Efficient multilevel preconditioners for large size geomechanical simulations

The FE numerical discretization of complex geomechanical models usually gives rise to non-linear systems of equations whose solution is obtained by a Newton-like method. Such a strategy requires the solution of a sequence of linear systems where the number of unknowns, depending on the size of the domain and the required numerical accuracy, may easily grow up to several hundreds of thousands. As the solution of such systems by direct solvers is usually unfeasible due to the huge memory consumption, the use of Krylov subspace methods is becoming a popular practice with the development of relatively cheap and effective preconditioners a key factor for their computational efficiency. In the present communication the somewhat natural level partition of some geomechanical problems is used to enhance the numerical performance of incomplete factorizations, a popular and widely used class of algebraic preconditioners. It is shown that the proposed multilevel preconditioner compares very favourably with classical incomplete factorizations in terms of robustness and time performance especially in long term simulations.