Non-Gaussian positive-definite matrix-valued random fields for elliptic stochastic partial differential operators

This paper deals with the construction of a class of non-Gaussian positive-definite matrix-valued random fields whose mathematical properties allow elliptic stochastic partial differential operators to be modeled. The properties of this class is studied in details and the numerical procedure for constructing numerical realizations of the trajectories is explicitly given. Such a matrix-valued random field can directly be used for modeling random uncertainties in computational sciences with a stochastic model having a small number of parameters. The class of random fields which can be approximated is presented and their experimental identification is analyzed. An example is given in three-dimensional linear elasticity for which the fourth-order elasticity tensor-valued random field is constructed for a random non-homogeneous anisotropic elastic material.