Gaussian Beam Methods for Large-Scale Computational Electromagnetics and Applications

研究人员建议为工业和军事应用的大规模计算电磁学开发和实施新颖有效的基于高斯束的计算方法。该项目涉及科学计算和应用数学中的几个基本问题，如多尺度建模、模拟和逆问题，这些问题在材料科学和纳米技术中至关重要。计算电磁学已经成为各种科学和工程学科中一项基础的、蓬勃发展的技术，包括雷达、声纳、地震成像、医学成像、光刻处理、陆地地雷探测、潜艇探测、隐身技术、遥感、电子显微镜和纳米技术。由欧拉高斯波束方法产生的新方法对计算电磁学和应用具有重大影响，特别是在高频下。研究了高波数电磁波传播的大尺度正散射和逆散射问题。研究人员将开发高效、准确的高斯光束方法来求解非均匀介质中高波数域的麦克斯韦方程组。此外，研究人员将把新的高斯方法应用于麦克斯韦方程组的三个具有挑战性和实际意义的问题：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用于这些应用。高斯光束方法将能够产生高波数波传播的均匀渐近解。这些新的欧拉高斯波束方法也应该为非均匀介质中电磁波的许多其他应用提供有效的工具。-------------------------------------------------------------------

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.-------------------------------------------------------------------