Abstract de la publi numéro 12563

Low-rank approximations are commonly used to compress the representation of data structures. The loss of information induced is often negligible and can be controlled. Although the dense internal datastructures involved in a multifrontal method, the so-called frontal matrices or fronts, are full-rank, they can be represented by a set of low-rank matrices. Applying to our context the notion of geometric clustering used by M. Bebendorf to define hierarchical matrices, we show that the efficiency of this representation to reduce the complexity of both the factorization and solve phases strongly depends on how variables are grouped. The proposed approach can be used either to accelerate the factorization and solution phases or to build a preconditioner, and aims at exploiting and completing the features of the MUMPS solver for general sparse matrices.