Abstract
We consider Uncertainty Quantification (UQ) by expanding the solution in so-called generalized Polynomial Chaos expansions. In these expansions the solution is decomposed into a series with orthogonal polynomials in which the parameter dependency becomes an argument of the orthogonal polynomial basis functions. The time and space dependency remains in the coefficients. In UQ two main approaches are in use: Stochastic Collocation (SC) and Stochastic Galerkin (SG). Practice shows that in many cases SC is more efficient for similar accuracy as obtained by SG. In SC the coefficients in the expansion are approximated by quadrature and thus lead to a large series of deterministic simulations for several parameters. We consider strategies to efficiently perform this sequence of deterministic simulations within SC.
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Acknowledgements
The first and last author did part of the work within the project ARTEMOS (Ref. 270683-2), http://www.artmeos.eu/ (ENIAC Joint Undertaking).
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Maten, E.J.W.t., Pulch, R., Schilders, W.H.A., Janssen, H.H.J.M. (2014). Efficient Calculation of Uncertainty Quantification. In: Fontes, M., Günther, M., Marheineke, N. (eds) Progress in Industrial Mathematics at ECMI 2012. Mathematics in Industry(), vol 19. Springer, Cham. https://doi.org/10.1007/978-3-319-05365-3_50
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DOI: https://doi.org/10.1007/978-3-319-05365-3_50
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