对称域基本解函数的构造及应用

Reconstruction and Application of Fundamental Function in Symmetrical Region

在对称区域中,构造出满足对称边界条件的基本解函数,并推广到基本解方法(MFS)中求解Poisson方程的边界值问题.利用构造出的基本解,输入数据和所需求解的线性方程组数目可减少到原来(不利用对称性的基本解函数所需的方程组数目)的1/2或1/4,具有计算时间短、精度高、编程简单、输入数据少等优点.通过数值计算可以看出,计算结果与解析解之间的误差很小,说明该方法值得推广使用.

The method of fundamental solution（MFS） with reconstructed fundamental functions is introduced to solve the boundary problems of Poisson equations in the symmetrical region.With the help of these reconstructed functions,the amount of inputting data and linear equations are only the half or quarter of those which uses the original fundamental functions.MFS with reconstructed fundamental functions has the merits of less computing time,high accuracy and simple programming.The numerical examples show that the results of MFS are coincident with the analytical solutions.