Abstract de la publi numéro 14775

We consider the solution of large sparse linear systems with a multifrontal method using low-rank matrix approximations. Low-rank approximation techniques are commonly used to obtain a compressed representation of data structures. The loss of information that is induced is often insignificant. Although the internal structures involved in a multifrontal method, the so-called frontal matrices, are full rank, we show that they can be represented by a set of low-rank matrices. A good exploitation of these representations offers important gains in term of memory consumption and complexity, mainly for matrices coming from finite elements problems. The quality of the numerical compression is strongly related to the ability to decompose the frontal matrices into blocks that we can represent through low-rank approximation. We show that the mesh geometry can, in a certain way, guide this blocking.