Ajith, Gopika and Ghosh, Debraj (2022) A FETI-DP-BASED PARALLEL ALGORITHM FOR SOLVING HIGH DIMENSIONAL STOCHASTIC PDES USING COLLOCATION. In: International Journal for Uncertainty Quantification, 12 (3). pp. 1-15. ISSN 2152-5080
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Numerical solution of stochastic partial differential equations often faces the challenge of large dimensionality due to discretization of the equation, random field coefficients, and the source term. Recently, domain decomposition (DD) methods have been successful in reducing the computational complexity and achieving parallelization for such problems. This improvement is due to reduction in the number of random variables, and inherent parallelizability of DD methods. However, in order to make this approach more amenable to easier parallel implementation, an efficient non-intrusive method is necessary. With this goal, a stochastic collocation method−based formulation is proposed here in the finite element tearing and interconnecting−dual primal (FETI-DP) framework. This nonintrusive formulation uses the collocation method at both subdomain and interface levels of FETI-DP. Finally, at the postprocessing stage, realizations of subdomain solutions are computed by sampling from the true distribution. From an implementation viewpoint, this method has two advantages: (1) existing mechanics solvers can be reused with minimal modification, and (2) it is independent of the probability distribution of the input random variables. Numerical studies suggest a significant improvement in speed-up compared to the current literature and scalable parallel performance.
| Item Type: | Journal Article |
|---|---|
| Publication: | International Journal for Uncertainty Quantification |
| Publisher: | Begell House Inc. |
| Additional Information: | The copyright of this article belongs to the Begell House Inc. |
| Keywords: | domain decomposition; FETI-DP; Nonintrusive; paral-lelization; stochastic collocation method |
| Department/Centre: | Division of Mechanical Sciences > Civil Engineering |
| Date Deposited: | 25 May 2022 04:33 |
| Last Modified: | 25 May 2022 04:33 |
| URI: | https://eprints.iisc.ac.in/id/eprint/72380 |
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