000134924 001__ 134924 000134924 005__ 20260112133347.0 000134924 0247_ $$2doi$$a10.1007/s40324-023-00336-2 000134924 0248_ $$2sideral$$a138450 000134924 037__ $$aART-2024-138450 000134924 041__ $$aeng 000134924 100__ $$0(orcid)0000-0002-1598-2831$$aRodrigo, Carmen$$uUniversidad de Zaragoza 000134924 245__ $$aParameter-robust preconditioners for Biot’s model 000134924 260__ $$c2024 000134924 5060_ $$aAccess copy available to the general public$$fUnrestricted 000134924 5203_ $$aThis work presents an overview of the most relevant results obtained by the authors regarding the numerical solution of the Biot’s consolidation problem by preconditioning techniques. The emphasis here is on the design of parameter-robust preconditioners for the efficient solution of the algebraic system of equations resulting after proper discretization of such poroelastic problems. The classical two- and three-field formulations of the problem are considered, and block preconditioners are presented for some of the discretization schemes that have been proposed by the authors for these formulations. These discretizations have been proved to be well-posed with respect to the physical and discretization parameters, what provides a framework to develop preconditioners that are robust with respect to such parameters as well. In particular, we construct both norm-equivalent (block diagonal) and field-of-value-equivalent (block triangular) preconditioners, which are proved to be parameter-robust. The theoretical results on this parameter-robustness are demonstrated by considering typical benchmark problems in the literature for Biot’s model. 000134924 536__ $$9info:eu-repo/grantAgreement/ES/DGA-FSE/E24-17R$$9info:eu-repo/grantAgreement/ES/MCIU-AEI-FEDER/PGC2018-099536-A-I00$$9info:eu-repo/grantAgreement/ES/MCIU/PID2019-105574GB-I00 000134924 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttps://creativecommons.org/licenses/by/4.0/deed.es 000134924 592__ $$a0.516$$b2024 000134924 593__ $$aApplied Mathematics$$c2024$$dQ2 000134924 593__ $$aNumerical Analysis$$c2024$$dQ2 000134924 593__ $$aModeling and Simulation$$c2024$$dQ2 000134924 593__ $$aControl and Optimization$$c2024$$dQ2 000134924 594__ $$a3.3$$b2024 000134924 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000134924 700__ $$0(orcid)0000-0002-9777-5245$$aGaspar, Francisco J.$$uUniversidad de Zaragoza 000134924 700__ $$aAdler, James 000134924 700__ $$aHu, Xiaozhe 000134924 700__ $$aOhm, Peter 000134924 700__ $$aZikatanov, Ludmil 000134924 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada 000134924 773__ $$g81, 1 (2024), 51-80$$pSEMA j.$$tSEMA Journal$$x2254-3902 000134924 8564_ $$s676250$$uhttps://zaguan.unizar.es/record/134924/files/texto_completo.pdf$$yVersión publicada 000134924 8564_ $$s1161386$$uhttps://zaguan.unizar.es/record/134924/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000134924 909CO $$ooai:zaguan.unizar.es:134924$$particulos$$pdriver 000134924 951__ $$a2026-01-12-13:17:50 000134924 980__ $$aARTICLE