Task-Parallel LU Factorization of Hierarchical Matrices Using OmpSs

Task-parallelism has been exposed as an efficient approach for the solution of dense and sparse linear algebra problems. Hierarchical matrices lie in-between the dense and sparse scenarios and, therefore, it is natural to target this niche of problems via a runtime-based solution that has reported successful results in the recent past for related linear algebra problems. Concretely, in this paper we investigate the multithreaded parallelization of the LU factorization of hierarchical matrices using the OmpSs task-parallel programming model and runtime. The focus of our study is in the adoption of an efficient storage layout for this type of matrices, and the analysis of the consequences that this decision exerts on the detection of task dependencies, the programming effort, and the performance of the solution.