doi:10.1007/s40314-018-0603-9engFranco, S.R.Rodrigo, C.Gaspar, F.J.Pinto, M.A.V.A multigrid waveform relaxation method for solving the poroelasticity equationsART-2018-107958In 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.2018http://zaguan.unizar.es/record/17009210.1007/s40314-018-0603-9http://zaguan.unizar.es/record/170092oai:zaguan.unizar.es:170092Computational & Applied Mathematics 37, 4 (2018), 4805-4820All rights reservedhttp://www.europeana.eu/rights/rr-f/info:eu-repo/semantics/closedAccess