We present a novel theoretical framework for the domain decomposition of uncertain systems defined by stochastic partial differential equations. The methodology involves a domain decomposition method in the geometric space and a functional decomposition in the probabilistic space. The probabilistic decomposition is based on a version of stochastic finite elements based on orthogonal decompositions and projections of stochastic processes. The spatial decomposition is achieved through a Schur-complement-based domain decomposition. The methodology aims to exploit the full potential of high-performance computing platforms by reducing discretization errors with high-resolution numerical model in conjunction to giving due regards to uncertainty in the system. The mathematical formulation is numerically validated with an example of waves in random media. Copyright

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Keywords Domain decomposition, Polynomial chaos, Random media, Schur complement method, Stochastic finite element
Persistent URL dx.doi.org/10.1002/nme.2431
Journal International Journal for Numerical Methods in Engineering
Sarkar, A, Benabbou, N. (Nabil), & Ghanem, R. (Roger). (2009). Domain decomposition of stochastic PDEs: Theoretical formulations. International Journal for Numerical Methods in Engineering, 77(5), 689–701. doi:10.1002/nme.2431