Parallel computation of entries of A-1

Patrick Amestoy (1, 2) , Iain S. Duff (3, 4) , Jean-Yves L'Excellent (5, 6) , François-Henry Rouet (7, 2)

1 IRIT-APO - Algorithmes Parallèles et Optimisation
2 ENSEEIHT - Ecole Nationale Supérieure d'Electrotechnique, d'Electronique, d'Informatique, d'Hydraulique et de Télécommunications
3 CERFACS - Centre Européen de Recherche et de Formation Avancée en Calcul Scientifique
4 RAL - STFC Rutherford Appleton Laboratory
5 LIP - Laboratoire de l'Informatique du Parallélisme
6 ROMA - Optimisation des ressources : modèles, algorithmes et ordonnancement
7 IRIT - Institut de recherche en informatique de Toulouse

In this paper, we are concerned about computing in parallel several entries of the inverse of a large sparse matrix. We assume that the matrix has already been factorized by a direct method and that the factors are distributed. Entries are efficiently computed by exploiting sparsity of the right-hand sides and the solution vectors in the triangular solution phase. We demonstrate that in this setting, parallelism and computational efficiency are two contrasting objectives. We develop an efficient approach and show its efficacy by runs using the MUMPS code that implements a parallel multifrontal method.

Mots clés: sparse matrices; matrix inverse; direct methods; direct solver; parallelism

Domaines: Calcul parallèle, distribué et partagé [cs.DC]

Patrick Amestoy, Iain S. Duff, Jean-Yves L'Excellent, François-Henry Rouet. Parallel computation of entries of A-1. [Research Report] RR-8142, INRIA. 2012. ⟨hal-00759556v2⟩