Neumann随机有限元的一种推广形式

针对Monte—Carlo随机有限元，研究在多样本环境下如何提高单样本计算效率的问题。证明了关于线性问题Neumann随机有限元法的算法与线性系统的等刚度迭代法是一致的；在此基础上，将迭代效率更高的算法一预处理共轭梯度法引入线性Monte—Carlo随机有限元系统，建立了相应的有限元列式；最后，利用两个算例比较了本方法与Neumann随机有限元法，结果显示随着随机变量离散度的增大，Neumann法的计算效率急剧下降，而本方法的计算效率表现稳定；对于离散度不太大的随机变量，Neumann法已经不收敛，而本方法在随机变量离散度很大的情况下，仍然保持很好的收敛性。

A extended form of neumann stochastic finite element method

In the field of Monte-Carlo Stochastic FEM,study how to improve the efficiency of solving single sample on the multi-samples condition.Proved the equivalence between the Neumann Stochastic FEM and the equal-stiffness iteration method on the algorithm.On this basis,a more efficient algorithm,pre-conditioning conjugate method,is introduced into linear Monte-Carlo stochastic FEM and the corresponding FEM program is established.Two examples are used to illustrate the two methods.Results show that the efficiency of the new method is more stable than Neumann Stochastic FEM as the dispersancy of random variable increase.Neumann Stochastic FEM diverges althogh the dispersancy of random variable isn't large,on the contrary,the new method still converge when the dispersancy is quite large.