电磁散射的交替方向隐格式宽角抛物线方程方法研究

发布时间：2018-06-22 00:29

本文选题：抛物线方程方法 + 宽角度抛物线方程方法　；参考：《南京邮电大学》2015年硕士论文

【摘要】：电磁计算主要可以分为低频方法和高频方法两大类,常见的低频方法比如时域有限差分方法,矩量法以及有限元法等,这些方法虽然可以有效地分析电小尺寸物体的电磁散射问题,计算精度也比较高,但是在分析电大尺寸物体的电磁散射问题时,由于精确方法对计算机的配置要求过高,因此很多时候精确方法不能有效地分析电大尺寸物体的电磁散射问题。而高频方法比如射线跟踪、物理光学等虽然对计算机的配置要求不高,可以用来分析电大物体的电磁散射问题,但是计算精度差。而抛物线方程方法(Parabolic Equation)则介于这两种方法之间,它相比于矩量法等精确方法来说对计算机的配置要求较低,而相比于高频方法来说它的计算精度更高。传统基于有限差分格式的抛物线方程方法的主要思想是将原本要分析的三维问题转化为一系列二维问题,逐面来求解原问题,这样相比于直接分析三维问题大大节省了计算资源。本文介绍的基于交替方向隐格式(ADI)的抛物线方程方法将三维问题转换成一系列的一维问题,逐行或逐列来求解,因此相比于传统的有限差分方法更节省了计算资源且计算速度更快。抛物线方程的交替方向隐格式解法原理清晰,计算简单,相比于矩量法等精确方法大大提高了计算速度,有很高的应用价值。本文主要对基于交替方向隐格式的抛物线方程方法进行了研究和分析,主要内容包括:首先,介绍了抛物线方程方法的基本原理以及用来分析三维目标双站RCS的步骤。其次,研究了抛物线方程的交替方向隐(ADI)格式解法,并给出了宽角度抛物线方程的ADI格式,通过算例验证了算法的正确性,这是本文的一大创新点。最后,对程序进行了并行加速处理,进一步加快了算法的计算速度。
[Abstract]:Electromagnetic calculation can be divided into two categories: low frequency method and high frequency method. The common low frequency methods such as finite-difference time-domain method, moment method and finite element method, etc. Although these methods can effectively analyze the electromagnetic scattering problem of electrically small size objects, and the calculation accuracy is also relatively high, but in the analysis of electromagnetic scattering problems of electrically large size objects, the precise method requires too high a computer configuration. Therefore, in many cases, the accurate method can not effectively analyze the electromagnetic scattering problem of electrically large objects. Although the high frequency methods such as ray tracing physical optics and so on have low requirements for computer configuration they can be used to analyze the electromagnetic scattering problem of electrically large objects but the calculation accuracy is poor. The parabolic equation method is between these two methods. Compared with the accurate methods such as the moment method, it requires less computer configuration, and its calculation accuracy is higher than that of the high-frequency method. The main idea of the traditional parabolic equation method based on finite difference scheme is to transform the three-dimensional problem into a series of two-dimensional problems, and solve the original problem one by one. Compared with the direct analysis of three-dimensional problems, the computational resources are greatly saved. The parabolic equation method based on alternating direction implicit scheme (ADI) is introduced in this paper to transform the three-dimensional problem into a series of one-dimensional problems, which can be solved line by line or column by column. Therefore, compared with the traditional finite difference method, the computational resources are saved and the computation speed is faster. The method of alternating direction implicit scheme for solving parabolic equations is clear in principle and simple in calculation. Compared with accurate methods such as the method of moments the calculation speed is greatly improved and the application value is very high. In this paper, the parabolic equation method based on alternating direction implicit scheme is studied and analyzed. The main contents are as follows: firstly, the basic principle of the parabolic equation method and the steps used to analyze the bistatic RCS of 3D target are introduced. Secondly, the alternating direction implicit (ADI) scheme of parabola equation is studied, and the ADI scheme of wide angle parabola equation is given. The correctness of the algorithm is verified by an example, which is a great innovation of this paper. Finally, the parallel acceleration processing of the program is carried out, which further speeds up the calculation speed of the algorithm.
【学位授予单位】：南京邮电大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TN011

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