OPTIMAL DISCRETIZATION OF RANDOM-FIELDS

A new method for efficient discretization of random fields (i.e., thei r representation in terms of random variables) is introduced. The effi ciency of the discretization is measured by the number of random varia bles required to represent the field with a specified level of accurac y. The method is based on principles of optimal linear estimation theo ry. It represents the field as a linear function of nodal random varia bles and a set of shape functions, which are determined by minimizing an error variance. Further efficiency is achieved by spectral decompos ition of the nodal covariance matrix. The new method is found to be mo re efficient than other existing discretization methods, and more prac tical than a series expansion method employing the Karhunen-Loeve theo rem. The method is particularly useful for stochastic finite element s tudies involving random media, where there is a need to reduce the num ber of random variables so that the amount of required computations ca n be reduced.