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Pré-Publication, Document De Travail Année : 2021

Toward a new fully algebraic preconditioner for symmetric positive definite problems

Résumé

A new domain decomposition preconditioner is introduced for efficiently solving linear systems Ax = b with a symmetric positive definite matrix A. The particularity of the new preconditioner is that it is not necessary to have access to the so-called Neumann matrices (i.e.: the matrices that result from assembling the variational problem underlying A restricted to each subdomain). All the components in the preconditioner can be computed with the knowledge only of A (and this is the meaning given here to the word algebraic). The new preconditioner relies on the GenEO coarse space for a matrix that is a low-rank modification of A and on the Woodbury matrix identity. The idea underlying the new preconditioner is introduced here for the first time with a first version of the preconditioner. Some numerical illustrations are presented. A more efficient version will be proposed in a full-length article.
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Dates et versions

hal-03187092 , version 1 (31-03-2021)
hal-03187092 , version 2 (21-06-2021)

Identifiants

  • HAL Id : hal-03187092 , version 1

Citer

Nicole Spillane. Toward a new fully algebraic preconditioner for symmetric positive definite problems. 2021. ⟨hal-03187092v1⟩
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