We have presented a fast method for solving a specific type of block four-by-four saddlepoint problem arising from the finite element discretization of the generalized 3D Stokes problem. We analyze the eigenvalue distribution and the eigenvectors of the preconditioned matrix. Furthermore, we suggested utilizing the preconditioned global conjugate gradient method (PGCG) as a block iterative solver for handling multiple right-hand sides within the sub-system and give some new convergence results. Numerical experiments have shown that our preconditioned iterative approach is very efficient for solving the 3D Stokes problem

翻译：我们提出了一种快速方法，用于求解由广义三维Stokes问题的有限元离散化产生的特定类型块四乘四鞍点问题。我们分析了预处理矩阵的特征值分布和特征向量。此外，我们建议利用预处理全局共轭梯度法（PGCG）作为块迭代求解器，以处理子系统中的多个右端项，并给出了一些新的收敛性结果。数值实验表明，我们的预处理迭代方法在求解三维Stokes问题时非常高效。