M2 : Génie Civil
Géo-mécanique : Ouvrages, Eau, Réservoirs (GEO2)
Année 2015-2016
Proposition de projet d’initiation à la recherche
Titre: Efficient sparse matrix storage for applications of the Finite Element Method
Description:
Three-dimensional numerical models used to understand the effects of soil-structure interaction (one
structure) and structure-soil-structure interaction (more structures) demand the solution of big
systems of equations in matrix form. Assemblage operation in a finite element scheme produces big
sparse matrices.
Specific numerical tools are applied in the case of sparse matrix storage and solving finite element
equations. The traditional assemblage operation is replaced by “bandwidth matrix” storage and
“skyline matrix” storage.
The aim of this project is to undertake a literature review of existing tools in this topic, understand
advantages and detriments of each method and to perform a numerical application.
Some available references
George A., Liu J.W.H. (1981). Computer solution of large sparse positive definite systems, PrenticeHall.
Duff I.S., Erisman A.M., Reid J.K. (1986). Direct methods for sparse matrices, Oxford University
Press.
Watkins, D.S. (2002). Fundamentals of matrix computations, John Wiley & Sons.
Mots clés : Sparse matrix storage, Finite Element equation solution
Laboratoire / entreprise : LJAD, Université de Nice Sophia Antipolis
Responsable, co-encadrant éventuel :
Maria Paola Santisi d’Avila, msantisi@unice.fr