Section: New Results

Improving multifrontal methods by means of low-Rank representations

Matrices coming from elliptic PDEs have been shown to have a low-rank property. Although the dense internal datastructures involved in a multifrontal method, the so-called frontal matrices or fronts, are full-rank, their off-diagonal blocks can then be approximated by low-rank products. We have studied a low-rank format called Block Low Rank and explained how it can be used to reduce the memory footprint and complexity of both the factorization and solve phases, depending on the way variables are grouped. The proposed approach can be used either to accelerate the factorization and solution phases or to build a preconditioner [47] . We have started the development of a version of MUMPS that exploits such properties. This work is in collaboration with EDF (contract funding for the Ph.D. thesis of C. Weisbecker at INPT) and C. Ashcraft (LSTC).