三维目标电磁散射的时域积分方程方法

【作者】 武胜波；

【导师】 赵延文；

【作者基本信息】 电子科技大学 ， 电磁场与微波技术， 2005， 硕士

【摘要】 由于高分辨短时脉冲雷达和目标精确识别的急切需求,用时域积分方程分析任意复杂宽带电磁散射和辐射现象得到了电磁领域的广泛关注。本文研究了用于分析三维目标瞬态电磁散射的时域积分方程方法。全文内容包括了时域积分方程的稳定精确求解方法和时域积分方程的高阶方法。首先,详细推导了时域电场积分方程(TDEFIE)、磁场积分方程(TDMFIE)和混合场积分方程(TDCFIE)。对矩量法求解时域积分方程所涉及的细节进行了分析,并介绍了求解矩阵方程的数值算法。其次,在简要分析了引起时域积分方程时间步进算法求解的后时不稳定性问题的几个原因后,指出引起时域积分方程时间步进算法的后时不稳定性的主要原因是离散TDIE 时采用了不精确的数值计算方法和不恰当的近似。详细讨论了时域积分方程的时间步进算法(MOT)。从精确计算时域阻抗矩阵元素的观点出发,详细分析了时域积分方程矩量法求解过程中的奇异性积分处理技术,给出精确快速计算时域阻抗矩阵的方法,并将这些方法用于求解时域积分方程的MOT算法。对任意三维导体散射体表面用三角贴片离散,采用RWG 空间基函数和三角型时间基函数,运用时间步进算法(MOT)求解了时域磁场、电场和混合场积分方程。几个典型数值算例表明,利用本文方法求解时域积分方程的结果具有非常好的后时稳定性和精确性,并且对低频成分、高频成分不敏感。最后,为提高MOT 算法的计算效率和降低内存需求,研究了时域积分方程的高阶算法。分别详细介绍了高阶方法的两个方面:高阶几何建模和高阶基函数。分析了几种常用的高阶贴片单元和高阶基函数。针对复杂三维导体目标电磁散射问题,本文采用曲面三角形贴片模拟散射体表面,采用高阶插值散度共形基函数,建立了三维任意导体目标的时域积分方程高阶算法。对高阶方法中涉及的奇异性积分的处理方法进行了分析和推导。计算实例显示出本文高阶方法的精确稳定性。在相同精度的情况下,采用高阶方法,未知量数目大大减少;与低阶方法相比,高阶方法明显地提高了利用时域积分方程分析电磁散射问题的计算效率。本文的工作为分析时域电磁散射现象提供了有效的方法途径,也为求解时域积分方程的快速算法等的研究打下了坚实的基础。更多还原

【Abstract】 Because of the increasing interest in short-pulse radar design for high-resolutionand target identification problems, time domain integral equation (TDIE)-basedsolvers are poised to be increasingly applied throughout the computationalelectromagnetic community to the analysis of complex wide-band electromagneticscattering phenomena . In this dissertation, time domain integral equation method isstudied for transient electromagnetic scattering by arbitrarily three dimensionalconducting bodies.In the first, the time-domain electric field integral equation (EFIE), magneticfield integral equation (MFIE), and combined field integral equation (CFIE)formulations are described in detail. The general implementation of time-domainintegral equation solver is presented. The details that relate to the method of momentsused to solve the TDIE are discussed. Furthermore, two numerical algorithms to solvethe linear system are introduced.Next, after briefly discussing several causes of the late-time instability of theTDIE solvers, a novel viewpoint about the instability is proposed. Themarching-on-in-time algorithm (MOT) is described and some temporal bases arediscussed. Due to the importance of the accuracy of the time-domain impedancematrix elements, the techniques by which treating of the singular integrals arose fromthe TDIE-MOM solving process are analyzed in detail, and these techniques areutilized to solve the TDIE. Using triangle patches discretizing an arbitrarily 3-DPEC body surface and utilizing spatial RWG and temporal triangular bases, theTD-MFIE, EFIE, and CFIE are solved by MOT algorithm. Several numerical resultsshow that the proposed method is stable and accurate, and the proposed method isnearly not sensitive to the high-, low-frequency component of the incidence wave andisn’t sensitive to these internal resonance modes.The dissertation also investigates the higher-order algorithm to solve TDIE. Anddetailed discussion about two aspects of higher-order method: the higher-ordergeometrical modeling and higher-order basis functions are presented. Thehigher-order TDIE algorithm for analysis of electromagnetic scattering phenomenafrom 3-D PEC bodies is founded by utilizing curvilinear triangular patches andhigher-order divergence conforming interpolatory vector basis functions. The singularintegrals are also considered. Numerical results demonstrate that the higher-order更多还原