高频方法与积分方程方法混合研究及应用
发布时间：2019-03-30 13:17
【摘要】：混合算法均是取彼之长、补己之短。高频方法结合积分方程方法能克服各自局限、发扬各自优势,特别适合求解电大尺寸和精细结构并存的电磁问题。往往在电大尺寸部分使用高频方法,而在精细结构部分使用积分方程方法,这样就可以扬长避短。在满足所需精度的同时,大大提高计算的速度和节省计算的内存等。本文就是围绕这类电磁问题而展开,研究主要内容可以归纳如下:一、基于剪裁NURBS参数曲面的研究。首先介绍矩量法(MoM)和物理光学法(PO)基本理论,再针对平面几何建模的不足,引入NURBS参数曲面建模。发现使用物理光学在矩形参数曲面上计算电磁散射时,无法剔除冗余面元的贡献而造成误差太大,引入了剪裁NURBS参数曲面。相比未剪裁曲面,在剪裁NURBS参数曲面上散射场的计算具有非常高的准确性,同时给出了相应的算例来验证。二、基于高效迭代混合算法的研究。针对在传统矩量法和物理光学混合(MoM-PO)中,物理光学区域对矩量法区域的耦合矩阵占用了大量内存和时间,提出一种高效迭代混合算法(EI-MoM-PO),它是一种直接更新矩量法区域的电压矩阵来进行迭代计算,能在相同网格的情况下,保持良好精度的同时还能节省计算资源;为了扩大计算能力,在原来Mo M区域引入多层快速多级子,形成EI-MLFMA-PO,进一步节省内存和时间,并求解电大尺寸的电磁问题;最后首次提出一种针对具有大量近似平面结构目标混合算法时,提出两套剖分网格的形式来对PO区域进行高效消隐,它具有简单、高效的特点。三、基于积分区域分解方法(IE-DDM)结合PO的研究。IE-DDM采取“分而治之”的思想,它一方面可以针对不同的子区采取更加适合的计算方法,并拥有天然并行的优势。在另一方面,不同子区可以采取非共性的网格来进行剖分计算。本文在积分区域分解方法的框架下,针对电大尺寸和复杂精细结构是整体还是分开两种情况,提出使用两种方式加入物理光学方法。前者采用目标整体分区,后者分开目标采用矩量法区域内部分区。由物理光学方法的加入极大地丰富和充实了积分区域分解方法的框架,在以后计算具有电大光滑尺寸的复合结构时大大提高了求解速度,同时为后续加入有限元等其他求解器做铺垫,为更进一步求解复杂多尺度问题提供一种可能。
[Abstract]:The hybrid algorithm is to take their strengths and make up for their own short. The high-frequency method combined with the integral equation method can overcome their limitations and carry forward their advantages. It is especially suitable for solving electromagnetic problems in which large size and fine structure coexist. The high frequency method is often used in the electrically large size part, while the integral equation method is used in the fine structure part, so that the advantages and disadvantages can be improved. While satisfying the required precision, the speed of calculation is greatly improved and the memory of calculation is saved. The main contents of this paper can be summarized as follows: first, the research based on clipped NURBS parametric surfaces. The basic theory of moment method (MoM) and physical optics method (PO) are introduced firstly. Then NURBS parametric surface modeling is introduced to solve the deficiency of plane geometry modeling. It is found that when using physical optics to calculate electromagnetic scattering on rectangular parametric surfaces, the contribution of redundant surface elements cannot be eliminated and the error is too large. A clipping NURBS parametric surface is introduced. Compared with the unclipped surface, the calculation of scattering field on the clipped NURBS parametric surface is very accurate. At the same time, an example is given to verify it. Second, the research based on efficient iterative hybrid algorithm. In the traditional method of moments (mom) and physical optics mixing (MoM-PO), an efficient iterative hybrid algorithm (EI-MoM-PO) is proposed to solve the problem that the coupling matrix in the physical optics region takes up a large amount of memory and time in the moment method region. It is a direct updating of the voltage matrix in the region of the moment method to calculate iteratively. It can keep good precision and save computing resources under the same grid condition. In order to expand the computing ability, the multi-layer fast multi-stage sub is introduced into the original Mo M region, which further saves the memory and time of the EI-MLFMA-PO, and solves the electromagnetic problem of the electrically large size. Finally, for the first time, a hybrid algorithm with a large number of approximate planar structures is proposed, and two sets of mesh forms are proposed to efficiently eliminate the hidden space in the PO region. It has the characteristics of simplicity and efficiency. Thirdly, based on the integration domain decomposition (IE-DDM) method combined with the research of PO, IE-DDM adopts the idea of "divide and conquer", on the one hand, it can adopt more suitable computing methods for different sub-regions, and it has the advantage of natural parallelism. On the other hand, different sub-regions can adopt non-common grid to calculate the partition. In this paper, under the framework of the integral domain decomposition method, two physical optics methods are proposed to solve the problem of whether the complex fine structure and the electrically large size are whole or separate. The former adopts the integral partition of the target, and the latter adopts the internal partition of the region of the moment method to separate the target. The framework of the integral domain decomposition method is greatly enriched and enriched by the addition of the physical optics method, and the solution speed is greatly improved when calculating the composite structure with electrically large smooth size in the future. At the same time, it provides a possibility for further solving complex multi-scale problems by adding other solvers such as finite element.
