Applications and Innovations for Computational Electromagnetics

了解器件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。在过去的几十年里，随着计算能力的指数级增长，人们对计算电磁学工具的需求不断增加，这些工具可以解决工程问题。虽然有几十种方法来解决这类问题，但时域有限差分（FDTD）方法已经成为事实上的标准之一，因为它能够鲁棒地处理复杂结构和材料的场的相互作用。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，以适用于更大范围和更复杂的建模场景。本研究的目的是进一步改进和扩展该方法，从而使其成为具有复杂材料模型和/或大型结构的场景建模不可或缺的工具。本提案所涉及的工作包括两个主要研究领域。首先是利用时域有限差分法中的有效波源在复杂环境中进行建模。二是研究FDTD方法在复杂材料建模的替代网格上的持续增强和创新。

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.