An Efficient Preconditioning Strategy for Schur Complements Arising from Biphasic Models

Marco Favino, Rolf Krause, and Johannes Steiner


biphasic model, periodontal ligament, Schur complement, finite element method, relaxation


We consider the mathematical modeling, the numerical simulation and an efficient solution strategy of the periodontal ligament. For the modeling, we employ a biphasic approach which takes the fibrous tissue in the PDL into account as well as the fluid between the fibres. After discretization in space and time, a coupled system with saddle point structure has to be solved at each time step. We present and discuss a preconditioning strategy for the Schur complement of this problem. And we apply it for predicting the behavior of realistic problems from dental biomechanics.

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