A stochastic collocation method based on sparse grids for a stochastic Stokes-Darcy model
A stochastic collocation method based on sparse grids for a stochastic Stokes-Darcy model
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DOI：
10.3934/dcdss.2021104
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
Zhipeng Yang;Xuejian Li;Xiaoming He;J. Ming
中科院分区：
文献类型：
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作者：
Zhipeng Yang;Xuejian Li;Xiaoming He;J. Ming
本文提出了一种稀疏网格随机配点法，以提高求解具有随机渗透系数的Stokes-Darcy模型的计算效率。为了表示随机水力传导率，使用截断的Karhunen-Loève展开。对于概率空间中的离散形式，采用随机配点法，然后采用稀疏网格法提高计算效率。对于配置点处的非耦合确定性子问题，我们采用一般耦合有限元方法。数值实验结果表明，该方法具有样本容量小、收敛性好、随机性通过界面传递等特点。
In this paper, we develop a sparse grid stochastic collocation method to improve the computational efficiency in handling the steady Stokes-Darcy model with random hydraulic conductivity. To represent the random hydraulic conductivity, the truncated Karhunen-Loève expansion is used. For the discrete form in probability space, we adopt the stochastic collocation method and then use the Smolyak sparse grid method to improve the efficiency. For the uncoupled deterministic subproblems at collocation nodes, we apply the general coupled finite element method. Numerical experiment results are presented to illustrate the features of this method, such as the sample size, convergence, and randomness transmission through the interface.