000065238 001__ 65238
000065238 005__ 20190709135610.0
000065238 0247_ $$2doi$$a10.1137/16M1090193
000065238 0248_ $$2sideral$$a104079
000065238 037__ $$aART-2017-104079
000065238 041__ $$aeng
000065238 100__ $$0(orcid)0000-0002-9777-5245$$aGaspar Lorenz, Francisco José$$uUniversidad de Zaragoza
000065238 245__ $$aMultigrid waveform relaxation for the time-fractional heat equation
000065238 260__ $$c2017
000065238 5060_ $$aAccess copy available to the general public$$fUnrestricted
000065238 5203_ $$aIn 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.
000065238 536__ $$9info:eu-repo/grantAgreement/ES/MICINN/MTM2016-75139-R$$9This project has received funding from the European Union’s Horizon 2020 research and innovation program under grant agreement No H2020 705402-poro sos$$9info:eu-repo/grantAgreement/EC/H2020/705402/EU/Efficient numerical methods for deformable porous media. Application to carbon dioxide storage./poro sos$$9info:eu-repo/grantAgreement/ES/DGA/PDIE
000065238 540__ $$9info:eu-repo/semantics/openAccess$$aAll rights reserved$$uhttp://www.europeana.eu/rights/rr-f/
000065238 590__ $$a2.046$$b2017
000065238 591__ $$aMATHEMATICS, APPLIED$$b27 / 252 = 0.107$$c2017$$dQ1$$eT1
000065238 592__ $$a1.973$$b2017
000065238 593__ $$aComputational Mathematics$$c2017$$dQ1
000065238 593__ $$aApplied Mathematics$$c2017$$dQ1
000065238 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion
000065238 700__ $$0(orcid)0000-0002-1598-2831$$aRodrigo Cardiel, Carmen$$uUniversidad de Zaragoza
000065238 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada
000065238 773__ $$g39, 4 (2017), A1201-A1224$$pSIAM j. sci. comput.$$tSIAM JOURNAL ON SCIENTIFIC COMPUTING$$x1064-8275
000065238 8564_ $$s412399$$uhttps://zaguan.unizar.es/record/65238/files/texto_completo.pdf$$yVersión publicada
000065238 8564_ $$s82851$$uhttps://zaguan.unizar.es/record/65238/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada
000065238 909CO $$ooai:zaguan.unizar.es:65238$$particulos$$pdriver
000065238 951__ $$a2019-07-09-12:22:12
000065238 980__ $$aARTICLE