Multilevel block ILU preconditioner for sparse nonsymmetric M-matrices

We develop in this paper a multilevel block ILU preconditioner for solving sparse nonsymmetric M-matrices, arising from convection–diffusion equations, discretized by finite difference scheme. This preconditioner is based on recursive block ILU factorization, where the Schur complement matrices are successively approached by some sparse matrices satisfying some hypothesis. We study the preconditioned GMRES iterative method and multigrid method for solving linear systems arising from this scheme.