Article2011

A nonintrusive stochastic multiscale solver

44 citations0/0 files storedInternational Journal for Numerical Methods in Engineering

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Probabilistic and Robust Engineering Design Model Reduction and Neural Networks Advanced Mathematical Modeling in Engineering

Abstract

Abstract In this paper, we describe a practical nonintrusive multiscale solver that permits consideration of uncertainties in heterogeneous materials without exhausting the available computational resources. The computational complexity of analyzing heterogeneous material systems is governed by the physical and probability spaces at multiple scales. To deal with these large spaces, we employ reduced order homogenization approach in combination with the Karhunen–Loeve expansion and stochastic collocation method based on sparse grid. The resulting nonintrusive multiscale solver, which is aimed at providing practical solutions for complex multiscale stochastic problems, has been verified against the Latin Hypercube Monte–Carlo method. Copyright © 2011 John Wiley & Sons, Ltd.

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References

1991Stochastic Finite Elements: A Spectral Approach 2002The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations 2008A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data 1980Small sample sensitivity analysis techniques for computer models.with an application to risk assessment 2009An adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations 2007Sparse grid collocation schemes for stochastic natural convection problems 2009Recent Advances in Non-Intrusive Polynomial Chaos and Stochastic Collocation Methods for Uncertainty Analysis and Design 2009Comparison of Non-Intrusive Polynomial Chaos and Stochastic Collocation Methods for Uncertainty Quantification

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