A block version of left-looking AINV preconditioner with one by one or two by two block pivots

Abstract

In this paper, we present a block format of left-looking AINV preconditioner for a nonsymmetric matrix. This preconditioner has block 1 × 1 or 2 × 2 pivot entries. It is introduced based on a block format of Gaussian Elimination process which has been studied in [14]. We have applied the multilevel nested dissection reordering as the preprocessing and have compared this block preconditioner by the plain left-looking AINV preconditioner. If we mix the multilevel nested dissection by the maximum weighted matching process, then the numerical experiments indicate that the number of 2 × 2 pivot entries in the block preconditioner will grow up. In this case, the block preconditioner makes GMRES method convergent in a smaller number of iterations. In the numerical section, we have also compared the ILUT and block left-looking AINV preconditioners.