We propose a multi-level type operator that can be used in the framework of operator (or Calderon) preconditioning to construct uniform preconditioners for negative order operators discretized by piecewise polynomials on a family of possibly locally refined partitions. The cost of applying this multi-level operator scales linearly in the number of mesh cells. Therefore, it provides a uniform preconditioner that can be applied in linear complexity when used within the preconditioning framework from our earlier work [Math. of Comp., 322(89) (2020), pp. 645-674].

中文翻译：

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负序问题的线性复杂度统一预处理器

我们提出了一种多级类型运算符，可以在运算符（或 Calderon）预处理的框架中使用，为负序运算符构建统一预处理器，该运算符由可能局部细化的分区系列上的分段多项式离散。应用这种多级算子的成本与网格单元的数量呈线性关系。因此，它提供了一个统一的预处理器，当在我们早期工作 [Math. Comp.，322(89) (2020)，第 645-674 页]。