Uniform preconditioners for problems of negative order
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- by Rob Stevenson and Raymond van Venetië HTML | PDF
- Math. Comp. 89 (2020), 645-674 Request permission
Abstract:
Uniform preconditioners for operators of negative order discretized by (dis)continuous piecewise polynomials of any order are constructed from a boundedly invertible operator of opposite order discretized by continuous piecewise linears. Besides the cost of the application of the latter discretized operator, the other cost of the preconditioner scales linearly with the number of mesh cells. Compared to earlier proposals, the preconditioner has the following advantages: It does not require the inverse of a non-diagonal matrix; it applies without any mildly grading assumption on the mesh; and it does not require a barycentric refinement of the mesh underlying the trial space.References
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Additional Information
- Rob Stevenson
- Affiliation: Korteweg-de Vries Institute for Mathematics, University of Amsterdam, P.O. Box 94248, 1090 GE Amsterdam, The Netherlands
- MR Author ID: 310898
- Email: r.p.stevenson@uva.nl
- Raymond van Venetië
- Affiliation: Korteweg-de Vries Institute for Mathematics, University of Amsterdam, P.O. Box 94248, 1090 GE Amsterdam, The Netherlands
- Email: r.vanvenetie@uva.nl
- Received by editor(s): March 14, 2018
- Received by editor(s) in revised form: September 24, 2018, and April 5, 2019
- Published electronically: August 23, 2019
- Additional Notes: This work was initiated during the trimester programme “Multiscale Problems: Algorithms, Numerical Analysis and Computation” January-April 2017 at the Hausdorff Research Institute for Mathematics, Bonn, Germany, whose support is gratefully acknowledged by the first author. In addition, he has been supported by NSF Grant DMS 1720297.
The second author has been supported by the Netherlands Organization for Scientific Research (NWO) under contract. no. 613.001.652 - © Copyright 2019 American Mathematical Society
- Journal: Math. Comp. 89 (2020), 645-674
- MSC (2010): Primary 65F08, 65N38, 65N30, 45Exx
- DOI: https://doi.org/10.1090/mcom/3481
- MathSciNet review: 4044445