Multigrid solvers and multigrid preconditioners for the solution of variational data assimilation problems
Multigrid solvers and multigrid preconditioners for the solution of variational data assimilation problems
复制标题
用于解决变分数据同化问题的多重网格求解器和多重网格预处理器
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
A. Vidard
中科院分区：
文献类型：
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作者：
L. Debreu;Émilie Neveu;E. Simon;F. Le Dimet;A. Vidard
为了降低变分数据同化过程的计算成本，我们研究了使用多重网格方法来求解相关的最优控制系统。在线性平流方程中，我们研究了正则化项对最优控制的影响以及离散化误差对粗网格校正步骤效率的影响。我们表明，即使最优控制问题导致椭圆系统的解，离散化引入的数值误差也会改变多重网格方法的成功。将多重网格迭代作为 Krylov 优化方法的预处理器的观点导致了更鲁棒的算法。提出了多重网格预处理器的尺度相关加权和通常的基于背景误差协方差矩阵的预处理器，并带来了显着的改进。
In order to lower the computational cost of the variational data assimilation process, we investigate the use of multigrid methods to solve the associated optimal control system. In a linear advection equation, we study the impact of the regularization term on the optimal control and the impact of discretization errors on the efficiency of the coarse‐grid correction step. We show that, even if the optimal control problem leads to the solution of an elliptic system, numerical errors introduced by the discretization can alter the success of the multigrid method. The view of multigrid iteration as a preconditioner for a Krylov optimization method leads to a more robust algorithm. A scale‐dependent weighting of the multigrid preconditioner and the usual background‐error covariance‐matrix based preconditioner is proposed and brings significant improvements.