This article presents deflation strategies related to recycling Krylov subspace methods for solving one or a sequence of linear systems of equations. Besides well-known strategies of deflation, Ritz-, and harmonic Ritz-based deflation, we introduce an Singular Value Decomposition based deflation technique. We consider the recycling in two contexts: recycling the Krylov subspace between the restart cycles and recycling a deflation subspace when the matrix changes in a sequence of linear systems. Numerical experiments on real-life reservoir simulation demonstrate the impact of our proposed strategy.

中文翻译：

---

回收 Krylov 子空间和截断通货紧缩子空间求解线性系统的序列

本文介绍了与用于求解一个或一系列线性方程组的循环 Krylov 子空间方法相关的通缩策略。除了众所周知的通货紧缩策略、基于 Ritz 和谐波 Ritz 的通货紧缩之外，我们还引入了基于奇异值分解的通货紧缩技术。我们在两种情况下考虑回收：在重新启动周期之间回收 Krylov 子空间，以及当矩阵在一系列线性系统中发生变化时回收通货紧缩子空间。真实油藏模拟的数值实验证明了我们提出的策略的影响。