A Stochastic Collocation Algorithm for Uncertainty Analysis

Lionel Mathelin · M. Yousuff Hussaini

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Probabilistic and Robust Engineering Design Mathematical functions and polynomials Model Reduction and Neural Networks

Abstract

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.

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References

1991Stochastic Finite Elements: A Spectral Approach 2002The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations 2003Modeling uncertainty in flow simulations via generalized polynomial chaos 2001Stochastic Modeling of Flow-Structure Interactions Using Generalized Polynomial Chaos

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