Block FSAI performance with graph partitioning in large size subsurface problems

Adaptive Block FSAI (ABF) is a novel and promising preconditioner for the efficient parallel solution of linear systems and eigenproblems arising from subsurface applications. However, one of its main drawbacks stems from the reduced scalability, as the iteration count to converge tends to grow increasing the number of processors. Graph partitioning techniques can help improve both the preconditioner performance and scalability. Different algorithms are experimented with in a test problem arising from a groundwater flow application. The results show that coupling graph partitioning with ABF appears to be an important factor to increase significantly the preconditioner efficiency, allowing for its effective use also on massively parallel simulations.