复杂目标电磁散射的快速非均匀平面波算法

【作者】 陈涌频；

【导师】 胡俊；

【作者基本信息】 电子科技大学 ， 电磁场与微波技术， 2006， 硕士

【摘要】 复杂目标电磁散射研究长期以来广受关注,本文研究的快速非均匀平面波算法,可以快速精确的求解任意复杂目标的电磁散射问题,其多层形式的计算复杂度与多层快速多极子相当。同时,该算法较之多层快速多极子方法有明显的数值实现优势和潜在优势。本文首先回顾了电磁建模的常用分析方法,介绍了基于积分方程方法的多层快速多极子方法,及其某些潜在的缺陷,引出本文研究的快速非均匀平面波算法。接着,重点研究了二维快速非均匀平面波算法,对其复平面上的修正最陡下降路径及内插外推技术进行了深入研究。为进一步提高求解效率,将快速远场近似与之混合;采用一种新型的动态控制耦合半径的局部迭代技术。另外,本文还首次研究了基于体表面积分方程方法的快速非均匀平面波算法,成功应用于分析金属介质复合结构。在二维问题的基础上,本文继续研究了三维快速非均匀平面波算法,使之可用于处理实际三维目标。首先研究了基于电场积分方程的快速非均匀平面波算法,对索末菲恒等式(基于贝塞尔积分核)展开的格林函数进行了深入研究,分两种情形解决了修正最陡下降路径的设计问题。为改善其迭代特性和有效避免内谐振,本文进而研究了基于混合场积分方程的快速非均匀平面波算法。本文还研究了几种预条件技术,用于改善算子的条件数,进一步加速迭代,同时用数值结果对比了各自的优劣。最后,本文研究了基于一种新型积分方程形式――修正电场积分方程的快速非均匀平面波算法,用于高效求解非常规目标散射,并用前述预条件技术进一步提高该方法的计算效率。所有数值结果均与测量值或文献结果或精确方法计算结果吻合良好,数据显示计算复杂度与多层快速多极子方法相当,充分说明本算法的高效性及精确性。本文的研究工作为复杂目标尤其是电大尺寸复杂目标电磁散射提供了又一高效的分析手段。更多还原

【Abstract】 Research on electromagnetic scattering of complex targets has been received much attention for a long time, the fast inhomogeneous plane wave algorithm(FIPWA) in this paper performs well in this purpose, and the computation complexity of its multilevel version(MLFIPWA)is of the same order as the multilevel fast multipole algorithm(MLFMA). Meanwhile, the MLFIPWA is superior to the MLFMA in numerical operation and some other potential aspects.The common methods for analysis of electromagnetic modeling have been reviewed firstly, the MLFMA based on integral equation method and its potential deficiency is briefly presented, and the FIPWA is introduced then.In the next chapter, the two dimensional FIPWA especially the modified steepest decent path (MSDP) in angular complex plane and the interpolate/extrapolate technique have been carefully studied. In order to improve the efficiency, the fast far field approximation(FAFFA) and a novel local iteration technique based on dynamic coupling region controlling are applied to the original FIPWA. A volumn/surface integral equation(VSIE) FIPWA is developed successfully to analyze scattering of conductor dielectric composite structure.Besides the above two dimensional algorithm, the three Dimensional FIPWA has also been studied. The FIPWA based on electric integral equation(EFIE) is presented firstly, the Green’s function expansion with Sommerfeld identity (based on Bessel kernel) is studied and the MSDP for two cases is formulated. In order to improve the iteration property and avoid inner resonance, the combined field integral equation(CFIE) FIPWA is then constructed successfully.Some preconditioner technique is also studied to improve the condition number and further accelerate iterations, comparisons are made between them by numerical results. Finally, a FIPWA based on a novel integral equation—modified EFIE has been developed, which is especially suitable for analyzing scattering of irregular targets. The preconditioner technique presented before is also applied to it.The numerical results in this paper agree well with measurement results or results更多还原