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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 extensive presentation including some improved variants of the new preconditioner can be found in [7] (https://hal.archives-ouvertes.fr/hal-03258644).
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-03187092
Contributor : Nicole Spillane <>
Submitted on : Monday, June 21, 2021 - 9:54:49 AM
Last modification on : Wednesday, June 23, 2021 - 3:38:50 AM

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  • HAL Id : hal-03187092, version 2
  • ARXIV : 2106.11574

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Nicole Spillane. Toward a new fully algebraic preconditioner for symmetric positive definite problems. 2021. ⟨hal-03187092v2⟩

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