Exploiting the recently proposed domain decomposition solvers for Stochastic Partial Differential Equations (SPDEs) (Sarkar, Benabbou, & Ghanem 2009, Subber & Sarkar 2010a, Subber & Sarkar 2010b, Subber & Sarkar 2011, Subber & Sarkar 2012b, Subber & Sarkar 2012a), a parallel filtering algorithm is developed by the authors (Khalil, Subber, & Sarkar 2013) based on the Polynomial Chaos Kalman Filter (PCKF) of Saad and Ghanem (Saad & Ghanem 2009). In the intrusive spectral stochastic finite element based domain decomposition formalism, the update/analysis step of PCK performs subdomain level (local) computations using the spatially decomposed state vector leading to a scalable parallel algorithm and its efficient implementation using the Message Passing Interface (MPI) (MPI 2009). In this paper, we demonstrate the usefulness of the parallel PCKF update step using a stochastic Poisson's equation having non-Gaussian coefficients.

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Conference 11th International Conference on Structural Safety and Reliability, ICOSSAR 2013
Citation
Khalil, M. (M.), Subber, W. (W.), & Sarkar, A. (2013). Parallel data assimilation for high dimensional state space models. In Safety, Reliability, Risk and Life-Cycle Performance of Structures and Infrastructures - Proceedings of the 11th International Conference on Structural Safety and Reliability, ICOSSAR 2013 (pp. 829–831).