【学位授予单位】：电子科技大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TN011
本文编号：2450113
[Abstract]:The hybrid algorithm is to take their strengths and make up for their own short. The high-frequency method combined with the integral equation method can overcome their limitations and carry forward their advantages. It is especially suitable for solving electromagnetic problems in which large size and fine structure coexist. The high frequency method is often used in the electrically large size part, while the integral equation method is used in the fine structure part, so that the advantages and disadvantages can be improved. While satisfying the required precision, the speed of calculation is greatly improved and the memory of calculation is saved. The main contents of this paper can be summarized as follows: first, the research based on clipped NURBS parametric surfaces. The basic theory of moment method (MoM) and physical optics method (PO) are introduced firstly. Then NURBS parametric surface modeling is introduced to solve the deficiency of plane geometry modeling. It is found that when using physical optics to calculate electromagnetic scattering on rectangular parametric surfaces, the contribution of redundant surface elements cannot be eliminated and the error is too large. A clipping NURBS parametric surface is introduced. Compared with the unclipped surface, the calculation of scattering field on the clipped NURBS parametric surface is very accurate. At the same time, an example is given to verify it. Second, the research based on efficient iterative hybrid algorithm. In the traditional method of moments (mom) and physical optics mixing (MoM-PO), an efficient iterative hybrid algorithm (EI-MoM-PO) is proposed to solve the problem that the coupling matrix in the physical optics region takes up a large amount of memory and time in the moment method region. It is a direct updating of the voltage matrix in the region of the moment method to calculate iteratively. It can keep good precision and save computing resources under the same grid condition. In order to expand the computing ability, the multi-layer fast multi-stage sub is introduced into the original Mo M region, which further saves the memory and time of the EI-MLFMA-PO, and solves the electromagnetic problem of the electrically large size. Finally, for the first time, a hybrid algorithm with a large number of approximate planar structures is proposed, and two sets of mesh forms are proposed to efficiently eliminate the hidden space in the PO region. It has the characteristics of simplicity and efficiency. Thirdly, based on the integration domain decomposition (IE-DDM) method combined with the research of PO, IE-DDM adopts the idea of "divide and conquer", on the one hand, it can adopt more suitable computing methods for different sub-regions, and it has the advantage of natural parallelism. On the other hand, different sub-regions can adopt non-common grid to calculate the partition. In this paper, under the framework of the integral domain decomposition method, two physical optics methods are proposed to solve the problem of whether the complex fine structure and the electrically large size are whole or separate. The former adopts the integral partition of the target, and the latter adopts the internal partition of the region of the moment method to separate the target. The framework of the integral domain decomposition method is greatly enriched and enriched by the addition of the physical optics method, and the solution speed is greatly improved when calculating the composite structure with electrically large smooth size in the future. At the same time, it provides a possibility for further solving complex multi-scale problems by adding other solvers such as finite element.
【学位授予单位】：电子科技大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TN011
【参考文献】
相关博士学位论文 前2条
1 黄锴;混合方法分析电大目标附近天线受扰方向图[D];西安电子科技大学;2012年
2 宗显政;平台与天线的一体化电磁建模及工程实践研究[D];电子科技大学;2008年
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