Gaussian Beam Methods for Large-Scale Computational Electromagnetics and Applications

用于大规模计算电磁学的高斯束方法及其应用

• 批准号: 0830161
• 负责人: Gang Bao
• 金额: $ 25万
• 依托单位: Michigan State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-09-01 至 2012-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0830161&HistoricalAwards=false
• 关键词: Gaussian; Beam; Methods; Large; Scale

The Investigators propose to develop and implement novel andefficient Gaussian-beam-based computational methods for large-scale computationalelectromagnetics motivated by industrial and military applications. The project addressesseveral fundamental issues in scientific computing and applied mathematics, such asmulti-scale modeling, simulation, and inverse problems, which are essential in materialsciences and nanotechnology. Computational electromagnetics has become a fundamental,vigorously growing technology in diverse science and engineering disciplines, rangingfrom radar, sonar, seismic imaging, medical imaging, lithography processing, detection ofland mines, submarine detection, stealth technology, remote sensing, electronics tomicroscopy and nanotechnology. The new methodology resulting from Eulerian Gaussian beammethods has substantial impact on computational electromagnetics and applications,particularly at high frequencies.The research involves large-scale direct and inverse scattering problems for electromagneticwave propagation with high wave numbers. The Investigators will develop efficient and accurateEulerian Gaussian beam methods for Maxwell's equations in inhomogeneous media in the highwave number regime. Furthermore, the Investigators will apply the new Gaussian methods to threechallenging and practically important problems for Maxwell's equations: inverse mediumproblems, large cavity problems, and diffraction grating problems. New EulerianGaussian-beam-based algorithms will be developed for the first time for these applications.The Gaussian beam method will be capable of producing uniform asymptotic solutions beyondcaustics for wave propagation with high wave numbers. These new Eulerian Gaussian beammethods should also provide an efficient tool for many other applications related toelectromagnetic waves in inhomogeneous media.-------------------------------------------------------------------

研究人员建议开发和实施新颖且高效的基于高斯束的计算方法，用于工业和军事应用推动的大规模计算电磁学。该项目解决了科学计算和应用数学中的几个基本问​​题，例如多尺度建模、模拟和反问题，这些在材料科学和纳米技术中至关重要。计算电磁学已成为各种科学和工程学科中蓬勃发展的基础技术，涵盖雷达、声纳、地震成像、医学成像、光刻处理、地雷探测、潜艇探测、隐形技术、遥感、电子学、显微镜和纳米技术。欧拉高斯波束方法产生的新方法对计算电磁学和应用产生了重大影响，特别是在高频方面。该研究涉及高波数电磁波传播的大规模直接和逆散射问题。研究人员将为高波数区域的非均匀介质中的麦克斯韦方程开发高效且准确的欧拉高斯光束方法。此外，研究人员将应用新的高斯方法来解决麦克斯韦方程组的三个具有挑战性和实际重要的问题：逆介质问题、大腔问题和衍射光栅问题。新的基于欧拉高斯光束的算法将首次针对这些应用而开发。高斯光束方法将能够为高波数的波传播产生超越焦散的均匀渐近解。这些新的欧拉高斯光束方法还应该为与非均匀介质中的电磁波相关的许多其他应用提供有效的工具。--------------------------------------------------------------------------------