Task-Based Sparse Hybrid Linear Solver for Distributed Memory Heterogeneous Architectures.

Heterogeneity is emerging as one of the most challenging characteristics of today's parallel environments. However, not many fully-featured advanced numerical, scientific libraries have been ported on such architectures. In this paper, we propose to extend a sparse hybrid solver for handling distributed memory heterogeneous platforms. As in the original solver, we perform a domain decomposition and associate one subdomain with one MPI process. However, while each subdomain was processed sequentially (binded onto a single CPU core) in the original solver, the new solver instead relies on task-based local solvers, delegating tasks to available computing units. We show that this "MPI+task" design conveniently allows for exploiting distributed memory heterogeneous machines. Indeed, a subdomain can now be processed on multiple CPU cores (such as a whole multicore processor or a subset of the available cores) possibly enhanced with GPUs. We illustrate our discussion with the MaPHyS sparse hybrid solver relying on the PaStiX and Chameleon dense and sparse direct libraries, respectively. Interestingly, this two-level MPI+task design furthermore provides extra flexibility for controlling the number of subdomains, enhancing the numerical stability of the considered hybrid method. While the rise of heterogeneous computing has been strongly carried out by the theoretical community, this study aims at showing that it is now also possible to build complex software layers on top of runtime systems to exploit heterogeneous architectures.