Article2016

Probabilistic collocation method for strongly nonlinear problems: 3. Transform by time

37 citations0/0 files storedWater Resources Research

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Probabilistic and Robust Engineering Design Hydrology and Watershed Management Studies Groundwater flow and contamination studies

Abstract

Abstract The probabilistic collocation method (PCM) has drawn wide attention for stochastic analysis recently. Its results may become inaccurate in case of a strongly nonlinear relation between random parameters and model responses. To tackle this problem, we proposed a location‐based transformed PCM (xTPCM) and a displacement‐based transformed PCM (dTPCM) in previous parts of this series. Making use of the transform between response and space, the above two methods, however, have certain limitations. In this study, we introduce a time‐based transformed PCM (tTPCM) employing the transform between response and time. We conduct numerical experiments to investigate its performance in uncertainty quantification. The results show that the tTPCM greatly improves the accuracy of the traditional PCM in a cost‐effective manner and is more general and convenient than the xTPCM/dTPCM.

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References

1991Stochastic Finite Elements: A Spectral Approach 2005High-Order Collocation Methods for Differential Equations with Random Inputs 2007A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data 2010Numerical Methods for Stochastic Computations: A Spectral Method Approach 2010Spectral Methods for Uncertainty Quantification 2008Polynomial chaos expansion for sensitivity analysis 2005An adaptive multi-element generalized polynomial chaos method for stochastic differential equations 2010Spectral methods for uncertainty quantification : with applications to computational fluid dynamics

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