A Distributed and Parallel Asynchronous Unite and Conquer Method to Solve Large Scale Non-Hermitian Linear Systems

Xinzhe Wu (1, 2, 3) , Serge Petiton (1, 2, 3)

1 CNRS - Centre National de la Recherche Scientifique
2 CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189
3 MDLS - Maison de la Simulation

Parallel Krylov Subspace Methods are commonly used for solving large-scale sparse linear systems. Facing the development of extreme scale platforms, the minimization of synchronous global communication becomes critical to obtain good efficiency and scal-ability. This paper highlights a recent development of a hybrid (unite and conquer) method, which combines three computation algorithms together with asynchronous communication to accelerate the resolution of non-Hermitian linear systems and to improve its fault tolerance and reusability. Experimentation shows that our method has an up to 5× speedup and better scalability than the conventional methods for the resolution on hierarchical clusters with hundreds of nodes.

Mots clés: iterative methods; asynchronous communication; linear algebra

Domaines: Calcul parallèle, distribué et partagé [cs.DC]; Analyse numérique [cs.NA]

Xinzhe Wu, Serge Petiton. A Distributed and Parallel Asynchronous Unite and Conquer Method to Solve Large Scale Non-Hermitian Linear Systems. HPC Asia 2018 - International Conference on High Performance Computing in Asia-Pacific Region, Jan 2018, Tokyo, Japan. ⟨10.1145/3149457.3154481⟩. ⟨hal-01677110⟩