Hybrid Methods for the Time Domain Integral Equations of Computational Electromagnetics

计算电磁学时域积分方程的混合方法

• 批准号: 1114889
• 负责人: Daniel Weile
• 金额: $ 28.99万
• 依托单位: University of Delaware
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-08-15 至 2015-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1114889&HistoricalAwards=false
• 关键词: Hybrid; Methods; Time; Domain; Integral

The project "Hybrid methods for the time domain integral equations of electromagnetics" advances a multidisciplinary program consisting of basic numerical analysis of time domain integral equations (TDIEs) and a two-fold program of hybridization. The basic numerical analysis is devoted to issues of sparsification, quadrature error, error estimates and fast solvers for a new and exciting class of TDIE methods based on convolution quadrature (CQ-TDIE). The first prong of the hybridization work concerns combining CQ-TDIE with the volume finite element method. Not only would this hybridization allow for the easy simulation of inhomogeneous and complex media, but it also raises the tantalizing prospect of a perfect time domain integral based boundary condition. The second, and more speculative, hybridization approach combines CQ-TDIE with older Galerkin-based techniques with the aim of controlling dispersion and dissipation. It is anticipated that the resulting hybrid methods have the stability and spatial accuracy of CQ, but with the greater efficiency and reduced dispersion associated with Galerkin approaches. In particular, the technique would be ideally suited for the analysis of certain classes of modern technology involving long propagation distances through homogeneous regions (as occur in electromagnetic interference analysis) or mechanically moving parts (as necessary in many nanotechnology problems).Numerical simulation of physical processes reduces business prototyping costs, enables the safe prediction of the outcome of dangerous experiments, and can even make scientific discoveries by illuminating internal processes difficult to examine in the laboratory. In an era dominated by personal communication technology, the simulation of electromagnetic phenomena becomes especially crucial. "Hybrid methods for the time domain integral equations of electromagnetics" creates two new methods for the simulation of the interaction between electromagnetic fields and matter. While computerized approaches to electromagnetic analysis already exist, the methods to be created by the investigators allow for more accurate and efficient simulation of problems involving biological tissue, long propagation distances (such as occur in communications simulations), and mechanically moving parts (as needed in nanotechnology simulations). In addition to these benefits, the new method represents an important mathematical advance: it is based on a technique thought unstable for over three decades, which has only recently been made practical. The investigators therefore expect that the advances made in the analysis of electromagnetic problems under the auspices of this work will be easily translated to other scientific areas including acoustics, solid mechanics, and fluid mechanics.

“电磁学时域积分方程的混合方法”项目提出了一个多学科项目，包括时域积分方程的基本数值分析和双重杂交程序。基本的数值分析致力于稀疏化、正交误差、误差估计和基于卷积正交（CQ-TDIE）的一种新的令人兴奋的TDIE方法的快速求解问题。杂化工作的第一个重点是将CQ-TDIE与体积有限元法相结合。这种杂交不仅可以很容易地模拟非均匀和复杂的介质，而且还提出了一个基于完美时域积分的边界条件的诱人前景。第二种，也是更具推测性的，杂化方法结合了CQ-TDIE和旧的基于伽辽金的技术，目的是控制色散和耗散。预计所得到的混合方法具有CQ的稳定性和空间精度，但具有与伽辽金方法相关的更高的效率和更小的色散。特别是，该技术将非常适合分析某些类型的现代技术，这些技术涉及通过均匀区域的长距离传播（如电磁干扰分析中所发生的）或机械运动部件（如许多纳米技术问题中所必需的）。物理过程的数值模拟降低了商业原型的成本，能够对危险实验的结果进行安全预测，甚至可以通过阐明难以在实验室中检查的内部过程来进行科学发现。在一个以个人通信技术为主导的时代，电磁现象的仿真变得尤为重要。“电磁学时域积分方程的混合方法”为模拟电磁场与物质相互作用创造了两种新的方法。虽然计算机化的电磁分析方法已经存在，但研究者们将要创造的方法允许更精确和有效地模拟涉及生物组织、长距离传播（如在通信模拟中发生的）和机械运动部件（如在纳米技术模拟中需要的）的问题。除了这些好处之外，这种新方法还代表了一种重要的数学进步：它基于一种30多年来一直被认为不稳定的技术，直到最近才被付诸实践。因此，研究人员期望在这项工作的支持下，在电磁问题分析方面取得的进展将很容易地转化为其他科学领域，包括声学、固体力学和流体力学。