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.