A supernodal block factorized sparse approximate inverse for non-symmetric linear systems

The concept of supernodes, originally developed to accelerate direct solution methods for linear systems, is generalized to block factorized sparse approximate inverse (Block FSAI) preconditioning of non-symmetric linear systems. It is shown that aggregating the unknowns in clusters that are processed together is particularly useful both to reduce the cost for the preconditioner setup and accelerate the convergence of the iterative solver. A set of numerical experiments performed on matrices arising from the meshfree discretization of 2D and 3D potential problems, where a very large number of nodal contacts is usually found, shows that the supernodal Block FSAI preconditioner outperforms the native algorithm and exhibits a much more stable behavior with respect to the variation of the user-specified parameters.