New High-Order High-Frequency Methods for Computational Electromagnetics

The present text proposes development of a high-order, high-frequency simulation infrastructure for the evaluation of radar cross-sections in the high-frequency regime. Relying on newly developed high-frequency integral equation methods, the proposedapproach is entirely rigorous: it accounts fully for all scatterer complexities and all electromagnetic effects, including edges and corners, multiple-scattering, diffraction, caustics, creeping waves, shadowing, penumbrae, etc. Proof-of-conceptcalculations based on these ideas, produced under funding from the Phase I STTR contract F49620-02-C-0006 have demonstrated the feasibility of the proposed approach. For a given scattering configuration (scattering body and incident direction), thecomputation time required by our algorithms to solve the scattering problem at a given frequency and with a prescribed accuracy remains bounded as the frequency grows without bound. That is to say, the proposed methods run in O(1) operations, with aconstant independent of the scatterer size. The Phase II effort proposed in this text will result in efficient computational codes, based on the high-frequency methods described above, that remain applicable and accurate throughout the electromagneticspectrum. Such codes will give rise to significant improvements in the description of high-frequency scattering processes in science and engineering - and they thus carry a substantial potential for commercial impact. As indicated in the AF01T009 topicaldescription, the scattering attributes of actual-size inventory frequently needs to be obtained through high frequency approximations --- the previous versions of which suffer from various shortcomings. The proposed algorithms avoid such shortcomings -which arise from neglect of curvatures, shadow boundaries, diffraction effects, etc - by introducing a paradigm which deals explicitly with multiple scattering and shadow boundaries, and which produces rigorous (convergent) solutions for the integralequations of the problem. The applications of such algorithms are very numerous indeed: they range from remote sensing of vehicles to terrain mapping, antenna design, altimetry and communications. The successful completion of the proposed work will leadto significant improvements in the description of high-frequency scattering processes: an area of great importance for both national security and commercial concerns.