Monte Carlo-type simulation for solving stochastic ordinary differential equations
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Acceleration of uncertainty propagation through Lagrange multipliers in partitioned stochastic method
2020, Computer Methods in Applied Mechanics and EngineeringCitation Excerpt :In particular, the parametric uncertainties (or statistical variations) are widely studied for design dimensions, material properties, boundary conditions, external loads, etc. In early days, existing statistical analysis methods such as Monte-Carlo methods [9–12], perturbation methods [13], spectral methods [14–16], (e.g. the Karhunen–Loéve expansion (KLE) [13], and the generalized Polynomial Chaos Expansion (gPCE) [17–31]) have been applied to uncertainty quantification. In one of the other tracts, namely in the structural mechanics community, various stochastic finite element methods (SFEMs) [32,33] have been developed to address model uncertainties as a natural extension of the deterministic FEM.
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2007, Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis
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