A robust and scalable multi-level domain decomposition preconditioner for multi-core architecture with large number of cores

Jean-Marc Gratien (1)

1 IFPEN - IFP Energies nouvelles

With the evolution of High Performance Computing, multi-core and many-core systems are a common feature of new hardware architectures. The required programming efforts induced by the introduction of these architectures are challenging due to the increasing number of cores. Parallel programming models based on the data flow model and the task programming paradigm intend to fix this issue. Iterative linear solvers are a key part of petroleum reservoir simulation as they can represent up to 80% of the total computing time. In these algorithms, the standard preconditioning methods for large, sparse and unstructured matrices-such as Incomplete LU Factorization (ILU) or Algebraic Multigrid (AMG)-fail to scale on shared-memory architectures with large number of cores. Multi-level domain decomposition (DDML) preconditioners recently introduced seem to be both numerically robust and scalable on emerging architectures because of their parallel nature. This paper proposes a parallel implementation of these preconditioners using the task programming paradigm with a data flow model. This approach is validated on linear systems extracted from realistic petroleum reservoir simulations. This shows that, given an appropriate coarse operator in such preconditioners, the method has good convergence rates while our implementation ensures interesting scalability on multi-core architectures.

Mots clés: Domain decomposition methods; Linear algebra; Parallel computing; Runtime systems; Multi-core architecture; Reservoir simulation

Domaines: Algèbre commutative [math.AC]; Mathématiques [math]

Jean-Marc Gratien. A robust and scalable multi-level domain decomposition preconditioner for multi-core architecture with large number of cores. Journal of Computational and Applied Mathematics, 2020, 373, pp.112614. ⟨10.1016/j.cam.2019.112614⟩. ⟨hal-02551346⟩