Numerical Methods for Wave Propagations in Inhomogeneous Media

非均匀介质中波传播的数值方法

• 批准号: 1005441
• 负责人: Wei Cai
• 金额: $ 20万
• 依托单位: University of North Carolina at Charlotte
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-09-15 至 2014-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1005441&HistoricalAwards=false
• 关键词: Numerical; Methods; Wave; Propagations; Inhomogeneous

In this proposal, the PI will develop numerical methods and their mathematical analysis, ultimately their implementations in studying wave phenomena in nano-electronics, coupled arrays of quantum dots, and phase shift masks in lithography. Propagation of classical electromagnetic and quantum waves plays a key role in these physical and engineering systems. In order to gain a quantitative understanding of the wave phenomena in those systems, accurate and efficient numerical simulations are needed with appropriately designed numerical algorithms. The targeted applications motivate our research with the following three proposed numerical methods: [1] An adaptive conservative cell average spectral method for Wigner equations in electron transport of nano-electronics; [2] A fast integral solver for quantum wave scattering in 3-D quantum dots in layered media [3] A parallel spectral element method based on eigen-oscillations for complex Helmholtz equations. The potential technology impact of this research is to understand the physics involved and provide design guidelines for nano-electronics such as nano-MOSFETs, phase shift masks, and quantum dots. The numerical methods developed in this research will be used for the engineering design of quantum devices with significant impact on maintaining US technology preeminence in the development of new VLSI microchips, and next generation X-ray lithography in microchip manufacturing. Also, graduate students trained in this project will provide skilled workforce in the competitive high technology job market as well as potential academic researchers.

在此提案中，PI将开发数值方法及其数学分析，最终在研究纳米电子中的波浪现象，量子点的耦合阵列以及光刻中的相移掩码中的实现。经典电磁波和量子波的传播在这些物理和工程系统中起关键作用。为了对这些系统中的波现象有定量的理解，使用适当设计的数值算法需要准确有效的数值模拟。 有针对性的应用通过以下三种提出的数值方法激发了我们的研究：[1]一种自适应保守的细胞平均光谱方法，用于纳米电子电子的电子传输中的Wigner方程； [2]在分层介质中3-D量子点中的量子波散射的快速积分求解器[3]基于复杂Helmholtz方程的本征振荡的平行光谱元件方法。这项研究的潜在技术影响是了解所涉及的物理学，并为纳米电子学，例如纳米弹性，相移面罩和量子点提供设计准则。 这项研究中开发的数值方法将用于量子设备的工程设计，对在新的VLSI微芯片的开发以及Microchip Manufacturing中的下一代X射线光刻方面的开发中维持美国技术的卓越。此外，接受该项目培训的研究生将在竞争性高科技工作市场以及潜在的学术研究人员中提供熟练的劳动力。