88253 20200716101605.0 doi 10.1137/18M1194407 sideral 116359 ART-2019-116359 eng Pe de la Riva, Álvaro Universidad de Zaragoza A Robust Multigrid Solver for Isogeometric Analysis Based on Multiplicative Schwarz Smoothers 2019 Access copy available to the general public Unrestricted The 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. info:eu-repo/grantAgreement/ES/DGA-FEDER/E24-17R info:eu-repo/grantAgreement/EC/H2020/705402/EU/Efficient numerical methods for deformable porous media. Application to carbon dioxide storage./poro sos This project has received funding from the European Union’s Horizon 2020 research and innovation program under grant agreement No H2020 705402-poro sos info:eu-repo/grantAgreement/ES/MCYT-FEDER/MTM2016-75139-R info:eu-repo/semantics/openAccess All rights reserved http://www.europeana.eu/rights/rr-f/ 1.976 2019 MATHEMATICS, APPLIED 47 / 260 = 0.181 2019 Q1 T1 1.928 2019 Computational Mathematics 2019 Q1 Applied Mathematics 2019 Q1 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion (orcid)0000-0002-1598-2831 Rodrigo, Carmen Universidad de Zaragoza (orcid)0000-0002-9777-5245 Gaspar Lorenz, Francisco Universidad de Zaragoza 2005 595 Universidad de Zaragoza Dpto. Matemática Aplicada Área Matemática Aplicada 41, 5 (2019), S321–S345 SIAM j. sci. comput. SIAM JOURNAL ON SCIENTIFIC COMPUTING 1064-8275 1688321 http://zaguan.unizar.es/record/88253/files/texto_completo.pdf Versión publicada 421144 http://zaguan.unizar.es/record/88253/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:88253 articulos driver 2020-07-16-09:54:23 ARTICLE