| mots-clés : Décomposition de domaines – Méthodes itératives – Méthodes directes – Méthodes hybrides – Complément de Schur – Systèmes linéaires – Méthodes de Krylov – GMRES – Flexible GMRES – CG – Calcul haute performace – Deux niveaux de parallèlisme – Calcul parallèle distribué – Calcul sientifique – Simulation numériques de grande taille – Techniques de préconditionnement – Préconditionneur de type Schwarz additive |
|
| On the parallel scalability of hybrid linear solvers for large 3D problems |
| Large-scale scientific applications and industrial simulations are nowadays fully integrated in many engineering areas. They involve the solution of large sparse linear systems. The use of large high performance computers is mandatory to solve these problems. The main topic of this research work was the study of a numerical technique that had attractive features for an efficient solution of large scale linear systems on large massively parallel platforms. The goal is to develop a high performance hybrid direct/iterative approach for solving large 3D problems. We focus specifically on the associated domain decomposition techniques for the parallel solution of large linear systems. We have investigated several algebraic preconditioning techniques, discussed their numerical be- haviours, their parallel implementations and scalabilities. We have compared their performances on a set of 3D grand challenge problems. |
| mots-clés en anglais : Domain decomposition – Iterative methods – Direct methods – Hybrid methods – Schur complements – Linear systems – Krylov methods – GMRES – flexible GMRES – CG – High performance computing – Two levels of parallelism – Distributed computing – Scientific computing – Large scale numerical simulations – Preconditioning techniques – Additive Schwarz preconditioner |
