Applications and Innovations for Computational Electromagnetics

了解设备和材料中电磁场的复杂相互作用在许多应用领域至关重要，从高速电路设计到成像和无损检测。随着过去几十年来计算能力的指数增长，对计算电磁学可以提供的解决工程问题的工具的需求不断增加。 虽然有几十种方法来处理这样的问题，时域有限差分法（FDTD）已经成为事实上的标准之一，因为它能够鲁棒地处理场与复杂结构和材料的相互作用。 该方法的适用性和效率仍然是一个充满活力的研究领域，特别是该方法正在不断扩展，以适用于更大范围的更大和更复杂的建模场景。所提出的研究的目的是进一步改进和扩展这种方法，从而使其成为一个更加不可或缺的工具，用于复杂的材料模型和/或大型结构的场景建模。本提案所涉工作包括两个主要研究领域。 第一个是利用有效的波源的FDTD方法建模在复杂的环境。第二个是研究FDTD方法在复杂材料建模的替代网格上的持续增强和创新。研究的第一个领域旨在克服复杂的天线几何形状对建模的限制，通过使用等效源的概念来按比例缩小所需的计算资源（例如，存储器和处理能力）。在FDTD方法中，等效源可以用来准确有效地表示辐射源，从而避免了对源进行明确建模的需要，从而大大减少了对计算机资源的需求，从而可以进行更快和/或更大的仿真。 这在正演建模作为逆散射过程的一部分在多次迭代中使用的情况下特别重要。这种反演程序用于需要绘制环境实际结构图的应用，例如绘制地下结构图以查明储油层（对加拿大能源工业特别重要），或绘制乳房结构的断层摄影图以查明恶性肿瘤。通过提高底层仿真工具的建模能力，我们本质上增强了处理越来越复杂和现实的实际问题的能力。第二个研究领域旨在克服由原始FDTD方法建模时的限制，该方法基于3D网格上场分量的矩形（笛卡尔）布局 *。 这种网格布局的选择固有地将近似和误差引入建模中，这可以通过在模拟中选择更高的空间分辨率和/或更好的数值近似来部分地减轻，但是以更高的计算资源为代价。最近，我们已经表明，这两种类型的错误可以显着减少简单地从一开始就围绕一个不同的网格，称为列别捷夫网格的FDTD方法。与现有方法相比，网格还允许我们以更高的精度对复杂材料进行建模。特别是，增强的方法将使我们能够更准确地模拟波在地球电离层系统中的传播。该系统对加拿大从事空间物理学和大气层/磁层建模的研究人员特别重要。

Understanding the complex interactions of electromagnetic fields in devices and materials is critical in many application areas, ranging from high-speed circuit design to imaging and non-destructive testing. With the exponential growth in computing power experienced over the past several decades, there has been an ever-increasing demand for the tools that computational electromagnetics can provide to tackle engineering problems. Although there are dozens of methodologies for approaching such problems, the Finite-Difference Time-Domain (FDTD) method has become one of the de facto standards, because of its ability to robustly handle interactions of fields with complicated structures and materials. The applicability and efficiency of the method continues to be a vibrant research area, and in particular the method is being continually expanded to apply to a greater range of larger and more complicated modeling scenarios. The aims of the proposed research are to further improve and extend this method, and thus make it an even more indispensable tool for modeling of scenarios with complex material models and/or large structures. The work covered in this proposal consists of two main research areas. The first is the utilization of efficient wave sources in the FDTD method for modeling in complex environments. The second is to investigate the continued augmentation and innovation of the FDTD method on alternative grids for complex material modeling.**The first area of research aims to overcome the restrictions placed upon modeling by complicated antenna geometries, by using the concept of equivalent sources to scale down the required computational resources (e.g. memory and processing power). In the FDTD method, equivalent sources can be used to accurately and efficiently represent radiating sources, thus obviating the need to model the source explicitly, allowing for considerable reduction in computer resource requirements, hence allowing for performance of quicker and/or larger simulations. This is particularly important where forward modeling is utilized in multiple iterations as part of an inverse scattering procedure. Such inversion procedures are used in applications where it is desired to build a map of the actual structure of the environment, for example for mapping underground structures to identify oil reservoirs (of particular importance for Canadian energy industries), or for building a tomographic map of the structure of the breast in order to identify malignant tumours. By improving the modeling capabilities of the underlying simulation tools we are inherently enhancing the capability to deal with more and more complicated and realistic practical problems of interest.**The second area of research is intended to overcome the restrictions placed upon modeling by the original FDTD method, which is based upon a rectangular (Cartesian) layout *of field components on a 3D grid. This choice of grid layout inherently introduces approximations and errors into the modeling, which can be partly mitigated by choosing a higher spatial resolution in simulation and/or better numerical appoximations, but at the cost of higher computational resources. Recently we have shown that both types of errors can be significantly reduced simply by structuring the FDTD method around a different grid from the outset, called the Lebedev grid. The grid also allows us to model complicated materials with higher accuracy compared to existing methods. In particular, augmentation of the method will allow us to model the propagation of waves in the earth-ionosphere system more accurately. This system is of partiuclar importance to Canadian reseachers involved with Space Physics and atmospheric/magnetospheric modelling.