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

计算电磁学的新前沿：迈向高精度解决方案和可靠的微波成像

• 批准号: RGPIN-2015-05144
• 负责人: Okhmatovski, Vladimir
• 金额: $ 2.19万
• 依托单位: University of Manitoba
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2019
• 资助国家: 加拿大
• 起止时间: 2019-01-01 至 2020-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=683558
• 关键词: New; Frontiers; Computational; Electromagnetics; Towards

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.**

快速的无线通信、可靠的电力传输和生物医学成像是决定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计算电磁学 (CEM) 方法和工具的新型设备和系统的设计。此类系统包括手机、数字电路板、GPS 装置、雷达和断层扫描系统 - 仅举几例。尽管最近取得了各种基本进展，但当前可用的 CEM 算法仍存在各种基本缺陷。这些缺点阻碍了新技术的开发，导致该行业因设计错误和上市时间延长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巨大计算复杂性以及应用于现实模型的电磁分析时精度不足。拟议的研究计划侧重于开发新颖的算法和高精度求解方法，克服计算复杂性障碍，实现复杂大型结构的鲁棒电磁分析。该计划的主要贡献在于开发新颖、更经济、更鲁棒的 CEM 积分方程公式及其解决方案的新颖高阶数值方案。该程序中提出的新颖积分方程将允许由于现实模型的离散化而将计算模型的大小减少一半。与业界传统使用的低阶方法相比，所提出的高阶求解方法将利用其指数级更高的效率进一步降低计算复杂性。 ***拟议研究计划的另一个重点领域是开发微波成像新方法。后者受到图像的非唯一性的影响，该图像可以根据感兴趣对象散射的场中包含的信息来重建。这种非唯一性源于成像问题的数学公式固有的不正确性（不适定性）。它提出了一个巨大的挑战，几十年来一直阻碍微波用于可靠的非侵入性成像，可能是癌症患者的生物医学筛查、地下石油和天然气勘探或飞机结构健康的无损检测。该研究计划将建立在申请人的先前工作的基础上，该工作已表明可以克服使用微波进行图像重建的这种非唯一性。这种新颖的微波断层扫描方法有望将其与 MRI 和 X 射线一起作为一种可行的成像方式，并进入地下探测和材料测试领域。**