A directed Monte Carlo solution of linear stochastic algebraic system of equations

A directed Monte Carlo solution of linear stochastic algebraic system of equations: "Publication year: 2010
Source: Finite Elements in Analysis and Design, In Press, Corrected Proof, Available online 12 February 2010
Y.T., Feng , C.F., Li , D.R.J., Owen
This paper proposes a modified Monte Carlo simulation method for the solution of a linear stochastic algebraic system of equations arising from the stochastic finite element modelling of linear elastic problems. The basic idea is to direct Monte Carlo samples along straight lines and then utilise their spatial proximity or order to provide high quality initial approximations in order to significantly accelerate the convergence of iterative solvers at each sample. The method, termed the directed Monte Carlo (DMC) simulation, is developed first for one random variable using the preconditioned conjugate gradient equipped with an initial approximation prediction scheme, and then..."