  This work is concerned with the propagation of uncertainty across coupled
domain problems with high-dimensional random inputs. A stochastic model
reduction approach based on low-rank separated representations is proposed for
the partitioned treatment of the uncertainty space. The construction of the
coupled domain solution is achieved though a sequence of approximations with
respect to the dimensionality of the random inputs associated with each
individual sub-domain and not the combined dimensionality, hence drastically
reducing the overall computational cost. The coupling between the sub-domain
solutions is done via the classical Finite Element Tearing and Interconnecting
(FETI) method, thus providing a well suited framework for parallel computing.
Two high-dimensional stochastic problems, a 2D elliptic PDE with random
diffusion coefficient and a stochastic linear elasticity problem, have been
considered to study the performance and accuracy of the proposed stochastic
coupling approach.
