目标电磁散射问题的嵌套等效源方法研究
发布时间：2018-08-15 11:41
【摘要】：多尺度目标电磁分析在计算电磁学领域是个挑战。论文针对介质材料的多尺度问题,不均匀网格剖分问题,分别作了深入研究。第二章简要介绍了传统的低秩压缩方法,自适应交叉近似算法。主要介绍了文章中所用的低秩压缩方法:嵌套等效源方法。第三章主要研究将嵌套等效源方法与介质表面积分方程相结合,分析多尺度的介质问题。嵌套等效源方法是一种精度较高的低秩压缩类方法,本章将其与表面积分方程结合,并将方程的内外区域部分分开压缩,以获得更好的压缩效果。分析了不同介电常数下该方法的近似精度,然后通过分析了一个介质球与幂级数对比验证了其正确性,分析了捕食者无人机来验证了算法的多尺度特性。为快速分析介质问题做了进一步的拓展。第四章主要在原来规则八叉树分组的嵌套等效源方法上研究了一种自适应八叉树分组的嵌套等效源方法。该方法主要针对带有精细结构的目标,需要局部密剖的情况。分析了不同尺寸的组之间如何压缩,以及分析了这样压缩后的精度。并通过分析一个金属球验证了该方法的正确性,还通过分析一个单极子天线阵列来讨论该方法的效率。为了完善该方法,还引入了不连续伽辽金方法,使得剖分更加灵活。也分析了一个非共形网格剖分的圆柱,与商业软件FEKO对比,验证了其正确性,也通过分析一个单极子天线阵列来讨论了它的效率。相比于原来的嵌套等效源方法更进一步地降低内存消耗和迭代求解时间,为分析不均匀剖分目标的电磁辐射或散射问题做了更进一步的改善。
[Abstract]:Multi-scale target electromagnetic analysis is a challenge in the field of computational electromagnetism. In this paper, the multi-scale problem and non-uniform mesh generation of dielectric materials are studied. In chapter 2, the traditional low rank compression method and the adaptive cross approximation algorithm are introduced briefly. This paper mainly introduces the low rank compression method used in this paper: the nested equivalent source method. In the third chapter, the nested equivalent source method is combined with the dielectric surface integral equation to analyze the multi-scale media problem. The nested equivalent source method is a kind of low rank compression method with high precision. In this chapter, we combine it with the surface integral equation, and compress the inner and outer parts of the equation separately, so as to obtain better compression effect. The approximate accuracy of the method under different dielectric constants is analyzed, and the correctness of the method is verified by comparing a dielectric sphere with power series. The multi-scale characteristic of the algorithm is verified by analyzing the predator UAV. A further development is made for the fast analysis of medium problems. In chapter 4, a nested equivalent source method of adaptive octree grouping is studied based on the nested equivalent source method of octree grouping. This method mainly aims at the target with fine structure and needs local dense profile. How to compress the groups of different sizes and the accuracy of the compression are analyzed. The correctness of the method is verified by analyzing a metal sphere, and the efficiency of the method is discussed by analyzing a monopole antenna array. In order to perfect the method, discontinuous Galerkin method is introduced, which makes the division more flexible. A non-conformal meshed cylinder is also analyzed and compared with commercial software FEKO to verify its correctness. Its efficiency is also discussed by analyzing a monopole antenna array. Compared with the original nested equivalent source method, the memory consumption and iterative solution time are further reduced, and the analysis of electromagnetic radiation or scattering problem of non-uniform subdivision targets is further improved.
【学位授予单位】：南京理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TN011
本文编号：2184091
[Abstract]:Multi-scale target electromagnetic analysis is a challenge in the field of computational electromagnetism. In this paper, the multi-scale problem and non-uniform mesh generation of dielectric materials are studied. In chapter 2, the traditional low rank compression method and the adaptive cross approximation algorithm are introduced briefly. This paper mainly introduces the low rank compression method used in this paper: the nested equivalent source method. In the third chapter, the nested equivalent source method is combined with the dielectric surface integral equation to analyze the multi-scale media problem. The nested equivalent source method is a kind of low rank compression method with high precision. In this chapter, we combine it with the surface integral equation, and compress the inner and outer parts of the equation separately, so as to obtain better compression effect. The approximate accuracy of the method under different dielectric constants is analyzed, and the correctness of the method is verified by comparing a dielectric sphere with power series. The multi-scale characteristic of the algorithm is verified by analyzing the predator UAV. A further development is made for the fast analysis of medium problems. In chapter 4, a nested equivalent source method of adaptive octree grouping is studied based on the nested equivalent source method of octree grouping. This method mainly aims at the target with fine structure and needs local dense profile. How to compress the groups of different sizes and the accuracy of the compression are analyzed. The correctness of the method is verified by analyzing a metal sphere, and the efficiency of the method is discussed by analyzing a monopole antenna array. In order to perfect the method, discontinuous Galerkin method is introduced, which makes the division more flexible. A non-conformal meshed cylinder is also analyzed and compared with commercial software FEKO to verify its correctness. Its efficiency is also discussed by analyzing a monopole antenna array. Compared with the original nested equivalent source method, the memory consumption and iterative solution time are further reduced, and the analysis of electromagnetic radiation or scattering problem of non-uniform subdivision targets is further improved.
【学位授予单位】：南京理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TN011
【参考文献】
相关硕士学位论文 前1条
1 陈睿;微波电路与天线问题的时域积分方法分析[D];南京理工大学;2015年
，本文编号：2184091
本文链接：https://www.wllwen.com/kejilunwen/dianzigongchenglunwen/2184091.html
