High-order electromagnetic modeling of antenna systems

评估线天线系统的电磁响应是一个非常重要的问题，也是一个非常复杂的数学问题。在本文中提出的工作的目标，准确地说，是推进这一重要和具有挑战性的数学问题的理论和计算水平。具体地，我们建议：(1)发展位于天线结构上的源驱动直线天线的理论和数值处理；(2)将以前的理论和解算器(包括发射和接收情况)推广到弯曲天线：(3)发展对附于导体的导线的高阶处理；(3)扩展以前的理论和解算器，使之能够求解由任意数目的直线段或曲线段组成的任意角度相交的天线。这项工作的成功完成将极大地提高对天线问题的数学理解，并为具有重大科学和工程意义的问题提供强大的算法基础。无论是否从事与波传播问题相关的职业，成功完成本建议所述方向的学位课程的学生都应该掌握最先进的应用数学和数值分析方面的重要专业知识，因此应该为在工业或学术界成功的研究生涯做好准备。

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.