New Frontiers in Computational Electromagnetics: Towards High-Accuracy Solutions and Reliable Microwave Imaging

快速的无线通信、可靠的电力传输和生物医学成像是定义数百万加拿大人生活质量的重要技术。这些技术进步的关键是依赖于计算电磁学(CEM)的方法和工具的新设备和系统的设计。在这些系统中，有手机、数字电路板、GPS装置、雷达和断层成像系统--仅举几个例子。尽管最近取得了各种根本性的进展，但目前可用的CEM算法存在各种根本性的缺陷。这些缺陷阻碍了新技术的发展，使各行业因错误的设计和延长的上市时间而蒙受数百万美元的损失。其中最具挑战性的是相关算法的计算复杂性很大，当应用于现实模型的电磁分析时，它们的精度不够高。提出的研究计划专注于开发新的算法和高精度的求解方法，这些算法克服了计算复杂性的障碍，使复杂大型结构的电磁分析成为可能。该程序的主要贡献是发展了新的、更经济、更稳健的积分方程列式，以及用于求解的新的高阶数值格式。该程序中提出的新的积分方程组将允许将由于现实模型的离散化而产生的计算模型的尺寸减少一半。所提出的高阶解方法将进一步降低计算复杂性，因为与传统的工业中使用的低阶方法相比，它们具有指数级更高的效率。*拟议研究计划的另一个主要领域是开发新的微波成像方法。后者的问题在于图像的不唯一性，该图像可以从由感兴趣对象散布的场中包含的信息重建。这种不唯一性源于成像问题的数学公式固有的不正确(病态)。这是一个巨大的挑战，几十年来，它一直在阻止微波用于可靠的非侵入性成像，无论是在癌症患者的生物医学筛查中，还是在地下石油和天然气勘探或飞机结构健康的无损检测中。该研究计划将建立在申请人先前的工作的基础上，该工作已经表明，使用微波重建图像的这种非唯一性是可以克服的。这种新的微波断层成像方法有望将其作为一种可行的成像方式，与核磁共振和X射线并驾齐驱，并进入地下探测和材料测试领域。**

Fast wireless communications, reliable power transmission, and biomedical imaging are the important technologies which define the quality of life for millions of Canadians. Critical to the advancements of these technologies is the design of novel devices and systems which rely on the methods and tools of computational electromagnetics (CEM). Among such systems are the cell phones, digital circuit boards, GPS units, radars, and tomography systems - just to name a few. Despite various fundamental advances made in the recent past, currently available algorithms of CEM suffer from various fundamental shortcomings. These shortcomings handicap development of the new technologies costing the industries millions of dollars in losses from faulty designs and prolonged time to market. The most challenging of these are large computational complexity of the pertinent algorithms and their inadequate accuracy when applied to electromagnetic analysis of realistic models. The proposed research program focuses on development of novel algorithms and high-accuracy solution methods, which overcome the computational complexity barrier and enable robust electromagnetic analysis of complex large-scale structures. The key contributions of the program are in development of novel, more economical, and more robust integral equation formulations for CEM as well as the novel higher-order numerical schemes for their solution. The novel integral equations proposed in the program will allow to reduce in half the size of the computational models stemming from the discretization of the realistic models. The proposed higher-order solution methods will further reduce the computational complexity by taking advantage of their exponentially higher efficiency compared to the low-order methods traditionally used in the industry. ***The other thrust area of the proposed research program is in development of new methods of microwave imaging. The latter suffers from non-uniqueness of the images which can be reconstructed from the information contained in the field scattered by the object of interest. This non-uniqueness stems from the inherent incorrectness (ill-posedness) of the mathematical formulations of the imaging problem. It presents a grand challenge which for decades has been preventing microwaves from being used for reliable non-invasive imaging may it be in biomedical screening of patients for cancer, for underground oil and gas exploration or non-destructive testing of an aircraft structural health. The research program will build on prior work of the applicant which has shown that this non-uniqueness in the image reconstruction using microwaves can be overcome. This novel approach to microwave tomography promises to place it as a viable imaging modality alongside with MRI and X-rays as well as into the fields of underground detection and material testing.**