2021/06/22 by Nicole Spillane, Spillane, Nicole
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Advanced Numerical Methods in Computational Mathematics #Electromagnetic Scattering and Analysis #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #cs.NA #math.NA
paper · pdf · doi:10.48550/arxiv.2106.11574
arxiv created 2021/06/22 · openalex publication_date 2021/06/22 · arxiv updated 2021/06/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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).