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

使用二维有限元电磁模型来模拟散射和导波结构的电特性由于强大而廉价的计算机的发展，这变得司空见惯。不幸的是，许多几何图形不能在两个维度上精确建模。从三维到二维的步骤在计算上是昂贵的，在分析上也是复杂的。传统的有限元格式会产生三维伪解。此外，场的矢量性质使得网格截断的任务非常困难。“比矩法”是一种有效的二维有限元网格截断方法。解决方案。人们认为，它的许多优势可以转化为三个维度。在本项目中，我们将把“多项式”方法推广到求解三维复杂目标的电磁散射问题。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，三维格式的发展可能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.