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A multiresolution adaptive grid method for solving the generalized probability density equation in stochastic dynamic analysis

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Abstract

The development of the generalized probability density evolution equation (GDEE) provides a new direction for analyzing stochastic dynamical systems. In particular, it offers an effective solution for nonlinear problems. In this paper, a multiresolution adaptive grid method (MAGM) is proposed for the numerical solution of the GDEE. In this method, the size of multiresolution adaptive grids, which are constructed based on the second-generation wavelet transform, can be dynamically adjusted according to the change of the probability density function (PDF). Besides, the MAGM, which combines the spatial discretization scheme WENO-Z and the temporal discretization scheme third-order TVD Runge–Kutta, ensures the accuracy of the PDF. The method's advantages and accuracy are verified by analyzing a single-degree-of-freedom system, a two-dimensional frame structure, and a three-dimensional frame structure. The adaptive grids can capture the local singularity of PDF and provide more details for local mutation areas. Moreover, the algorithm configures fewer grid points in the region with high regularity to speed up the calculation efficiency.

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Acknowledgements

The research is financially supported by the National Natural Science Foundation of China (Grant No. 51878274).

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Authors and Affiliations

  1. School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi’an, 710072, China

    Tianlong Wang & Xun’an Zhang

  2. College of Civil Engineering, Huaqiao University, Xiamen, 361021, China

    Shixuan Yang

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  1. Tianlong Wang
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  2. Xun’an Zhang
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Correspondence to Xun’an Zhang.

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Wang, T., Zhang, X. & Yang, S. A multiresolution adaptive grid method for solving the generalized probability density equation in stochastic dynamic analysis. Acta Mech 233, 1911–1940 (2022). https://doi.org/10.1007/s00707-022-03183-w

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  • DOI: https://doi.org/10.1007/s00707-022-03183-w

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