Reference : Dimension reduction in stochastic modeling of coupled problems
Scientific journals : Article
Engineering, computing & technology : Mechanical engineering
Dimension reduction in stochastic modeling of coupled problems
Arnst, Maarten mailto [Université de Liège - ULg > Département d'aérospatiale et mécanique > Computational and stochastic modeling >]
Ghanem, Roger mailto [University of Southern California > Department of Civil and Environmental Engineering > > >]
Phipps, Eric mailto [Sandia National Laboratories > > > >]
Red-Horse, John mailto [Sandia National Laboratories > > > >]
International Journal for Numerical Methods in Engineering
[en] uncertainty quantification ; coupled problems ; multiphysics ; polynomial chaos
[en] Coupled problems with various combinations of multiple physics, scales, and domains are found in numerous areas of science and engineering. A key challenge in the formulation and implementation of corresponding coupled numerical models is to facilitate the communication of information across physics, scale, and domain interfaces, as well as between the iterations of solvers used for response computations. In a probabilistic context, any information that is to be communicated between subproblems or iterations should be characterized by an appropriate probabilistic representation. Although the number of sources of uncertainty can be expected to be large in most coupled problems, our contention is that exchanged probabilistic information
often resides in a considerably lower dimensional space than the sources themselves. This work thus presents an investigation into the characterization of the exchanged information by a reduced-dimensional representation and in particular by an adaptation of the Karhunen-Loève decomposition. The effectiveness of the proposed dimension–reduction methodology is analyzed and demonstrated through a multiphysics problem relevant to nuclear engineering.

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