Ghosh, Debraj and Avery, Philip and Farhat, Charbel (2009) An FETI-preconditioned conjuerate gradient method for large-scale stochastic finite element problems. In: International Journal for Numerical Methods in Engineering, 80 (6-7, Sp. Iss. SI). pp. 914-931.
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In the spectral stochastic finite element method for analyzing an uncertain system. the uncertainty is represented by a set of random variables, and a quantity of Interest such as the system response is considered as a function of these random variables Consequently, the underlying Galerkin projection yields a block system of deterministic equations where the blocks are sparse but coupled. The solution of this algebraic system of equations becomes rapidly challenging when the size of the physical system and/or the level of uncertainty is increased This paper addresses this challenge by presenting a preconditioned conjugate gradient method for such block systems where the preconditioning step is based on the dual-primal finite element tearing and interconnecting method equipped with a Krylov subspace reusage technique for accelerating the iterative solution of systems with multiple and repeated right-hand sides. Preliminary performance results on a Linux Cluster suggest that the proposed Solution method is numerically scalable and demonstrate its potential for making the uncertainty quantification Of realistic systems tractable.
|Item Type:||Journal Article|
|Additional Information:||Copyright for this article belongs to John Wiley and Sons.|
|Keywords:||domain decomposition, FETI, polynomial chaos; stochastic finite element, uncertainty|
|Department/Centre:||Division of Mechanical Sciences > Civil Engineering|
|Date Deposited:||01 Dec 2009 05:52|
|Last Modified:||19 Sep 2010 05:52|
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