Numerical Methods for Maxwell Equations in Dispersive and Lossy Inhomogeneous Media

本项目旨在研究色散和有损非均匀介质中电磁散射的精确和高效的数值算法。电磁散射，也就是波的散射，在科学和工程应用中普遍存在。色散和有损非均匀介质中波散射的模拟对快速、准确的计算提出了两大挑战，即所涉及问题的大波数对分辨率的要求和由于材料不连续界面而导致的数值离散精度退化。为了应对这些挑战，研究人员提出了两种新的方法：(1)在时间域：基于高阶笛卡尔网格的上卷嵌入边界方法，求解色散和有损非均匀介质中的含时Maxwell方程；(2)在频率域：基于并矢格林函数快速计算算法的分层介质中波散射的快速积分方法。研究人员将应用在该项目下开发的数值算法来设计对下一代光技术发展具有重大影响的微尺度光子器件，以实现经济高效的家庭互联网宽带接入，并设计探地雷达。这将有助于开发用于地下矿山和工业污染物的现代检测设备。此外，该项目在新物理和数值方法领域的研究成果将被纳入应用数学和光学课程，将通过该中心和区域光学公司之间的现有合作伙伴关系，探索将结果转移到区域光学工业的潜在技术转移。在本研究过程中，调查员应积极参与中心与地区高中的技术培训计划。

This project is to develop accurate and efficient state-of-the art numerical algorithms for electromagnetic scattering in dispersive and lossy inhomogeneous media. Electromagnetic scattering, wave scattering in general, is ubiquitous in scientific and engineering applications. Simulation of wave scattering in dispersive and lossy inhomogeneous media poses two major challenges for fast and accurate computations, namely, the resolution requirement by the large wave number of the problems involved, and the accuracy degeneracy of numerical discretizations due to interfaces of material discontinuities. To address these challenges, the investigator proposed two new approaches: (1) In Time domain: A high order Cartesian grid based Upwinding Embedded Boundary Method for time dependent Maxwell equations in dispersive and lossy inhomogeneous media, and (2) In Frequency Domain: A fast integral method for wave scattering in layered media based on fast calculation algorithms of dyadic Green's functions.The investigator will apply the numerical algorithms developed under this project for the designing of microscale photonic devices with significant impact on the development of next generation optical technologies for cost efficient home internet broadband access, and also the design of ground penetrating radars, which will contribute to the development of modern detection devices for underground mines and industrial contaminants. Moreover, Research results from this project, in the area of new physics and numerical methods, will be incorporated into the applied mathematics and optics curriculum, potential technology transfer of the results to the area optics industrial will be explored through the existing partnership between the Center and area optics companies. The investigator shall participate actively in the Center's technology training programs with area high schools during the course of this research.