A Monte-Carlo Stochastic FEM Based on Conjugate Gradients Method

An improved Monte-Carlo stochastic FEM based on polynomial preconditioners is established through introduction of the conjugate gradients method into the traditional Monte-Carlo stochastic FEM. In the improved FEM, a certain characteristic sample is obtained first; then, using it as a preconditioner, the other samples are solved by polynomial preconditioners for conjugate gradients method. A comparison between the improved Monte-Carlo stochastic FEM and the Neumann expansion-based Monte-Carlo stochastic FEM shows that the latter is a retrogression of the former, and that the former is more efficient in dealing with stochastic problems. Finally, a numerical example is given to illustrate the advantage of the new method proposed in this paper.