FOV-equivalent block triangular preconditioners for generalized saddle-point problems

Eugenio Aulisa; Sara Calandrini; Giacomo Capodaglio

doi:10.1016/j.aml.2017.06.018

FOV-equivalent block triangular preconditioners for generalized saddle-point problems

Eugenio Aulisa, Sara Calandrini, Giacomo Capodaglio

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We present sufficient conditions for field-of-values-equivalence between block triangular preconditioners and generalized saddle-point matrices arising from inf–sup stable finite element discretizations. We generalize a result by Loghin and Wathen (2004) for matrices with a pure saddle-point structure to the case where the (2,2) block is non-zero. Moreover, we extend the analysis to the case where the (2,1) block is not the transpose of the (1,2) block.

Original language	English
Pages (from-to)	43-49
Number of pages	7
Journal	Applied Mathematics Letters
Volume	75
DOIs	https://doi.org/10.1016/j.aml.2017.06.018
State	Published - Jan 2018

Keywords

Field-of-values-equivalence
Finite elements
Generalized saddle-point problems
Preconditioning

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abstract = "We present sufficient conditions for field-of-values-equivalence between block triangular preconditioners and generalized saddle-point matrices arising from inf–sup stable finite element discretizations. We generalize a result by Loghin and Wathen (2004) for matrices with a pure saddle-point structure to the case where the (2,2) block is non-zero. Moreover, we extend the analysis to the case where the (2,1) block is not the transpose of the (1,2) block.",

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AU - Calandrini, Sara

AU - Capodaglio, Giacomo

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AB - We present sufficient conditions for field-of-values-equivalence between block triangular preconditioners and generalized saddle-point matrices arising from inf–sup stable finite element discretizations. We generalize a result by Loghin and Wathen (2004) for matrices with a pure saddle-point structure to the case where the (2,2) block is non-zero. Moreover, we extend the analysis to the case where the (2,1) block is not the transpose of the (1,2) block.

KW - Field-of-values-equivalence

KW - Finite elements

KW - Generalized saddle-point problems

KW - Preconditioning

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DO - 10.1016/j.aml.2017.06.018

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JF - Applied Mathematics Letters

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