| With the development of engineering technology in radar, communication and electronic technique fields, the diffraction of electromagnetic wave by surfaces become the interest to many researchers, such as radiation problem of carrier antennas, electromagnetic compatibility, radar detection and so on. Based on the requirement from engineering, the modeling method for electromagnetic waves diffraction on arbitrarily shaped smooth surfaces is investigated in this paper.The main content of this paper includes the following parts.1) The parametric surfaces is employed to describe the geometry of target, and complex targets are described by a combination of several surface patches. Considering that NURBS format is more efficient for the storage and representation of a model, while Bezier is more stable for the numerical computations, the NURBS patches are subsequently subdivided into a combination of rational Bezier patches using Cox-De Boor algorithm. Then targets are described using Bernstein basis function.2) The geodesic differential equations are solved using difference method to realize the fast creeping-ray tracing (or geodesic computation) on one single parametric surface patch. According to the numerical results, the creeping-ray tracing method based on difference method may produce discretization error on arbitrarily shaped surface patches. The reason for the discretization error is analyzed in the paper to lay the foundation for the accurate creeping-ray tracing in the further reaserch.3) In order to realize the accurate creeping-ray tracing on arbitrarily parametric surface patch, the geodesic equations are solved by using Runge-Kutta method. With the aim to raise the accuracy of creeping-ray tracing, the paper employed the4th-order Runge-Kutta method instead of difference method to solve the geodesic equations. In this way, the high-order accurate numerical solution of the geodesic equations can be obtained.4) A new method is developed based on the property of geodesic in this paper to realize the accurate and efficient creeping-ray tracing on one parametric surface patch. In differential geometry, the principle normal vector of every point on a geodesic curve coin side with the normal vector to the surface which it lays. According to the principle, and together with Taylor series, the accurate and efficient creeping-ray tracing on one arbitrarily shaped parametric surface patch can be performed.5) The transition method is presented in the paper to deal with the transition of creeping-ray tracing between adjacent parametric surface patches. Since the independence of the parameters between surface patches, the parameters are discontinuous between the surface patches. In order to solve the problem, the author employed a parametric line function to deal with the transition across the common sides between two adjacent surface patches, and improving the format of Bernstein basic function to remove the parameter discontinuity at the common point among several adjacent surface patches, in this way the transition of creeping-ray tracing across the common point can be performed.6) The simulation method is proposed in this paper for the surface diffraction by arbitrarily shaped PEC convex surface targets. On the base of the accurate creeping-ray tracing for the surface targets with arbitrary shapes, the diffraction by the PEC targets can be analyzed by using the uniform geometric theory of diffraction (UTD).7) The creeping-ray tracing method for arbitrarily shaped anisotropic convex surface targets is preliminarily studied in this paper. On the isotropical surfaces, the creeping-ray tracing is the same as that on PEC surfaces, but on the anisotropic surfaces, not only the affect from surface shapes (curvature radius) but also that from the optical axis should be considered in the creeping-ray tracing. This paper employed the knowledge of variation calculus to develop the differential equations for the creeping-ray on the anisotropic surfaces. |
PDF Full Text Request