Multigrid waveform relaxation for the time-fractional heat equation
Financiación H2020 / H2020 Funds
Resumen: 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.
Idioma: Inglés
DOI: 10.1137/16M1090193
Año: 2017
Publicado en: SIAM JOURNAL ON SCIENTIFIC COMPUTING 39, 4 (2017), A1201-A1224
ISSN: 1064-8275

Factor impacto JCR: 2.046 (2017)
Categ. JCR: MATHEMATICS, APPLIED rank: 27 / 252 = 0.107 (2017) - Q1 - T1
Factor impacto SCIMAGO: 1.973 - Computational Mathematics (Q1) - Applied Mathematics (Q1)

Financiación: info:eu-repo/grantAgreement/ES/DGA/PDIE
Financiación: info:eu-repo/grantAgreement/EC/H2020/705402/EU/Efficient numerical methods for deformable porous media. Application to carbon dioxide storage./poro sos
Financiación: info:eu-repo/grantAgreement/ES/MICINN/MTM2016-75139-R
Tipo y forma: Article (Published version)
Área (Departamento): Área Matemática Aplicada (Dpto. Matemática Aplicada)

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