High Performance Computing preconditioners for the efficient solution of geomechanical models

Geomechanical models solved by Finite Element (FE) techniques ask for the solution of a sequence of linearized systems of equations. The stiffness matrix can be very large, sparse and often illconditioned due to grid distortion and spatial variability of the rock properties. Computing the solution to these linear systems is typically the most time- and memory-consuming effort in a geomechanical simulation. The present work describes the FSAIPACK software package, that was developed for the efficient solution of ill-conditioned linear systems by exploiting a High Performance Computing (HPC) environment. FSAIPACK is based on the Conjugate Gradient method preconditioned by factored sparse approximate inverses. Its performance with large size geomechanical problems is investigated, showing a great efficiency as compared with other solvers. The FSAIPACK software package is freely available for research purposes at the website http://www.dmsa.unipd.it/?janna/software.html.