径向基函数及其耦合方法在电磁场数值计算中的应用

Radial Basis Functions and Coupled Method in Computational Electromagnetics

针对带电导体附近急剧变化的位函数和场函数这一难于处理的边界条件,将小波函数的紧支撑特性和全域径向基函数(RBF)的高精度逼近能力相结合,提出电磁场边值问题求解的耦合方法并应用于接地金属槽/箱的数值计算中;将径向基函数无网格方法引入波导本征值的计算中,给出其求解本征问题的思路,建立相应的离散方程,分析矩形、圆形和脊形波导的本征值并与有限元方法进行比较.数值仿真实验表明,径向基函数及其耦合方法在分析电磁场边值和本征值问题时是有效的且具有实现简单、节点少和精度高的优势.

For boundary conditions with functions changing rapidly, especially in charged conductors, we combine compact feature of wavelet functions and high accuracy of RBF in a coupled method and solve ground metal trough/box problems. Rectangular, ridge and round waveguides are analyzed with RBF and FEM methods. Numerical experiments show that RBF method is efficient in solving electromagnetic boundary and eigenvalue problems. RBF method is easier and more accurate with less nodes.