Exploiting nested task-parallelism in the $\mathcal{H}-LU$ factorization

Abstract: We address the parallelization of the LU factorization of hierarchical matrices ($\mathcal{H}$-matrices) arising from boundary element methods. Our approach exploits task-parallelism via the OmpSs programming model and runtime, which discovers the data-flow parallelism intrinsic to the operation at execution time, via the analysis of data dependencies based on the memory addresses of the tasks' operands. This is especially challenging for $\mathcal{H}$-matrices, as the structures containing the data vary in dimension during the execution. We tackle this issue by decoupling the data structure from that used to detect dependencies. Furthermore, we leverage the support for weak operands and early release of dependencies, recently introduced in OmpSs-2, to accelerate the execution of parallel codes with nested task-parallelism and fine-grain tasks.