Open Access
Efficient uncertainty quantification using a two-step approach with chaos collocation
Alex Loeven,J.A.S. Witteveen,H. Bijl +2 more
- 06 Sep 2006
TL;DR: In this article, a two-step approach with Chaos Collocation for efficient uncertainty quantification in computational fluid-structure interactions is followed, where a Sensitivity Analysis is used to efficiently narrow the problem down from multiple uncertain parameters to one parameter which has the largest influence on the solution.
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Abstract: In this paper a Two Step approach with Chaos Collocation for efficient uncertainty quantification in computational fluid-structure interactions is followed. In Step I, a Sensitivity Analysis is used to efficiently narrow the problem down from multiple uncertain parameters to one parameter which has the largest influence on the solution. In Step II, for this most important parameter the Chaos Collocation method is employed to obtain the stochastic response of the solution. The Chaos Collocation method is presented in this paper, since a previous study showed that no efficient method was available for arbitrary probability distributions. The Chaos Collocation method is compared on efficiency with Monte Carlo simulation, the Polynomial Chaos method, and the Stochastic Collocation method. The Chaos Collocation method is non-intrusive and shows exponential convergence with respect to the polynomial order for arbitrary parameter distributions. Finally, the efficiency of the Two Step approach with Chaos Collocation is demonstrated for the linear piston problem with an unsteady boundary condition. A speed-up of a factor of 100 is obtained compared to a full uncertainty analysis for all parameters.
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Citations
Partitioned Fluid-Structure Interaction on Massively Parallel Systems
Benjamin Uekermann
- 01 Jan 2016
TL;DR: This thesis introduces parallelized on two levels into preCICE without compromising its flexibility: parallelization on an intra-solver level by avoiding central coupling instances and parallelization in an inter-solve level by novel parallel quasi-Newton coupling schemes.
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Probabilistic collocation used in a Two-Step approached for efficient uncertainty quantification in computational fluid dynamics
G. J. A. Loeven,Hester Bijl +1 more
TL;DR: In this paper, a two-step approach is presented for uncertainty quantification for expensive problems with multiple uncertain parameters, where the first step consists of a sensitivity analysis to identify the most important parameters of the problem.
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Prediction of geometric uncertainty effects on Fluid Dynamics by Polynomial Chaos and Fictitious Domain method
TL;DR: The main advantage of the Tensorial-expanded Chaos Collocation method is its non-intrusive formulation, so existing deterministic solvers can be used, and a Least-Squares Spectral Element Method has been employed for the analysis of the deterministic differential problems obtained by Tensorial/Chaos Collocation.
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Fictitious Domain with Least-Squares Spectral Element Method to Explore Geometric Uncertainties by Non-Intrusive Polynomial Chaos Method
TL;DR: The Non-Intrusive Polynomial Chaos Method coupled to a Fictitious Domain approach has been applied to one and twodimensional elliptic problems with geometric uncertainties, in order to demonstrate the accuracy and convergence of the methodology.
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