SIAM Journal on Scientific Computing, Volume 42, Issue 4, Page A2360-A2370, January 2020.
The additive Schwarz method is usually presented as a preconditioner for a PDE linearization based on overlapping subsets of nodes from a global discretization. It has previously been shown how to apply Schwarz preconditioning to a nonlinear problem. By first replacing the original global PDE with the Schwarz overlapping problem, the global discretization becomes a simple union of subdomain discretizations, and unknowns do not need to be shared. In this way, restrictive-type updates can be avoided, and subdomains need to communicate only via interface interpolations. The resulting preconditioner can be applied linearly or nonlinearly. In the latter case, nonlinear subdomain problems are solved independently in parallel, and the frequency and amount of interprocess communication can be greatly reduced compared to global preconditioning of the sequence of linearized problems.

中文翻译：

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带独立网格的切比雪夫离散化的预处理非线性迭代

SIAM科学计算杂志，第42卷，第4期，第A2360-A2370页，2020年1月。
通常将加性Schwarz方法作为基于全局离散化的节点重叠子集的PDE线性化的前提条件。先前已经展示了如何将Schwarz预处理应用于非线性问题。通过首先用Schwarz重叠问题替换原始的全局PDE，全局离散化成为子域离散化的简单联合，并且不需要共享未知数。这样，可以避免限制性类型的更新，并且子域仅需要通过接口插值进行通信。所得的预处理器可以线性或非线性地应用。在后一种情况下，非线性子域问题可以并行并行解决，