Stochastic finite elements: a spectral approach
Stochastic finite elements: a spectral approach
The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
SIAM Journal on Scientific Computing
Uncertainty propagation using Wiener-Haar expansions
Journal of Computational Physics
Multi-resolution analysis of wiener-type uncertainty propagation schemes
Journal of Computational Physics
An adaptive multi-element generalized polynomial chaos method for stochastic differential equations
Journal of Computational Physics
Mesh deformation based on radial basis function interpolation
Computers and Structures
A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data
SIAM Journal on Numerical Analysis
Journal of Computational Physics
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An adaptive stochastic finite elements approach for unsteady problems is developed. Time-dependent solutions of dynamical systems are known to be sensitive to small input variations. Stochastic finite elements methods usually require a fast increasing number of elements with time to capture the effect of random input parameters in these unsteady problems. The resulting large number of samples required for resolving the asymptotic stochastic behavior, results for computationally intensive fluid-structure interaction simulations in impractically high computational costs. The unsteady adaptive stochastic finite elements (UASFE) formulation proposed in this paper maintains a constant interpolation accuracy in time with a constant number of samples. The approach is based on a time-independent parametrization of the sampled time series in terms of frequency, phase, amplitude, reference value, damping, and higher-period shape function. This parametrization is interpolated using a robust adaptive stochastic finite elements method based on Newton-Cotes quadrature in simplex elements. The effectiveness of the UASFE approach is illustrated by applications to a mass-spring-damper system, the Duffing equation, and a rigid-airfoil fluid-structure interaction problem with multiple random input parameters. The results are verified by comparison to those of Monte Carlo simulations.