A local Fourier analysis for additive Schwarz smoothers

Pé de la Riva, Álvaro (Universidad de Zaragoza) ; Rodrigo, Carmen (Universidad de Zaragoza) ; Gaspar, Francisco J. (Universidad de Zaragoza) ; Adler, James H. ; Hu, Xiaozhe ; Zikatanov, Ludmil

Resumen: In this work, a local Fourier analysis is presented to study the convergence of multigrid methods based on additive Schwarz smoothers. This analysis is presented as a general framework which allows us to study these smoothers for any type of discretization and problem. The presented framework is crucial in practice since it allows one to know a priori the answer to questions such as what is the size of the patch to use within these relaxations, the size of the overlap, or even the optimal values for the weights involved in the smoother. Results are shown for a class of additive and restricted additive Schwarz relaxations used within a multigrid framework applied to high-order finite-element discretizations and saddle point problems, which are two of the contexts in which these types of relaxations are widely used.

Idioma: Inglés

DOI: 10.1016/j.camwa.2023.12.039

Año: 2024

Publicado en: COMPUTERS & MATHEMATICS WITH APPLICATIONS 158 (2024), 13-20
ISSN: 0898-1221

Factor impacto JCR: 2.5 (2024)

Categ. JCR: MATHEMATICS, APPLIED rank: 39 / 343 = 0.114 (2024) - Q1 - T1

Factor impacto CITESCORE: 5.0 - Computational Mathematics (Q1) - Modeling and Simulation (Q1) - Computational Theory and Mathematics (Q1)

Factor impacto SCIMAGO: 0.951 - Computational Mathematics (Q1) - Modeling and Simulation (Q1) - Computational Theory and Mathematics (Q1)

Financiación: info:eu-repo/grantAgreement/ES/DGA-FSE/E24-17R
Financiación: info:eu-repo/grantAgreement/ES/MCIU/PID2019-105574GB-I00
Financiación: info:eu-repo/grantAgreement/ES/MICINN/PID2022-140108NB-I00

Tipo y forma: Artículo (PostPrint)

Área (Departamento): Área Matemática Aplicada (Dpto. Matemática Aplicada)