000088253 001__ 88253
000088253 005__ 20200716101605.0
000088253 0247_ $$2doi$$a10.1137/18M1194407
000088253 0248_ $$2sideral$$a116359
000088253 037__ $$aART-2019-116359
000088253 041__ $$aeng
000088253 100__ $$aPe de la Riva, Álvaro$$uUniversidad de Zaragoza
000088253 245__ $$aA Robust Multigrid Solver for Isogeometric Analysis Based on Multiplicative Schwarz Smoothers
000088253 260__ $$c2019
000088253 5060_ $$aAccess copy available to the general public$$fUnrestricted
000088253 5203_ $$aThe design of fast solvers for isogeometric analysis is receiving a lot of attention due to the challenge that offers to find an algorithm with a robust convergence with respect to the spline degree. Here, we analyze the application of geometric multigrid methods to this type of discretization, and we propose a multigrid approach based on overlapping multiplicative Schwarz methods as smoothers. The size of the blocks considered within these relaxation procedures is adapted to the spline degree. A simple multigrid V-cycle with only one step of presmoothing results in a very efficient algorithm, whose convergence is independent on the spline degree and the spatial discretization parameter. Local Fourier analysis is shown to be very useful for the understanding of the problems encountered in the design of a robust multigrid method for IGA, and it is performed to support the good convergence properties of the proposed solver. In fact, an analysis for any spline degree and an arbitrary size of the blocks within the Schwarz smoother is presented for the one-dimensional case. The efficiency of the solver is also demonstrated through several numerical experiments, including a two-dimensional problem on a nontrivial computational domain.
000088253 536__ $$9info:eu-repo/grantAgreement/ES/DGA-FEDER/E24-17R$$9info:eu-repo/grantAgreement/EC/H2020/705402/EU/Efficient numerical methods for deformable porous media. Application to carbon dioxide storage./poro sos$$9This project has received funding from the European Union’s Horizon 2020 research and innovation program under grant agreement No H2020 705402-poro sos$$9info:eu-repo/grantAgreement/ES/MCYT-FEDER/MTM2016-75139-R
000088253 540__ $$9info:eu-repo/semantics/openAccess$$aAll rights reserved$$uhttp://www.europeana.eu/rights/rr-f/
000088253 590__ $$a1.976$$b2019
000088253 591__ $$aMATHEMATICS, APPLIED$$b47 / 260 = 0.181$$c2019$$dQ1$$eT1
000088253 592__ $$a1.928$$b2019
000088253 593__ $$aComputational Mathematics$$c2019$$dQ1
000088253 593__ $$aApplied Mathematics$$c2019$$dQ1
000088253 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion
000088253 700__ $$0(orcid)0000-0002-1598-2831$$aRodrigo, Carmen$$uUniversidad de Zaragoza
000088253 700__ $$0(orcid)0000-0002-9777-5245$$aGaspar Lorenz, Francisco$$uUniversidad de Zaragoza
000088253 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada
000088253 773__ $$g41, 5 (2019), S321–S345$$pSIAM j. sci. comput.$$tSIAM JOURNAL ON SCIENTIFIC COMPUTING$$x1064-8275
000088253 8564_ $$s1688321$$uhttps://zaguan.unizar.es/record/88253/files/texto_completo.pdf$$yVersión publicada
000088253 8564_ $$s421144$$uhttps://zaguan.unizar.es/record/88253/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada
000088253 909CO $$ooai:zaguan.unizar.es:88253$$particulos$$pdriver
000088253 951__ $$a2020-07-16-09:54:23
000088253 980__ $$aARTICLE