65238 20190709135610.0 doi 10.1137/16M1090193 sideral 104079 ART-2017-104079 eng (orcid)0000-0002-9777-5245 Gaspar Lorenz, Francisco José Universidad de Zaragoza Multigrid waveform relaxation for the time-fractional heat equation 2017 Access copy available to the general public Unrestricted In this work, we propose an efficient and robust multigrid method for solving the time-fractional heat equation. Due to the nonlocal property of fractional differential operators, numerical methods usually generate systems of equations for which the coefficient matrix is dense. Therefore, the design of efficient solvers for the numerical simulation of these problems is a difficult task. We develop a parallel-in-time multigrid algorithm based on the waveform relaxation approach, whose application to time-fractional problems seems very natural due to the fact that the fractional derivative at each spatial point depends on the values of the function at this point at all earlier times. Exploiting the Toeplitz-like structure of the coefficient matrix, the proposed multigrid waveform relaxation method has a computational cost of $O(NM\log(M))$ operations, where $M$ is the number of time steps and $N$ is the number of spatial grid points. A semialgebraic mode analysis is also developed to theoretically confirm the good results obtained. Several numerical experiments, including examples with nonsmooth solutions and a nonlinear problem with applications in porous media, are presented. info:eu-repo/grantAgreement/ES/MICINN/MTM2016-75139-R 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/EC/H2020/705402/EU/Efficient numerical methods for deformable porous media. Application to carbon dioxide storage./poro sos info:eu-repo/grantAgreement/ES/DGA/PDIE info:eu-repo/semantics/openAccess All rights reserved http://www.europeana.eu/rights/rr-f/ 2.046 2017 MATHEMATICS, APPLIED 27 / 252 = 0.107 2017 Q1 T1 1.973 2017 Computational Mathematics 2017 Q1 Applied Mathematics 2017 Q1 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion (orcid)0000-0002-1598-2831 Rodrigo Cardiel, Carmen Universidad de Zaragoza 2005 595 Universidad de Zaragoza Dpto. Matemática Aplicada Área Matemática Aplicada 39, 4 (2017), A1201-A1224 SIAM j. sci. comput. SIAM JOURNAL ON SCIENTIFIC COMPUTING 1064-8275 412399 http://zaguan.unizar.es/record/65238/files/texto_completo.pdf Versión publicada 82851 http://zaguan.unizar.es/record/65238/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:65238 articulos driver 2019-07-09-12:22:12 ARTICLE