For efficient numerical solution of stochastic partial differential equations (SPDEs) having random operators, a number of non-overlapping domain decomposition algorithms are formulated using the polynomial chaos expansion (PCE) (Sarkar, Benabbou, & Ghanem 2009, Subber & Sarkar 2010a, Subber & Sarkar 2010b, Subber & Sarkar 2011, Subber & Sarkar 2012b, Subber & Sarkar 2012a, Subber 2012, Subber & Sarkar 2013). The computational framework is based on the intrusive spectral stochastic finite element method (Ghanem & Spanos 1991, Ghanem & Spanos 1990, Ghanem, Saad, & Doostan 2007, Ghanem & Kruger 1996, Ghanem & Doostan 2006, Maitre & Knio 2010, Maitre, Knio, Debusschere, Najm, & Ghanem 2003, Eiermann & Ernst 2007). These domain decomposition solvers effectively exploit supercomputers in order to tackle the large-scale linear system when (1) the finite element mesh resolution is high and (2) the number of random systems parameters are large.The efficiency of some of these domain decomposition algorithms is primarily governed by the coarse grid used to construct a two-level parallel preconditioner for the preconditioned conjugate gradient method (PCGM) for the iterative solution of the linear system (e.g. Subber & Sarkar 2010a, Subber & Sarkar 2010b, Subber & Sarkar 2011, Subber & Sarkar 2012b, Subber & Sarkar 2012a, Subber 2012, Subber & Sarkar 2013). In this paper, we study the performance of a stochastic version of a primal two-level domain decomposition preconditioner (Subber & Sarkar 2010b, Subber & Sarkar 2011) through an application involving the stochastic seepage under a dam, implemented using MPI (MPI 2009) and PETSc (Balay, Buschelman, Gropp, Kaushik, Knepley, McInnes, Smith, & Zhang 2009) parallel libraries and METIS (Karypis & Kumar 1995) graph partitioning software.

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Conference 11th International Conference on Structural Safety and Reliability, ICOSSAR 2013
Citation
Subber, W. (W.), & Sarkar, A. (2013). Scalable two-level domain decomposition algorithm for stochastic systems. 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. 867–869).