Embedded Uncertainty Quantification Methods via Stokhos

Eric T. Phipps () and Andrew G. Salinger ()
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Eric T. Phipps: Center for Computing Research, Sandia National Laboratories
Andrew G. Salinger: Center for Computing Research, Sandia National Laboratories

Chapter 52 in Handbook of Uncertainty Quantification, 2017, pp 1765-1806 from Springer

Abstract: Abstract Stokhos (Phipps, Stokhos embedded uncertainty quantification methods. http://trilinos.org/packages/stokhos/ , 2015) is a package within Trilinos (Heroux et al., ACM Trans Math Softw 31(3), 2005; Michael et al., Sci Program 20(2):83–88, 2012) that enables embedded or intrusive uncertainty quantification capabilities to C++ codes. It provides tools for implementing stochastic Galerkin methods Stochastic Galerkin methods and embedded sample propagation through the use of template-based generic programming (Pawlowski et al., Sci Program 20:197–219, 2012; Roger et al., Sci Program 20:327–345, 2012) which allows deterministic simulation codes to be easily modified for embedded uncertainty quantification. It provides tools for forming and solving the resulting linear and nonlinear equations these methods generate, leveraging the large-scale linear and nonlinear solver capabilities provided by Trilinos. Furthermore, Stokhos is integrated with the emerging many-core architecture capabilities provided by the Kokkos (Edwards et al., Sci Program 20(2):89–114, 2012; Edwards et al., J Parallel Distrib Comput 74(12):3202–3216, 2014) and Tpetra packages (Baker and Heroux, Sci Program 20(2):115–128, 2012; Hoemmen et al., Tpetra: next-generation distributed linear algebra. http://trilinos.org/packages/tpetra , 2015) within Trilinos, allowing these embedded uncertainty quantification capabilities to be applied in both shared and distributed memory parallel computational environments. Finally, the Stokhos tools have been incorporated into the Albany simulation code (Pawlowski et al., Sci Program 20:327–345, 2012; Salinger et al., Albany multiphysics simulation code. https://github.com/gahansen/Albany , 2015) enabling embedded uncertainty quantification of a wide variety of large-scale PDE-based simulations.

Keywords: Stochastic Galerkin methods; Embedded sampling methods; Polynomial chaos; Sparse grids; C++ templates; Operator overloading; Linear solvers; Preconditioning; Parallel programming; Shared memory parallelism; Distributed memory parallelism; Fine-grained parallelism; Multicore architectures (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/978-3-319-12385-1_55

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