Partitioned treatment of uncertainty in coupled domain problems: A separated representation approach

TL;DR

This paper introduces a low-rank separated representation method for efficiently propagating uncertainty in coupled domain problems with high-dimensional random inputs, reducing computational costs and enabling parallel computation.

Contribution

It proposes a novel stochastic model reduction approach based on separated representations for coupled problems, improving efficiency by focusing on individual sub-domain uncertainties.

Findings

Effective in reducing computational cost for high-dimensional problems

Maintains accuracy in coupled stochastic PDE solutions

Suitable for parallel computing frameworks

Abstract

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.