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。这些技术的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。这些系统包括手机、数字电路板、GPS装置、雷达和断层扫描系统--仅举几例。尽管在最近的过去取得了各种基本的进步，目前可用的算法的CEM遭受各种基本的缺点。这些缺点阻碍了新技术的发展，使工业界因设计缺陷和上市时间延长而损失数百万美元。其中最具挑战性的是相关算法的计算复杂度大，并且在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稳健电磁分析。该计划的主要贡献是在开发新的，更经济，更强大的积分方程公式CEM以及新的高阶数值方案，其解决方案。在该计划中提出的新的积分方程将允许减少一半的计算模型的大小源于现实模型的离散化。所提出的高阶解方法将进一步降低计算复杂度，利用其指数更高的效率相比，传统上在工业中使用的低阶方法。* 拟议研究方案的另一个重点领域是开发微波成像的新方法。后者遭受的图像的非唯一性，可以从包含在由感兴趣的对象散射的字段中的信息重建。这种非唯一性源于成像问题的数学公式的固有不正确性（不适定性）。它提出了一个巨大的挑战，几十年来一直阻止微波用于可靠的非侵入性成像，可能是在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非破坏性测试中。该研究计划将建立在申请人的先前工作的基础上，申请人的先前工作已经表明，可以克服使用微波的图像重建中的这种非唯一性。这种新颖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MRI和X射线一起，并进入地下探测和材料测试领域。