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Simplex Elements Stochastic Collocation in Higher-Dimensional Probability Spaces

Jeroen A. S. Witteveen · Gianluca Iaccarino

18 citations0/0 files storedAIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference (SDM)

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Probabilistic and Robust Engineering Design Mathematical Approximation and Integration Gaussian Processes and Bayesian Inference

Abstract

A Simplex Elements Stochastic Collocation (SESC) method is introduced for robust and efficient propagation of uncertainty through computational models. The presented non– intrusive Uncertainty Quantification (UQ) method is based on adaptive grid refinement of a simplex elements discretization in probability space. The approach is equally robust as Monte Carlo (MC) simulation in terms of the Extremum Diminishing (ED) robustness concept. The efficiency of SESC is based on high degree polynomial interpolation, randomized refinement sampling, and Essentially Extremum Diminishing (EED) extrapolation. This results in a superlinear convergence rate and a linear increase of the initial number of samples with dimensionality. The flexibility of simplex elements is further employed to discretize non–hypercube probability spaces with correlated random parameters.

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References

1991Stochastic Finite Elements: A Spectral Approach 2002The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations 2005High-Order Collocation Methods for Differential Equations with Random Inputs 2007A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data 2008A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data 2008Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics 2009Fast Numerical Methods for Stochastic Computations: A Review 2006Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures

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