Shifted FSAI preconditioners for the efficient parallel solution of non-linear groundwater flow models

The present paper investigates the performance of a shifted factorized sparse approximate inverse as a parallel preconditioner for the iterative solution to the linear systems arising in the finite element discretization of non-linear groundwater flow models. The shift strategy is based on an inexpensive preconditioner update exploiting the structure of the coefficient matrix. The proposed algorithm is experimented with in the parallel simulation of a large-scale real multi-aquifer system characterized by a stochastic distribution of the hydraulic conductivity. The numerical results show that the shifted factorized sparse approximate inverse algorithm may yield an overall computational gain up to 300% with respect to the non-shifted scheme with an excellent parallel efficiency