000058466 001__ 58466 000058466 005__ 20190709135425.0 000058466 0247_ $$2doi$$a10.1002/nla.2074 000058466 0248_ $$2sideral$$a97521 000058466 037__ $$aART-2017-97521 000058466 041__ $$aeng 000058466 100__ $$aLuo, P. 000058466 245__ $$aOn an Uzawa smoother in multigrid for poroelasticity equations 000058466 260__ $$c2017 000058466 5060_ $$aAccess copy available to the general public$$fUnrestricted 000058466 5203_ $$aA poroelastic saturated medium can be modeled by means of Biot''s theory of consolidation. It describes the time-dependent interaction between the deformation of porous material and the fluid flow inside of it. Here, for the efficient solution of the poroelastic equations, a multigrid method is employed with an Uzawa-type iteration as the smoother. The Uzawa smoother is an equation-wise procedure. It shall be interpreted as a combination of the symmetric Gauss-Seidel smoothing for displacements, together with a Richardson iteration for the Schur complement in the pressure field. The Richardson iteration involves a relaxation parameter which affects the convergence speed, and has to be carefully determined. The analysis of the smoother is based on the framework of local Fourier analysis (LFA) and it allows us to provide an analytic bound of the smoothing factor of the Uzawa smoother as well as an optimal value of the relaxation parameter. Numerical experiments show that our upper bound provides a satisfactory estimate of the exact smoothing factor, and the selected relaxation parameter is optimal. In order to improve the convergence performance, the acceleration of multigrid by iterant recombination is taken into account. Numerical results confirm the efficiency and robustness of the acceleration scheme. 000058466 536__ $$9info:eu-repo/grantAgreement/ES/MICINN/MTM2013-40842-P$$9This project has received funding from the European Union’s Horizon 2020 research and innovation program under grant agreement No H2020 705402-poro sos$$9info:eu-repo/grantAgreement/EC/H2020/705402/EU/Efficient numerical methods for deformable porous media. Application to carbon dioxide storage./poro sos 000058466 540__ $$9info:eu-repo/semantics/openAccess$$aby-nc-nd$$uhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/ 000058466 590__ $$a1.281$$b2017 000058466 591__ $$aMATHEMATICS$$b39 / 309 = 0.126$$c2017$$dQ1$$eT1 000058466 591__ $$aMATHEMATICS, APPLIED$$b81 / 252 = 0.321$$c2017$$dQ2$$eT1 000058466 592__ $$a1.104$$b2017 000058466 593__ $$aApplied Mathematics$$c2017$$dQ1 000058466 593__ $$aAlgebra and Number Theory$$c2017$$dQ1 000058466 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000058466 700__ $$0(orcid)0000-0002-1598-2831$$aRodrigo, C.$$uUniversidad de Zaragoza 000058466 700__ $$0(orcid)0000-0002-9777-5245$$aGaspar, F.J.$$uUniversidad de Zaragoza 000058466 700__ $$aOosterlee, C.W. 000058466 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada 000058466 773__ $$g24, 1 (2017), e2074 [14 pp]$$pNumer. linear algebra appl.$$tNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS$$x1070-5325 000058466 8564_ $$s680806$$uhttps://zaguan.unizar.es/record/58466/files/texto_completo.pdf$$yVersión publicada 000058466 8564_ $$s97998$$uhttps://zaguan.unizar.es/record/58466/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000058466 909CO $$ooai:zaguan.unizar.es:58466$$particulos$$pdriver 000058466 951__ $$a2019-07-09-11:29:04 000058466 980__ $$aARTICLE