为了考核随机过程数值仿真中采用的混沌多项式展开，小波动态自适应网格等的可靠性和近似程度，本文构造了一个具有解析解的随机过程，随后进行数值仿真。比较了数值仿真结果与解析解，证明两者是相互一致的。说明所采用的数值仿真方法是成立和近似度是可以接受的。所进行比较的随机过程解析解是相对比较简单的，当对更复杂的情况需要进一步数值实验验证。在文中并讨论了影响数值仿真精度和增加数值仿真工作难度的因素。
In order to evaluate the accuracy of the numerical simulations for the stochastic process using chaos expansion and the dynamically adaptive wavelet approach, a stochastic process with analytical solution has been constructed. Numerical experiment is performed and in good agreement with the analytical solution. This thus validates the numerical approach and demonstrates its acceptable accuracy. The factors effecting on the accuracy in the numerical simulations and the required computational expenses are also discussed in the paper.
参考文献
| [1] | Ren, X.;Wu, W.;Xanthis, L.S. .A dynamically adaptive wavelet approach to stochastic computations based on polynomial chaos - capturing all scales of random modes on independent grids[J].Journal of Computational Physics,2011(19):7332-7346. |
| [2] | 吴文权,任孝安.随机对流扩散方程的数值仿真[J].工程热物理学报,2011(11):1833-1837. |
| [3] | 任孝安,吴文权.随机过程动态自适应小波独立网格多尺度模拟[J].工程热物理学报,2012(02):222-227. |
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