Grant: Discovery Grants Program - Individual

The problem of evaluating the electromagnetic response of wire antenna systems is one of great import and significant mathematical complexity. The goal of the work proposed in this text is, precisely, to advance the theoretical and computational state of the art in this important and challenging mathematical problem. In detail, we propose to: (1) develop the theoretical and numerical treatment of the straight wire antenna driven by source located on the antenna structure; (2) extend the previous theory and solvers (both transmit and receive cases) to curved antennas; (3) develop high-order treatment of wires attached to conducting bodies; and (3) extend the previous theory and solvers to enable solution for antennas composed of arbitrary numbers of either straight or curved segments intersecting at arbitrary angles.A successful completion of the proposed work should give rise to significantly improved understanding of the mathematics of antenna problems, as well as a powerful algorithm base applicable to significant problems of scientific and engineering interest. Whether or not pursuing a career related to problems involving wave propagation, a student successfully completing a degree program along the lines described in this proposal should have mastered a significant expertise in state-of-the-art applied mathematics and numerical analysis, and should thus be well prepared for a successful research career in industry or academia.