A generalized Block FSAI preconditioner for nonsymmetric linear systems

The efficient solution to nonsymmetric linear systems is still an open issue, especially on parallel computers. In this paper we generalize to the unsymmetric case the Block Factorized Sparse Approximate Inverse (Block FSAI) preconditioner which has already proved very effective on symmetric positive definite (SPD) problems. Block FSAI is a hybrid approach combining an “inner” preconditioner, with the aim of transforming the system matrix structure to block diagonal, with an “outer” one, a block diagonal incomplete or exact factorization intended to improve the conditioning of each block. The proposed algorithm is experimented with in a number of large size matrices showing both a good robustness and scalability.