Abstract
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.
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Foundation item: the Scientific Research Foundation of State Education Ministry for the Returned Overseas Scholars (No. 14Z102050011)
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Shi, HQ., He, J. Smolyak type sparse grid collocation method for uncertainty quantification of nonlinear stochastic dynamic equations. J. Shanghai Jiaotong Univ. (Sci.) 20, 612–617 (2015). https://doi.org/10.1007/s12204-015-1621-z
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DOI: https://doi.org/10.1007/s12204-015-1621-z