A high-performance calculation scheme for stochastic dynamic problems

The goal of stochastic dynamic problems is to efficiently and accurately calculate statistical moments and random dynamic responses. Thus, a high-performance calculation scheme is proposed to achieve the goal. First, to enhance the accuracy of the statistical moments, we proposed an adaptive weights quasi-Monte Carlo (AWQMC) method. Compared to the integration weights of the traditional quasi-Monte Carlo method, the adaptive weights can better reflect the discrepancy of the sample points to obtain more accurate statistical moments. Additionally, the adaptive weights only depend on the sample set, which can be applied to other stochastic problems. Second, the reduced-order model technology is introduced to improve the calculation efficiency of random dynamic responses. Combining of the Galerkin method, a novel reduced-order model based on deterministic reduced bases is proposed for random dynamic system. Then, an efficient dynamic equation solver is constructed based on the deterministic reduced bases and the Newmark method. Finally, according to the three numerical examples, the high-performance calculation scheme combined the AWQMC method and the efficient dynamic equation solver can significantly improve the accuracy and efficiency of statistical moments for stochastic dynamic problems.