AI 中文总结
研究针对斯托克斯流质量守恒混合应力公式提出最优块对角和三角预条件器，分析了配备相应预条件器的MINRES和GMRES，通过二维和三维模型问题数值结果验证预条件器参数鲁棒性。
AI 中文摘要
我们提出了用于斯托克斯流的质量守恒混合应力公式的最优块对角和三角预条件器。代数公式导致一个双鞍点系统，其未知数对应于离散应力、速度、涡度和压力。分析了配备块对角预条件器的MINRES用于该系统的增广拉格朗日公式，并证明其是最优的，即收敛速度与网格大小和运动粘度等关键参数无关。还使用值域方法分析了配备块三角预条件器的GMRES。最后，给出了二维和三维模型问题的数值结果，以验证所提出预条件器的参数鲁棒性。
英文摘要
We present optimal block diagonal and triangular preconditioners for a mass-conserving mixed stress formulation of Stokes flow. The algebraic formulation leads to a double saddle point system with unknowns corresponding to discrete stress, velocity, vorticity, and pressure. MINRES equipped with a block diagonal preconditioner for an augmented Lagrangian formulation of this system is analyzed and shown to be optimal, in the sense that the convergence rate is independent of key parameters such as mesh size and kinematic viscosity. GMRES equipped with a block triangular preconditioner is also analyzed using a field-of-values approach. Finally, we present numerical results for both two- and three-dimensional model problems to validate the parameter robustness of the proposed preconditioners.
