Hierarchical and Calderon Regularization of Time Domain Integral Equations for Electromagnetics

基于时间推进（MOT）的时域积分方程（TDIE）求解器为分析大型复杂结构的瞬变电磁相互作用提供了一个有吸引力的途径。不幸的是，这些求解器往往遭受时间（低频）和空间（密集网格）击穿现象时，应用于分析低频到中频电磁瞬态几何复杂和多尺度结构，从而防止其应用到许多重要的科学和工程问题。该项目旨在开发新的平面波时域加速，正则化MOT-TDIE解算器，这些解算器不受时间和空间崩溃现象的影响。 所提出的技术消除时间和空间的故障现象MOT-TDIE求解器利用分层基函数和新的时域Calderon身份，分别。此外，他们保证低频稳定性的MOT-TDIE求解器利用卡尔德龙正则化的频谱特性。由此产生的MOT-TDIE解算器将允许快速分析几何复杂和混合尺度结构上的低频到中频电磁瞬态。该项目的教育目标是开发一套全面的教育材料，支持涵盖快速MOT-TDIE技术所有方面的课程，并将其用于教学和推广。开发快速和高阶精度的MOT-TDIE解算器，这些解算器在空间和时间尺度上稳健无缝地应用，将允许分析广泛的科学和真实的数据。世界电磁工程问题是棘手的使用当今的方法。考虑到它们的网格鲁棒性，这项工作产生的电磁模拟器将使光学科学家能够严格分析非线性和无序超材料和纳米结构中的瞬态效应，而无需诉诸均匀化近似，从而为控制和引导纤维和芯片中的流动和电磁波和光创造了新的途径。此外，它们将允许电子工程师设计数字集成电路和RF无线传感器，而无需采用特殊的空间分解方法，从而大大节省了开发时间和成本。最后，它们将允许汽车和航空航天工程师适当地保护他们的设计免受不必要的电磁干扰，从而通过减少远程生成的系统干扰的威胁来提高安全性并影响国家安全。

Marching on in time (MOT)-based time domain integral equation (TDIE) solvers provide an appealing avenue for analyzing transient electromagnetic interactions with large and complex structures. Unfortunately, these solvers often suffer from temporal (low-frequency) and spatial (dense-mesh) breakdown phenomena when applied to the analysis of low- to medium-frequency electromagnetic transients on geometrically intricate and multiscale structures, thereby preventing their application to many important scientific and engineering problems. This project seeks the development of new plane wave time domain-accelerated, regularized MOT-TDIE solvers that are immune to temporal and spatial breakdown phenomena. The proposed techniques eliminate temporal and spatial breakdown phenomena in MOT-TDIE solvers by leveraging hierarchical basis functions and new time domain Calderon identities, respectively. In addition, they guaranty low-frequency stability in MOT-TDIE solvers by exploiting the spectral properties of the Calderon regularizer. MOT-TDIE solvers resulting from this effort will permit the fast analysis of low- to medium-frequency electromagnetic transients on geometrically intricate and mixed-scale structures. The educational objective of this project is to develop a comprehensive set of educational materials supporting a course covering all aspects of fast MOT-TDIE technology and to use them in teaching and outreach.The development of fast and higher-order accurate MOT-TDIE solvers that robustly and seamlessly apply across spatial and temporal scales will permit the analysis of a wide class of scientific and real-world electromagnetic engineering problems that are intractable using present day methods. Given their grid-robust nature, the electromagnetic simulators resulting from this effort will permit optical scientists to rigorously analyze transient effects in nonlinear and disordered metamaterials and nanostructures without resorting to homogenization approximations, thereby creating a new avenue for controlling and directing the flow and electromagnetic waves and light in fibers and on chips. In addition, they will allow electronic engineers to design digital integrated circuits and RF wireless sensors without resorting to ad-hoc spatial decomposition methods, thereby resulting in significant savings in development time and costs. And finally, they will permit automotive and aerospace engineers to appropriately protect their designs from unwanted electromagnetic interference, thereby improving safety and impacting national security by reducing the threat of remotely generated system upsets.