Research Initiation Award: A Three-Dimensional Finite Element Scheme for the Analysis of Electromagnetic Fields in an Unbounded Region

利用二维有限元电磁模型来模拟散射和导波结构的电特性已经成为普遍的发展功能强大又便宜的电脑。不幸的是，许多几何形状不能精确地在二维中建模。从二维到三维的步骤在计算上很昂贵，在分析上也很复杂。传统的有限元公式会导致三维的伪解。此外，场的矢量性质使得网格截断的任务非常困难。“逐矩”法是一种有效的二维有限元网格截断方法。人们相信，它的许多优点可以转化为三维空间。在这个项目中，“随矩”方法将被扩展到解决三维复杂物体的电磁散射问题。这种技术的发展将为目前用近似技术解决的许多问题提供解决方案。此外，三维方案的发展可以导致导波结构的应用。

The use of two dimensional finite element electromagnetic models to simulate the electrical characteristic of both scattering and guided wave structures has become commonplace due to the development of powerful and cheap computers. Unfortunately, many geometries cannot be accurately modeled in two dimensions. The step from two the three dimensions is both computationally expensive and analytically complex. A traditional finite element formulation results in spurious solutions in three dimensions. In addition, the vector nature of the fields makes the task of grid truncation very difficult. The "bymoment" method has shown itself to be an efficient technique for grid truncation in a two dimensional finite element solution. It is believed that many of its advantages can be translated to three dimensions. In this project the "bymoment" method will be extended to solve the problem of electromagnetic scattering from three dimensional complex objects. The development of such a technique will provide solutions for many problems which are currently solved by approximate techniques. In addition, the development of a three dimensional scheme can lead to applications for guided wave structures.