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.

在该提案中，PI 将开发数值方法及其数学分析，最终将其应用于研究纳米电子学中的波动现象、量子点耦合阵列以及光刻中的相移掩模。经典电磁波和量子波的传播在这些物理和工程系统中起着关键作用。为了定量了解这些系统中的波动现象，需要通过适当设计的数值算法进行准确、高效的数值模拟。 目标应用通过以下三种提出的数值方法激发了我们的研究： [1] 纳米电子学电子传输中维格纳方程的自适应保守单元平均谱方法； [2] 一种用于层状介质中 3-D 量子点量子波散射的快速积分求解器 [3] 一种基于复杂亥姆霍兹方程本征振荡的并行谱元方法。这项研究的潜在技术影响是了解所涉及的物理原理，并为纳米电子器件（例如纳米 MOSFET、相移掩模和量子点）提供设计指南。 这项研究开发的数值方法将用于量子器件的工程设计，这对保持美国在新型 VLSI 微芯片开发和微芯片制造中的下一代 X 射线光刻技术方面的领先地位具有重大影响。此外，在该项目中接受培训的研究生将为竞争激烈的高科技就业市场提供熟练的劳动力以及潜在的学术研究人员。