基于H~2矩阵快速求解线面体积分方程

发布时间：2018-05-03 07:16

本文选题：电介质 + 电场积分方程　；参考：《南京邮电大学》2015年硕士论文

【摘要】：当运用电磁场数值计算方法求解实际的电磁问题时,通常将求解目标看做为理想导体或者理想介质。然后运用面等效源原理建立面积分方程(SIE)求解电磁散射和辐射问题。然而在实际求解的过程中,遇到非均匀介质与导体结合的情况时,SIE并不适用求解此类的电磁问题。于是根据实际情况建立有效的积分方程来求解目标环境的电磁问题具有重要的意义。在矩量法的基础之上,本文根据求解区域所满足的电磁条件建立有效的电场积分方程(EFIE)求解目标电磁问题。采用MoM直接求解EFIE,分别需要O(N2)存储量和O(N3)计算复杂度。于是本文根据可容许条件,将阻抗矩阵划分为近场区和远场区。对于远场区矩阵块的计算,采用拉格朗日插值多项式退化核函数低秩存储,以降低求解过程中未知量与存储量、计算量之间的级数关系从而提高计算效率。最后在H矩阵的基础之上发展H2矩阵算法,并将其运用于实际的求解电磁问题中,验证该算法的高效性、可行性。最后,利用实现的计算程序计算了不同模型的电磁散射和辐射特性,以此验证算法的正确性和有效性。数值结果表明H矩阵可降低求解过程中的计算量和存储量,二者的复杂度均接近O(NlogN)。
[Abstract]:When the numerical method of electromagnetic field is used to solve the actual electromagnetic problem, the target is usually regarded as an ideal conductor or an ideal medium. Then the surface equivalent source principle is used to solve the electromagnetic scattering and radiation problems. However, in the process of practical solution, when the inhomogeneous medium and conductor are combined, sie is not suitable for solving this kind of electromagnetic problem. Therefore, it is of great significance to establish an effective integral equation to solve the electromagnetic problems in the target environment according to the actual situation. Based on the method of moments, an effective electric field integral equation (EFIEE) is established to solve the target electromagnetic problem according to the electromagnetic conditions satisfied by the solving region. Using MoM to solve EFIEs directly requires ON2) storage and ON3) computational complexity. In this paper, the impedance matrix is divided into the near field region and the far field region according to the admissible condition. For the calculation of far field matrix block, the Lagrange interpolation polynomial is used to degenerate the low rank storage of kernel function, so as to reduce the series relation between the unknown quantity and the storage amount and the calculation amount in order to improve the computational efficiency. Finally, the H _ 2 matrix algorithm is developed on the basis of H _ matrix, and is applied to solve electromagnetic problems in practice, which verifies the efficiency and feasibility of the algorithm. Finally, the electromagnetic scattering and radiation characteristics of different models are calculated by using the realized program, which verifies the correctness and validity of the algorithm. The numerical results show that H matrix can reduce the computational and storage complexity of the solution, and the complexity of both is close to that of ONlogN.
【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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