A Flexible Uncertainty Propagation Framework for General Multiphysics Systems

Abstract

We present an efficient “module-based” uncertainty propagation framework for stochastic multiphysics systems. Our proposed framework facilitates modeling flexibility and independence within each module of a stochastic multiphysics solver, and extends the framework, previously introduced by the authors, to general (nonlinear) multiphysics systems via generic restriction and prolongation operators, which transform between the global and local polynomial chaos representations of the input/output data. Moreover, these operators preserve the convergence rate of monolithic generalized-polynomial-chaos--based methods, and lower the rate of growth of the overall computational costs w.r.t. the global dimension. Following a discussion of these mathematical and algorithmic details, we implement our framework on a test problem, and demonstrate its superior computational performance over an implementation of the standard monolithic framework. (An erratum is attached.)