用于定常和非定常Navier-Stokes控制的Osen迭代参数鲁棒预处理
Parameter-Robust Preconditioning for Oseen Iteration Applied to Stationary and Instationary Navier--Stokes Control
摘要：
针对定常和时变Navier-Stokes控制问题，我们导出了新颖的、快速的、参数鲁棒的预处理迭代法。我们的方法可以应用于时间依赖的问题，离散使用向后欧拉或曲柄-尼科尔森，也是一个有价值的候选人斯托克斯控制问题离散使用曲柄-尼科尔森。求解器的关键成分是线性系的鞍点型近似，对流扩散控制的预条件加速的$(1,1)$块的内迭代，以及基于应用于适当块矩阵的有效换向器参数的近似Schur补。一系列的数值实验验证了我们的新方法的有效性。
英文摘要：
We derive novel, fast, and parameter-robust preconditioned iterative methods for steady and time-dependent Navier--Stokes control problems. Our approach may be applied to time-dependent problems which are discretized using backward Euler or Crank--Nicolson, and is also a valuable candidate for Stokes control problems discretized using Crank--Nicolson. The key ingredients of the solver are a saddle-point type approximation for the linear systems, an inner iteration for the $(1,1)$-block accelerated by a preconditioner for convection--diffusion control, and an approximation to the Schur complement based on a potent commutator argument applied to an appropriate block matrix. A range of numerical experiments validate the effectiveness of our new approach.
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