000132195 001__ 132195 000132195 005__ 20260113073211.0 000132195 0247_ $$2doi$$a10.1016/j.camwa.2023.12.039 000132195 0248_ $$2sideral$$a137279 000132195 037__ $$aART-2024-137279 000132195 041__ $$aeng 000132195 100__ $$aPé de la Riva, Álvaro$$uUniversidad de Zaragoza 000132195 245__ $$aA local Fourier analysis for additive Schwarz smoothers 000132195 260__ $$c2024 000132195 5203_ $$aIn this work, a local Fourier analysis is presented to study the convergence of multigrid methods based on additive Schwarz smoothers. This analysis is presented as a general framework which allows us to study these smoothers for any type of discretization and problem. The presented framework is crucial in practice since it allows one to know a priori the answer to questions such as what is the size of the patch to use within these relaxations, the size of the overlap, or even the optimal values for the weights involved in the smoother. Results are shown for a class of additive and restricted additive Schwarz relaxations used within a multigrid framework applied to high-order finite-element discretizations and saddle point problems, which are two of the contexts in which these types of relaxations are widely used. 000132195 536__ $$9info:eu-repo/grantAgreement/ES/DGA-FSE/E24-17R$$9info:eu-repo/grantAgreement/ES/MCIU/PID2019-105574GB-I00$$9info:eu-repo/grantAgreement/ES/MICINN/PID2022-140108NB-I00 000132195 540__ $$9info:eu-repo/semantics/openAccess$$aby-nc-nd$$uhttps://creativecommons.org/licenses/by-nc-nd/4.0/deed.es 000132195 590__ $$a2.5$$b2024 000132195 592__ $$a0.951$$b2024 000132195 591__ $$aMATHEMATICS, APPLIED$$b39 / 343 = 0.114$$c2024$$dQ1$$eT1 000132195 593__ $$aComputational Mathematics$$c2024$$dQ1 000132195 593__ $$aModeling and Simulation$$c2024$$dQ1 000132195 593__ $$aComputational Theory and Mathematics$$c2024$$dQ1 000132195 594__ $$a5.0$$b2024 000132195 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion 000132195 700__ $$0(orcid)0000-0002-1598-2831$$aRodrigo, Carmen$$uUniversidad de Zaragoza 000132195 700__ $$0(orcid)0000-0002-9777-5245$$aGaspar, Francisco J.$$uUniversidad de Zaragoza 000132195 700__ $$aAdler, James H. 000132195 700__ $$aHu, Xiaozhe 000132195 700__ $$aZikatanov, Ludmil 000132195 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada 000132195 773__ $$g158 (2024), 13-20$$pComput. math. appl.$$tCOMPUTERS & MATHEMATICS WITH APPLICATIONS$$x0898-1221 000132195 8564_ $$s383417$$uhttps://zaguan.unizar.es/record/132195/files/texto_completo.pdf$$yPostprint$$zinfo:eu-repo/date/embargoEnd/2025-01-19 000132195 8564_ $$s2621595$$uhttps://zaguan.unizar.es/record/132195/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint$$zinfo:eu-repo/date/embargoEnd/2025-01-19 000132195 909CO $$ooai:zaguan.unizar.es:132195$$particulos$$pdriver 000132195 951__ $$a2026-01-12-12:39:08 000132195 980__ $$aARTICLE