### 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.

Original language | English |
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Title of host publication | Progress in Industrial Mathematics at ECMI 2012 |

Editors | M. Fontes, M. Günther, N. Marheineke |

Place of Publication | Cham |

Publisher | Springer |

Pages | 361-370 |

ISBN (Print) | 978-3-319-05364-6 |

DOIs | |

Publication status | Published - 2014 |

Event | 17th European Conference on Mathematics for Industry (ECMI 2012), July 23-27, 2012, Lund, Sweden - Lund, Sweden Duration: 23 Jul 2012 → 27 Jul 2012 http://www.maths.lth.se/ecmi/ecmi2012_org/ |

### Publication series

Name | Mathematics in Industry |
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Volume | 19 |

ISSN (Print) | 1612-3956 |

### Conference

Conference | 17th European Conference on Mathematics for Industry (ECMI 2012), July 23-27, 2012, Lund, Sweden |
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Abbreviated title | ECMI 2012 |

Country | Sweden |

City | Lund |

Period | 23/07/12 → 27/07/12 |

Internet address |

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## Cite this

Maten, ter, E. J. W., Pulch, R., Schilders, W. H. A., & Janssen, H. H. J. M. (2014). Efficient calculation of uncertainty quantification. In M. Fontes, M. Günther, & N. Marheineke (Eds.),

*Progress in Industrial Mathematics at ECMI 2012*(pp. 361-370). (Mathematics in Industry; Vol. 19). Springer. https://doi.org/10.1007/978-3-319-05365-3_50