Research And Application Of Parametric Surface Based High Frequency Asymptotic Methods

The high-frequency asymptotic method(HF) is one of the numerical techniques for electromagnetic(EM) analysis and computation. Compared with other rigorous numerical techniques, such as method of moment(MoM), finite element method(FEM) and finite difference time domain(FDTD), the HF method is a favorable choice for solving the electrically large problem in applications, because of its conservation of computer resources(e.g. the computer storage and the speed of CPU) while holding a certain accuracy of computation. The computer aided geometric design(CAGD) enables components to be modeled by the accurate geometry of parameter forms, such as Bezier patches and non-uniform rational B-spline(NURBS) surfaces, which are the most widely used modeling technique. The CAGD based HF methods are capable of analyzing the components modeled with high accuracy, which are applied in EM engineering, including on-board antennas, propagation and radar cross section of complicated targets. However, there are still challenges in implementing the CAGD based HF method. For instance, the well developed NURBS based HF methods are not suitable for analyzing the NURBS surface defined by a free-form boundary, which is referred to as the trimmed NURBS surface. Besides, the deficiency of shadowing test as well as the lack of treatment for the geometrical discontinuities on the object surface has suspended the CAGD-HF from solving the real-life problems ever since their marriage in the 1990 s.In this dissertation, the keys to implement the CAGD supported HF methods are studied, including the implementation of the physical optics(PO) based on the trimmed NURBS surfaces, the fast shadowing test technique in scenarios modeled by trimmed NURBS surfaces, the physical theory of diffraction(PTD) and equivalent edge current method(ECM) for correcting the discontinuities on trimmed NURBS surfaces modeled bodies, as well as the ray-tracing technique of geometrical optics(GO) and uniform theory of diffraction(UTD). The contributions of this study are list as follows.1. The binary search tree based point classification algorithm is developed to solve the PO integral on the trimmed NURBS surface. Compared with traditional point classification algorithms, the proposed method gains significantly on conserving the CPU time, providing a lower computational time complexity.2. The patch classification algorithm is developed for further accelerating the PO integral evaluation on the trimmed NURBS surface. The divide-and-conquer strategy is employed for classifying the Bezier patch of the basis surface into different types, and with respect to each type of Bezier patch, different calculations strategy is applied to evaluating the PO integral on the Bezier patch. The proposed method makes it possible to solve the PO integral on the trimmed NURBS surface efficiently, which narrows the gap between the CAGD based HF method and the applications.3. A robust and efficient shadowing test technique is proposed for the trimmed NURBS modeled scenarios. The technique is based on the hierarchical space volume partitioning(HSVP), which is optimized by the surface area heuristic strategy to avoid as many the unnecessary ray-patch intersection solving as possible in a geometrical probability sense. The proposed shadowing test algorithm significantly improves the computational efficiency, which is capable of dealing with scenarios with high complexity in real-life. Moreover, the fast shadowing test technique can be commonly implemented in CAGD based HF methods, making the CAGD-HF methods real-life problem solving.4. The PTD and ECM are implemented to correct discontinuity of arbitrarily curved wedge, which is modeled with trimmed NURBS surface. The curvature adaptive tessellating scheme is proposed to cope with the wedge edge with varying curvature. The projection algorithm based parameter aligning technique is developed to maintain the 0C continuity between the wedge surfaces at the wedge edge. The proposed method provides a fully CAGD based numerical routine for solving the diffraction of discontinuities on the bodies modeled with parametric surfaces. Scattering of target with high complexity is successfully analyzed by the proposed method, validating the effectiveness of the method.5. The ray-tracing technique and GO/UTD on trimmed NURBS surface is studied. By tracking the direct and reflected ray on the trimmed NURBS surface, GO/UTD is applied to analyze the wide-band radiation pattern of dipole near the PEC body. Due to its frequency-irrelevant property of the ray, efficient GO/UTD based wide-band analyzing is possible to be implemented in the EM applications.