This report describes a stochastic collocation method to adequately handle a physically intrinsic uncertainty in the variables of a numerical simulation. For instance, while the standard Galerkin approach to Polynomial Chaos requires multi-dimensional summations over the stochastic basis functions, the stochastic collocation method enables to collapse those summations to a one-dimensional summation only. This report furnishes the essential algorithmic details of the new stochastic collocation method and provides as a numerical example the solution of the Riemann problem with the stochastic collocation method used for the discretization of the stochastic parameters. Mathelin, Lionel and Hussaini, M. Yousuff and Zang, Thomas A. (Technical Monitor) Langley Research Center NASA/CR-2003-212153, NAS 1.26:212153
A Stochastic Collocation Algorithm for Uncertainty Analysis
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