ABSTRACT In this work, we construct multigrid preconditioners to be used in the solution process of pathwise optimal control problems constrained by elliptic partial differential equations with random coefficients. We use a sparse-grid collocation method to discretize in the stochastic space and multigrid techniques in the physical space. Numerical results show that the proposed preconditioners lead to significant computational savings, with the number of preconditioned conjugate gradient iterations decreasing as the resolution in the physical space increases.

中文翻译：

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具有随机椭圆偏微分方程约束的最优控制问题的多重网格预处理器

摘要 在这项工作中，我们构建了多重网格预处理器，用于求解受具有随机系数的椭圆偏微分方程约束的路径最优控制问题。我们使用稀疏网格搭配方法在随机空间中离散化，在物理空间中使用多重网格技术。数值结果表明，所提出的预处理器可显着节省计算量，预处理共轭梯度迭代的次数随着物理空间分辨率的增加而减少。