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Toward a new fully algebraic preconditioner for symmetric positive definite problems

Abstract : 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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https://hal.archives-ouvertes.fr/hal-03187092
Contributor : Nicole Spillane <>
Submitted on : Wednesday, March 31, 2021 - 4:38:32 PM
Last modification on : Thursday, April 8, 2021 - 3:37:07 AM

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  • HAL Id : hal-03187092, version 1

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

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