A multigrid waveform relaxation method for solving the poroelasticity equations

Franco, S.R. ; Rodrigo, C. (Universidad de Zaragoza) ; Gaspar, F.J. (Universidad de Zaragoza) ; Pinto, M.A.V.

Resumen: In this work, a multigrid waveform relaxation method is proposed for solving a collocated finite difference discretization of the linear Biot''s model. This gives rise to the first space-time multigrid solver for poroelasticity equations in the literature. The waveform relaxation iteration is based on a point-wise Vanka smoother that couples the pressure variable at a grid-point with the displacements around it. A semi-algebraic mode analysis is proposed to theoretically analyze the convergence of the multigrid waveform relaxation algorithm. This analysis is novel since it combines the semi-algebraic analysis, suitable for parabolic problems, with the non-standard analysis for overlapping smoothers. The practical utility of the method is illustrated through several numerical experiments in one and two dimensions.

Idioma: Inglés

DOI: 10.1007/s40314-018-0603-9

Año: 2018

Publicado en: Computational & Applied Mathematics 37, 4 (2018), 4805-4820
ISSN: 2238-3603

Factor impacto JCR: 1.26 (2018)

Categ. JCR: MATHEMATICS, APPLIED rank: 100 / 254 = 0.394 (2018) - Q2 - T2

Tipo y forma: Article (Published version)

Área (Departamento): Área Matemática Aplicada (Dpto. Matemática Aplicada)