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

Additional Metadata
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
Citation
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