摘要
保角变换一直是求解边值问题的重要方法，但以往在电磁场领域的应用多限于求解静态和准静态问题。利用保角变换及椭圆函数的理论和方法结合数值技术求解导波问题中的二维Ｈｅｌｍｈｏｌｔｚ方程。这种半解析数值方法的优点是：利用保角变换解析的前处理将不规则的场域转化为规则域，从而可以消除最常用的矩形网格对复杂边界的离散化误差，降低算法复杂度，提高计算效率。根据我们提出的新型高功率导波结构的特点导出了从五边形族到矩形的椭圆函数保角变换式，采用有限差分法对变换后得到的非均匀Ｈｅｌｍｈｏｌｔｚ方程在变换域进行简单的五点格式剖分。通过保角变换有限差分算法（ＣＭＦＤ）得出各模式的截止频率和电磁场分布，从而进一步对该波导族做出全面的性能分析和优化。最后，对计算结果进行了全面验证。
The theory of Conformal Mapping and elliptic function, integrated with pure numerical methods such as Finite Difference Method, are utilized to solve twodimensional Helmholtz equation of guided wave problems in this paper.The unique advantage of the halfanalytical numerical method is that the analytical process of Conformal Mapping can transform an irregular area into a regular one such as a rectangle.Therefore, the discretization error of numerical methods on the boundary can be avoided, and the numerical algorithm can be implemented more easily,with the computing efficiency improved.In this paper,a novel family of high power microwave structures known as pentagonal waveguides or elliptic function waveguides is analyzed systematically by the Conformal Mapping Finite Difference method(CMFD). Being verified by the measurement results and compared with some other pure numerical methods such as FEM and FDTD, CMFD is proved to have such advantages as high accuracy, efficiency,convenience and versatility.This method is also promising for dealing with other novel guidedwave structures.
出处
《电波科学学报》
EI
CSCD
1999年第2期121-128,共8页
Chinese Journal of Radio Science
基金
国家自然科学基金
863计划
关键词
保角变换
椭圆函数
有限差分
波导
电磁场
Conformal mapping
Elliptic function
Finte difference
Waveguides
