## Section:
New Results2>
### Sparse matrix reordering for ILU solvers3>

Participants : Astrid Casadei, SÃ©bastien Fourestier, FranÃ§ois 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.