三维FDTD方法在多层全各向异性媒质结构上的Z变换算法研究

作为电磁材料的一种重要特征，各向异性是对分层材料科学和地下电磁勘查的关键研究对象。为了探索各向异性的电磁波传播过程，实现其正演数值算法，需要突破因复杂张量计算、算法稳定性和数值精度等因素而导致的学术难题。时域有限差分法（FDTD）通过网格平均电导率和导磁率，结合E和H的迭代关系，已成功实现在各向异性媒质上的Bloch-Floquet周期边界条件。为了延拓在各向异性媒质方面上的研究，本项目拟结合Z变换方法，研究基于D、E、B和H的迭代过程的三维全各向异性FDTD方法，应用于分层结构和周期问题上。针对这一方法具体研究，分别提出：（1）Bloch-Floquet周期边界条件来处理周期结构的边界截断问题；（2）Z变换完全匹配层来处理媒质的边界截断问题；（3）采用高性能Fortran语言环境来编译代码。项目的完成可以深入探讨电磁波在各向异性问题上的传播过程，为复杂电磁问题的研究节省时间和经济成本。

As an important feature of electromagnetic materials, anisotropy is the key research object of stratified materials science and underground electromagnetic exploration. For exploring the electromagnetic propagation and realizing the forward numerical algorithm in anisotropy, it is necessary to break through the academic problems caused by the factors such as complex tensor calculation, algorithm stability and numerical accuracy. Finite-Difference Time-Domain (FDTD) method in electromagnetic waves has successfully implemented the Bloch-Floquet Periodic Boundary Conditions on anisotropic media through the grid average electrical loss tensor and magnetic loss tensor, combining the iterative relationship of electric field intensity E and magnetic field intensity H. To further extend the research content on fully anisotropic media, this project intends to combine the Z transform method to study the three-dimensional fully anisotropic FDTD method based on the iterative process of electric flux D, electric field intensity E, magnetic flux B and magnetic field intensity H, and apply it to the problem of hierarchical structure and periodic processing. In view of the specific research of 3D fully anisotropic FDTD method combined with Z transform method, it is proposed that (1) Bloch-Floquet periodic boundary condition is applied to deal with the boundary truncation of periodic structure, (2) the perfectly matched layer under Z transform method is implemented to deal with the boundary truncation of general media, and (3) the high performance Fortran language is conducted to compile the code. The completion of the project can further explore the electromagnetic waves in anisotropy, and save time and economic cost for the study of the complex electromagnetic problems.