A domain decomposition method of stochastic PDEs: An iterative solution techniques using a two-level scalable preconditioner
نویسندگان
چکیده
Recent advances in high performance computing systems and sensing technologies motivate computational simulations with extremely high resolution models with capabilities to quantify uncertainties for credible numerical predictions. A two-level domain decomposition method is reported in this investigation to devise a linear solver for the large-scale system in the Galerkin spectral stochastic finite element method (SSFEM). In particular, a two-level scalable preconditioner is introduced in order to iteratively solve the largescale linear system in the intrusive SSFEM using an iterative substructuring based domain decomposition solver. The implementation of the algorithm involves solving a local problem on each subdomain that constructs the local part of the preconditioner and a coarse problem that propagates information globally among the subdomains. The numerical and parallel scalabilities of ∗Corresponding author Email addresses: [email protected] (Waad Subber), [email protected] (Abhijit Sarkar) The preliminary version of the paper is published in the proceeding of HPCS 2011 conference [1] Preprint submitted to Journal of Computational Physics August 3, 2013 the two-level preconditioner are contrasted with the previously developed one-level preconditioner for two-dimensional flow through porous media and elasticity problems with spatially varying non-Gaussian material properties. A distributed implementation of the parallel algorithm is carried out using MPI and PETSc parallel libraries. The scalabilities of the algorithm are investigated in a Linux cluster.
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ورودعنوان ژورنال:
- J. Comput. Physics
دوره 257 شماره
صفحات -
تاریخ انتشار 2014