Multigrid treatment and robustness enhancement for factored sparse approximate inverse preconditioning

We investigate the use of sparse approximate inverse techniques (SAI) in a grid based multilevel ILU preconditioner (GILUM) to design a robust and parallelizable preconditioner for solving general sparse matrices. Taking the advantages of grid based multilevel methods, the resulting preconditioner outperforms sparse approximate inverse in robustness and efficiency. Conversely, taking the advantages of sparse approximate inverse, it affords an easy and convenient way to introduce parallelism within multilevel structure. Moreover, an independent set search strategy with automatic diagonal thresholding and a relative threshold dropping strategy are proposed to improve preconditioner performance. Numerical experiments are used to show the effectiveness and efficiency of the proposed preconditioner, and to compare it with some single and multilevel preconditioners.