Section: New Results

Sparse matrix reordering for ILU solvers

Participants : Astrid Casadei, 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.

This year, we have set-up a software testbed for experimenting such methods. It comprises 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 are provided by the industrial partners of the PETALh project.

Our first experiments show that injecting information regarding off-diagonal terms can indeed improve convergence. However, many parameters have to be evaluated in a thorough experimentation plan. Since Scotch uses integer terms only, some scaling has to be performed, which imposes to determine how to scale the coefficients (type of scaling and range), whether to filter small values, etc. This work is in progress.