Numerical Methods for Maxwell Equations in Dispersive and Lossy Inhomogeneous Media

本计画旨在发展精确且有效率的数值演算法，以计算色散与有耗非均匀介质中的电磁散射。电磁散射，通常是波散射，在科学和工程应用中无处不在。在色散和有耗非均匀介质中的波散射的模拟提出了两个主要的挑战，快速和准确的计算，即，所涉及的问题的大波数的分辨率要求，和由于材料不连续性的接口的数值离散的精度退化。为了应对这些挑战，研究人员提出了两种新方法：（1）在时域：基于高阶笛卡尔网格的迎风嵌入边界法，用于色散和有耗非均匀介质中的时间相关麦克斯韦方程，以及（2）在频域：基于并矢绿色函数的快速计算算法，研究了层状介质中波散射的快速积分方法。在该项目下开发的用于设计微尺度光子器件的算法对开发下一代光学技术具有重大影响，用于具有成本效益的家庭互联网宽带接入，以及设计地面穿透雷达，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，将通过中心与区域光学公司之间的现有合作关系探索将成果转移到区域光学工业的潜在技术。在本研究过程中，研究者应积极参加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.