Bibtex de la publication

@TechReport{ Am2013.11,
author = {Amestoy, Patrick and Ashcraft, Cleve and Boiteau , Olivier and Buttari, Alfredo and L'Excellent, Jean-Yves and Weisbecker, Clément},
title = "{Version V1 de MUMPS finalisée, version V2 préliminaire de MUMPS, nouveaux résultats, première version incomplète du manuscript de thèse, manuel d’utilisation du prototype}",
year = {2013},
month = {juin},
type = {Rapport de contrat},
number = {EDF-INPT No 2010-0070 RT7},
institution = {IRIT},
address = {Université Paul Sabatier, Toulouse},
language = {français},
keywords = {multifrontal method, approximations, low-rank, factorization},
note = {RT-APO-13-5},
abstract = {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. }