MPI+X: task-based parallelisation and dynamic load balance of finite element assembly

Abstract

The main computing phases of numerical methods for solving partial differential equations are the algebraic system assembly and the iterative solver. This work focuses on the first task, in the context of a hybrid MPI+X paradigm. The matrix assembly consists of a loop over the elements, faces, edges or nodes of the MPI partitions to compute element matrices and vectors and then of their assemblies. In a MPI+X hybrid parallelism context, X has consisted traditionally of loop parallelism using OpenMP, with different techniques to avoid the race condition, but presenting efficiency or implementation drawbacks. We propose an alternative, based on task parallelism using some extensions to the OpenMP programming model. In addition, dynamic load balance will be applied, especially efficient in the presence of hybrid meshes. This paper presents the proposed methodology, its implementation and its validation through the solution of large computational mechanics problems up to 16k cores. ; The research leading to these results has received funding from: the European Union's Horizon 2020 Programme (2014–2020) and from Brazilian Ministry of Science, Technology and Innovation through Rede Nacional de Pesquisa (RNP), HPC4E Project, grant agreement 689772; the Energy oriented Centre of Excellence (EoCoE), grant agreement number 676629, funded within the Horizon2020 framework of the European Union; The Spanish Government (grant SEV2015-0493 of the Severo Ochoa Program); the Spanish Ministry of Science and Innovation (contract TIN2015-65316-P); the Generalitat de Catalunya (contract 2014-SGR-1051); the Intel-BSC Exascale Lab collaboration project. Comissió Interdepartamental de Recerca i Innovació Tecnológica(Interdepartmental Commission for Research and Technological Innovation) ; Peer Reviewed ; Postprint (author's final draft)