A multilevel block incomplete factorization preconditioning Original Research Article

Incomplete factorization preconditioners based on recursive red–black orderings have been shown efficient for discrete second order elliptic PDEs with isotropic coefficients. However, they suffer for some weakness in presence of anisotropy or grid stretching. Here we propose to combine these orderings with block incomplete factorization preconditioning techniques. For implementation considerations, the latter are extended to the case where the block pivots are generalized tridiagonal matrices, say matrices that have at most one nonzero entry per row in their strictly upper triangular part. On the other hand, a new block method is introduced for the improvement of the performance. This method is called IMBILU (improved modified block ILU). Numerical results show that the resulting preconditioner is efficient and robust with respect to both discontinuity and anisotropy in the PDE coefficients.