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

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 scalability. 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 5x speedup and better scalability than the conventional methods for the resolution on hierarchical clusters with hundreds of nodes.