This paper develops a Smolyak-type sparse-grid stochastic collocation method (SGSCM) for uncertainty
quantification of nonlinear stochastic dynamic equations. The solution obtained by the method is a linear
combination of tensor product formulas for multivariate polynomial interpolation. By choosing the collocation
point sets to coincide with cubature point sets of quadrature rules, we derive quadrature formulas to estimate
the expectations of the solution. The method does not suffer from the curse of dimensionality in the sense that
the computational cost does not increase exponentially with the number of input random variables. Numerical
analysis of a nonlinear elastic oscillator subjected to a discretized band-limited white noise process demonstrates
the computational efficiency and accuracy of the developed method.
SHI Hong-Qin1 (石红芹), HE Jun2* (何 军)
. Smolyak Type Sparse Grid Collocation Method for Uncertainty Quantification of Nonlinear Stochastic Dynamic Equations[J]. Journal of Shanghai Jiaotong University(Science), 2015
, 20(5)
: 612
-617
.
DOI: 10.1007/s12204-015-1621-z
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