【作者】 史琰；

【导师】 梁昌洪；

【作者基本信息】 西安电子科技大学 ， 电磁场与微波技术， 2005， 博士

【摘要】 计算电磁学因其具有精确、灵活地建模和仿真实际电子线路和电磁系统的能力而一直是一个重要的研究领域。特别是有效地分析宽带信号激励问题的需求推动了时域求解技术的发展。然而传统的时域计算方法无法满足在大量的时间周期上精确地模拟波传播的要求,这暗示了高阶时域计算方法应该被予以考虑。在另一方面,对于复杂几何形体的精确建模也需要对传统时域计算方法进行改进。针对上述问题,本文深入地研究了一些高阶、精确的时域计算方法,主要的工作可以概括如下: 1.针对传统的时域有限差分算法无法精确地处理曲边边界和交界面的问题,本文详细地研究了二维注入边界的时域有限差分算法。同时对该算法在处理曲边理想导体边界时存在的缺陷进行适当的修正。 2.详细地研究了傅立叶伪谱时域算法,并推导了该算法的色散关系和稳定性条件。基于傅立叶伪谱时域算法,将其与传统的时域有限差分算法的混合算法推广到该算法与任意阶时域有限差分算法的混合,并对混合后算法的色散关系和稳定性条件作了相应的分析。 3.深入讨论了多区域切比雪夫伪谱时域算法。在系统地推导该算法的区域映射、拼凑条件和良态提出的理想匹配层公式的基础上,将该算法应用到2维、2.5维和3维的电磁问题求解中。 4.针对多区域切比雪夫伪谱时域算法稳定性方面的问题,采用隐式和显式两种时间积分方式对此进行改善。在隐式时间积分中,将ADI技术与多区域切比雪夫伪谱时域算法相结合来改善该算法的稳定性条件从而提高了计算效率。在显式时间积分中,采用超时间步方法加速传统的显示时间积分策略进而改善多区域切比雪夫伪谱时域算法的稳定性条件和计算效率。 5.针对多区域伪谱时域算法在直角坐标系下计算旋转物体对平面波散射问题的复杂性,提出了圆柱坐标系和球坐标系下的多区域伪谱时域算法。在推导了圆柱坐标系和球坐标系下的、不分裂场的、良态提出的理想匹配层公式的同时,将傅立叶选配方法应用到方位角方向,切比雪夫选配方法应用到其它方向,从而形成了利用旋转物体对称性的多区域伪谱时域算法。 6.针对传统的谱域方法在对复杂的几何形体建模方面的不足,从一维、二维和三维的电磁问题入手,深入研究了不连续伽略金方法。在系统地讨论该算法的单元映射、伽略金方法的实施和单元间边界条件施加的基础上,将良态提出的理想匹配层公式应用到该算法中来以精确地建模无限大的计算区域。 7.利用高阶时域电磁计算方法对双负媒质的电磁特性进行了全波仿真。根据更多还原

【Abstract】 Computational electromagnetics has been an important research area because of its capability to accurately and flexibly model and simulate what is really occurring in electrical circuits and electromagnetic systems. In particular, the demands for efficient analysis of broadband signal excitation have driven the development of time-domain techniques. The requirement for the conventional time-domain techniques, however, that can not accurately simulate wave propagation over many periods of time suggests that high-order time-domain techniques should be considered. On the other hand, the accurately model for the geometric complexity also requires the further development of the conventional time-domain techniques. According to the problems above, the high-order accurate time-domain techniques have been deeply studied in this paper. The work of author mainly focuses on:1. The two-dimensional embedded boundary finite-difference time-domain algorithm (FDTD) is studied in detail in order to realize accurate model for curve boundary and interface, which is impossible for conventional FDTD algorithm. The proper modification about two-dimensional embedded boundary FDTD algorithm is made in the case of curve PEC boundary.2. The Fourier pesudospectral time-domain (FPSTD) algorithm is studied in detail and its dispersion relation and stability condition are derived. Based on it, the combination between FPSTD algorithm and conventional FDTD algorithm is extended into the combination between FPSTD algorithm and arbitrary-order FDTD algorithm, and dispersion relation and stability condition of new algorithm are analyzed.3. The multidomain Chebyshev pseudospectral time-domain (MCPSTD) algorithm is deeply discussed. On the basis of the systematical analyses of its domain mapping technique and patching condition and well-posed perfectly matched layer formula, the MCPSTD algorithm is used to solve two-dimensional and 2.5 dimensional and three-dimensional electromagnetic problems.4. The implicit and explicit time integration schemes are used to improve the stability condition of the MCPSTD algorithm. In implicit time integration, the combination between ADI technique and the MCPSTD algorithm is used to improve the stability condition and efficiency;in the explicit time integration, Super-Time-Stepping method is used to accelerate explicit time integrationscheme so that the stability condition and efficiency are improved.5. In cylindrical and spherical coordinates, the multidomain pseudospectral time-domain (MPSTD) algorithm is presented in order to improve the corresponding algorithm in Cartesian coordinate for the accurate and efficient time-domain computation of scattering by bodies of revolution (BOR). Unsplit-field well-posed PML formula in cylindrical and spherical coordinates are derived, and the Fourier collocation method is utilized in the azimuthal direction and the Chebyshev collocation method in others directions so that the MPSTD algorithm can utilize symmetry of BOR.6. Beginning with one-dimensional and two-dimensional and three dimensional electromagnetic problems, the discontinuous Galerkin method (DGM) is deeply studied in order to improve the limitations inherent in conventional spectral methods for model for the complex geometries. Based on systematical description of its element mapping technique and implementation of Galerkin method and boundary condition between elements, the well-posed PML formula are applied into DGM in order to simulate the infinite computational domain.7. The full-wave simulations of double negative (DNG) medium are made using higher-order time-domain computational electromagnetic methods. Based on complex coordinate stretching technique, the PML formula applied for Lorentz medium and DNG medium are developed, respectively. According to the formula above, MCPSTD algorithm and DGM are used to analyze unusual EM phenomena in DNG medium.更多还原