求解开域电磁场问题的区域映射有限元法

Domain map finite element method for open boundary electromagnetic field problem

为了求解开域电磁场问题,提出一种区域映射有限元方法。该方法把待求解的无限大区域划分为内部有限区域和外部无限区域。对内部区域,形成传统的有限元方程;对外部区域,引入几何中的Kelvin变换,对变换后的场域形成另一个有限元方程。内外区域的方程在公共边界上耦合。结果表明,该方法使用1/9甚至更少的单元即可达到传统有限元法的精度。与传统有限元法相比,该方法大量减少生成的网格单元数、计算所需的内存和时间。已在二维和三维开域问题计算中实现了该方法。

A domain map finite element method was developed to solve open boundary electromagnetic field problems. This method divides the infinite field domain into inner and outer field domains with the standard FEM equations solved in the inner domain and the Kelvin transformation used in outer domain,in a new finite element format. The equations for the two parts are coupled at the domains interface. This method used less than 1/9 the elements of the traditional FEM; thus this method has significantly less degrees of freedom and uses much less memory and CPU time than traditional FEM. The method has been successfully applied to 2-D and 3-D open boundary problems.