不连续伽辽金时域体面积分方程方法的电磁散射分析

发布时间：2018-04-11 22:00

  本文选题：不连续伽辽金 + 非共形网格　； 参考：《南京理工大学》2016年硕士论文

【摘要】：在工程实践中,由于时域积分方程方法在分析目标的电磁散射特性时,可以一次性地求解出多个频点,因此在处理宽频带问题时,时域积分方程方法得到了广泛地应用。然而基于伽辽金测试的普通时域积分方程方法为了满足物理上的连续性,目标模型剖分之后的网格必须保证共形。但是在现实世界里,目标一般都比较复杂,产生一套符合目标参数的共形网格因此也比较困难,所以研究能够处理非共形网格的算法是很有必要的。根据上述问题,本文提出了不连续伽辽金的时域体面积分方程方法。该方法通过将不连续伽辽金思想引入到时域体面积分方程中,从而实现了算法对非共形网格地处理。此方法在求解目标的电磁参数时不需要相邻单元之间隐含的连续性条件,所以对于不同的单元网格可以采用不同的基函数,从而在确保结果精确的前提下减少计算所消耗的内存与时间。基于以上优势,在求解复杂目标的宽频带电磁参数时,不连续伽辽金的时域体面积分方程方法具有比较大的通用性。本文首先介绍了时域积分方程的推导过程和不连续伽辽金方法的基本原理。然后详细推导了不连续伽辽金的时域体积分方程和改进之后的连续-不连续伽辽金的时域体积分方程,并对形成的矩阵进行分析和求解,然后又推导出了连续-不连续伽辽金的时域体面积分方程。最后为了分析电大尺寸目标,在体面积分方程方法的基础上又引入了时域平面波技术,极大地拓展了前者在求解实际电磁问题时的能力。
[Abstract]:In engineering practice, the time-domain integral equation method has been widely used in dealing with wide-band problems because it can solve multiple frequency points at one time when analyzing the electromagnetic scattering characteristics of the target.However, in order to satisfy the physical continuity of the ordinary time-domain integral equation method based on Galerkin test, the mesh of the target model must be conformal.However, in the real world, the target is generally more complex, so it is difficult to produce a set of conformal mesh which accords with the target parameters. Therefore, it is necessary to study the algorithm to deal with the non-conformal mesh.Based on the above problems, a method of discrete Galerkin time domain decent integral equation is presented.In this method, the discontinuous Galerkin idea is introduced into the time domain decent integral equation, and the algorithm is used to deal with non-conformal grids.In order to solve the electromagnetic parameters of the target, this method does not need the implicit continuity condition between adjacent elements, so different basis functions can be used for different element meshes.Thus reducing the memory and time consumed by the calculation while ensuring the accuracy of the results.Based on the above advantages, the discontinuous Galerkin's time domain decent integral equation method is of great generality in solving the broadband electromagnetic parameters of complex targets.In this paper, the derivation process of time domain integral equation and the basic principle of discontinuous Galerkin method are introduced.Then the time domain volume fraction equation of discontinuous Galerkin and the modified continuous discontinuous Galerkin time domain volume fraction equation are derived in detail, and the resulting matrix is analyzed and solved.Then the time-domain decent integral equation of continuous-discontinuous Galerkin is derived.Finally, in order to analyze the electrically large size target, the time domain plane wave technique is introduced on the basis of the decent integral equation method, which greatly expands the former's ability to solve the actual electromagnetic problem.
【学位授予单位】：南京理工大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：TN011
，

本文编号：1737823