论文标题
鞍点问题的维度一致的预处理
Dimensionally Consistent Preconditioning for Saddle-Point Problems
论文作者
论文摘要
大规模鞍点系统的预处理解决方案在许多应用领域非常重要，其中许多涉及部分微分方程。相对于某些问题参数的鲁棒性通常是一个问题，可以通过识别预处理构建块的适当尺度来解决。在本文中，我们考虑了寻找有效和强大的预处理的一种新观点。我们的方法是基于对各个鞍点问题基础的自然物理单位的考虑。我们称之为维度一致性的观点表明，该参数固有的自然组合。事实证明，在许多相关情况下，以这种方式获得的缩放导致了问题参数的鲁棒性。结果，我们宣传基于维度一致性的预处理是一种新的，系统的方式，用于设计由物理现象模型引起的鞍点系统的参数鲁棒前核。
The preconditioned iterative solution of large-scale saddle-point systems is of great importance in numerous application areas, many of them involving partial differential equations. Robustness with respect to certain problem parameters is often a concern, and it can be addressed by identifying proper scalings of preconditioner building blocks. In this paper, we consider a new perspective to finding effective and robust preconditioners. Our approach is based on the consideration of the natural physical units underlying the respective saddle-point problem. This point of view, which we refer to as dimensional consistency, suggests a natural combination of the parameters intrinsic to the problem. It turns out that the scaling obtained in this way leads to robustness with respect to problem parameters in many relevant cases. As a consequence, we advertise dimensional consistency based preconditioning as a new and systematic way to designing parameter robust preconditoners for saddle-point systems arising from models for physical phenomena.
