuracy even when the scatterer is straddling the interface of the half space, where extremely nonuniform mesh is always required in the traditional methods due to the distinct wavelengths of the surrounding media. The uniform discretization improves the properties of the matrix system and simplify the geometrical processing. Moreover, this higher-order method significantly simplifies the wide-band simulation, which is important in various half-space applications. In addition, the high-order basis function and fast solvers are combined to analyze typical electrical large problems in half-space applications.As a basic research on the composite electromagnetic scattering of arbitrarily shaped3-D objects within inhomogeneous half-space background, our research presented in the dissertation provides a powerful approach in rigorous modeling and effective solution,as well as a solid foundation for the further study on electromagnetic characteristic of objects reside in real earth/sea-air scenario. Integrated with a variety of efficient methods as well as Open MP parallel computing techniques, a set of numerical codes with good multi-platform portability and inheritance has been independently developed. Engineering numerical examples verify their accuracy and reliability.