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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。
In order to solve the problem of open-field electromagnetic field, a method of region mapping finite element method is proposed. The method divides the infinite area to be solved into the inner limited area and the outer infinite area. For the inner region, the traditional finite element equation is formed. For the outer region, the Kelvin transformation in geometry is introduced to form another finite element equation for the transformed field. The equations of the inner and outer regions are coupled on a common boundary. The results show that this method can achieve the accuracy of the traditional finite element method by using 1/9 or less elements. Compared with the traditional finite element method, this method greatly reduces the number of grid cells generated and calculates the required memory and time. This method has been implemented in 2D and 3D open-domain problems.