## On a multigrid solver for the threedimensional 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.

Author: A. Naumovich, F. J. Gaspar urn:nbn:de:hbz:386-kluedo-14141 Berichte des Fraunhofer-Instituts für Techno- und Wirtschaftsmathematik (ITWM Report) (85) Report English 2006 2006 Fraunhofer-Institut für Techno- und Wirtschaftsmathematik 2006/03/02 interface problem; multigrid; operator-dependent prolongation; poroelasticity Fraunhofer (ITWM) 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

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