Parallelization of iterative methods to solve sparse linear systems using task based runtime systems on multi and many-core architectures: application to Multi-Level Domain Decomposition methods

Numerical methods in reservoir engineering simulations lead to the resolution of unstructured, large and sparse linear systems. The performances of iterative methods employed in simulator to solve these systems are crucial in order to consider many more scenarios. In this work, we present a way to implement efficient parallel iterative methods on top of a task-based runtime system. It enables to simplify the development of methods while keeping control on parallelism management. We propose a linear algebra API which aims to implicitly express task dependencies: the semantic is sequential while the parallelism is implicit. We have extended the HARTS runtime system to monitor executions to better exploit NUMA architectures. Moreover, we implement a scheduling policy which exploits data locality for task placement. We have extended the API for KNL many-core systems while considering the various memory banks available. This work has led to the optimization of the SpMV kernel, one of the most time consuming operation in iterative methods. This work has been evaluated on iterative methods, and particularly on one method coming from domain decomposition. Hence, we demonstrate that the API enables to reach good performances on both multi-core and many-core architectures.