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

In this paper, we present a multigrid method with problem-dependent prolongation and restriction for the three-dimensional Biot poroelasticity system in a multilayered domain. The system is discretized on a staggered grid using the finite volume method. In the discretization special care is taken of the coefficients’ discontinuity. The prolongation and restriction operators are derived in a consistent manner with the discretization, so that 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 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 Diputación General de Aragón, and by the INTAS project 03-50-4395.