Section: New Results

Sparse matrix reordering for ILU solvers

Participants : Astrid Casadei [HIEPACS project-team, Inria Bordeaux - Sud-Ouest] , Sébastien Fourestier, François Pellegrini [Corresponding member] .

In the context of ANR PETALh , our task is to find ways of reordering sparse matrices so as to improve the robustness of incomplete LU factorization techniques. The path we are following is to favor the diagonal dominance of the matrices corresponding to the subdomains of the Schur complement. Our studies aim at injecting some information regarding off-diagonal numerical values into nested dissection like reordering methods, so as to favor the preservation of high off-diagonal values into either the subdomains or the separators of Schur complement techniques.

The experimental framework had been set-up last year. It consisted in a modified version of the Scotch sparse matrix ordering library for computing orderings and of the HIPS iterative sparse linear system solver for evaluating them. The text cases used were provided by the industrial partners of the PETALh project.

In order to improve diagonal dominance, several cut-off methods have been proposed in order to carve the matrix pattern and speed-up computations towards convergence. These cut-off methods were based on either linear or logarithmic scales, with cut-off values selected according to various distributions.

While some of these methods improve convergence on some restricted classes of matrices, as our first experiments showed last year, no method was able to provide overall improvement on a wide range of matrices. This research path is consequently considered as inefficient. A research report has been written.