Uniform Preconditioners of Linear Complexity for Problems of Negative Order
Uniform Preconditioners of Linear Complexity for Problems of Negative Order
复制标题
负序问题线性复杂度的一致预条件子
DOI：
10.1515/cmam-2020-0052
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发表时间：
2020
影响因子：
1.3
通讯作者：
Raymond van Venetië
中科院分区：
文献类型：
--
作者：
Rob Stevenson;Raymond van Venetië
摘要本文提出了一种多层型算子，它可以在算子（或Caldéron）预处理的框架下，在一族可能局部加细的剖分上，构造分段多项式离散化的负阶算子的一致预处理子。应用此多级运算符的成本与网格单元的数量成线性比例。因此，它提供了一个统一的预处理器，当在我们早期工作的预处理框架内使用时，可以应用于线性复杂度[Uniform preconditioners for problems of negative order，Math. Comp. 89（2020），645-674]。
Abstract We propose a multi-level type operator that can be used in the framework of operator (or Caldéron) 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 [Uniform preconditioners for problems of negative order, Math. Comp. 89 (2020), 645–674].