The Investigators propose to develop and implement novel and efficient Gaussian-beam-based computational methods for large-scale computational electromagnetics motivated by industrial and military applications. The project addresses several fundamental issues in scientific computing and applied mathematics, such as multi-scale modeling, simulation, and inverse problems, which are essential in material sciences and nanotechnology. Computational electromagnetics has become a fundamental, vigorously growing technology in diverse science and engineering disciplines, ranging from radar, sonar, seismic imaging, medical imaging, lithography processing, detection of land mines, submarine detection, stealth technology, remote sensing, electronics to microscopy and nanotechnology. The new methodology resulting from Eulerian Gaussian beam methods has substantial impact on computational electromagnetics and applications, particularly at high frequencies.
The research involves large-scale direct and inverse scattering problems for electromagnetic wave propagation with high wave numbers. The Investigators will develop efficient and accurate Eulerian Gaussian beam methods for Maxwell's equations in inhomogeneous media in the high wave number regime. Furthermore, the Investigators will apply the new Gaussian methods to three challenging and practically important problems for Maxwell's equations: inverse medium problems, large cavity problems, and diffraction grating problems. New Eulerian Gaussian-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 beyond caustics for wave propagation with high wave numbers. These new Eulerian Gaussian beam methods should also provide an efficient tool for many other applications related to electromagnetic waves in inhomogeneous media.
