On a multigrid solver for the three- dimensional Biot poroelasticity system in multilayered domains

In this paper, we present problem–dependent prolongation and problem–dependent restriction for a multigrid solver for the three-dimensional Biot poroelasticity system, which is solved in a multilayered domain. The system is discretized on a staggered grid using the finite volume method. During the discretization, special care is taken of the discontinuous coefficients. For the efficient multigrid solver, a need in operator-dependent restriction and/or prolongation arises. We derive these operators so that they are consistent with the discretization. They account for the discontinuities of the coefficients, as well as for the coupling of the unknowns within the Biot system. A set of numerical experiments shows necessity of use of the operator-dependent restriction and prolongation in the multigrid solver for the considered class of problems. This research has been partially supported by the Kaiserslautern Excellence Cluster Dependable Adaptive Systems and Mathematical Modelling, the Spanish project MEC/FEDER MTM 2004-019051, the Diputacin General de Aragn, and by the INTAS project 03-50-4395. A. Naumovich Fraunhofer Institut Technound Wirtschaftsmathematik Fraunhofer-Platz 1 D-67663 Kaiserslautern. Tel.: +49-0631-31600 4692 Fax: +49-0631-31600 5692 E-mail: [email protected] F.J. Gaspar Departamento de Matemática Aplicada. University of Zaragoza. Maria de Luna 3, 50018 Zaragoza Spain. Tel.: +34-976-762010 Fax: +34-976-761886 E-mail: [email protected]