Probabilistic finite elements for nonlinear structural dynamics
Computer Methods in Applied Mechanics and Engineering
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
Projective Methods for Stiff Differential Equations: Problems with Gaps in Their Eigenvalue Spectrum
SIAM Journal on Scientific Computing
Telescopic projective methods for parabolic differential equations
Journal of Computational Physics
Coarse projective kMC integration: forward/reverse initial and boundary value problems
Journal of Computational Physics
Uncertainty propagation using Wiener-Haar expansions
Journal of Computational Physics
Multi-resolution analysis of wiener-type uncertainty propagation schemes
Journal of Computational Physics
Uncertainty quantification of limit-cycle oscillations
Journal of Computational Physics - Special issue: Uncertainty quantification in simulation science
Uncertainty propagation in dynamical systems
Automatica (Journal of IFAC)
Uncertainty quantification and apportionment in air quality models using the polynomial chaos method
Environmental Modelling & Software
Efficient uncertainty quantification with the polynomial chaos method for stiff systems
Mathematics and Computers in Simulation
Modelling and Simulation in Engineering
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Recently, interest has grown in developing efficient computational methods (both sampling and nonsampling) for studying ordinary or partial differential equations with random inputs. Stochastic Galerkin (SG) methods based on generalized polynomial chaos (gPC) representations have several appealing features. However, when the model equations are complicated, the numerical implementation of such algorithms can become highly nontrivial, and care is needed to design robust and efficient solvers for the resulting systems of equations. The authors' equation- and Galerkin-free computational approach to uncertainty quantification (UQ) for dynamical systems lets them conduct UQ computations without explicitly deriving the SG equations for the gPC coefficients. They use short bursts of appropriately initialized ensembles of simulations with the basic model to estimate the quantities required in SG algorithms.