Gaussian Beam Methods for Large-Scale Computational Electromagnetics and Applications

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