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arXiv · 2004.06418

Uniform preconditioners of linear complexity for problems of negative order

Rob Stevenson·Raymond van Venetië
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Abstract

We propose a multi-level type operator that can be used in the framework of operator (or Cald\'{e}ron) 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].

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Rob Stevenson, Raymond van Venetië. 2020-04-14. Uniform preconditioners of linear complexity for problems of negative order. https://doi.org/10.1515/cmam-2020-0052

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