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Numerical simulations are widely used in studying underground processes, as direct measurements are extremely expensive or even unfeasible. Typical examples are the geomechanical processes involved in compacting reservoirs, the evolution of sedimentary basins or the fluid flows in deep, porous formations. Developing efficient, robust and scalable linear solvers to solve those problems is a crucial task. Graphics Processing Units (GPUs) are attracting a growing attention since they are well suited for massively parallel computations providing a very good balance among performance, price and power consumption. In the field of iterative methods, for instance, it is difficult to take advantage from preconditioners based on incomplete factorization and approximate inverses are generally preferred.
In this work, we will focus on the adaptive Factored Sparse Approximate Inverses (aFSAI) that have been already successfully tested on GPUs showing significant speed-ups with respect to the CPU counterpart. We will show in problems arising from geomechanics and basin modelling that, thanks to this GPU- accelerated, it is possible not only to speed-up the simulations but also to significantly reduce the energy consumption to power the hardware.