ShyLU: A Hybrid-Hybrid Solver for Multicore Platforms. With the ubiquity of multicore processors, it is crucial that solvers adapt to the hierarchical structure of modern architectures. We present ShyLU, a “hybrid-hybrid” solver for general sparse linear systems that is hybrid in two ways: First, it combines direct and iterative methods. The iterative part is based on approximate Schur complements where we compute the approximate Schur complement using a value-based dropping strategy or structure-based probing strategy. Second, the solver uses two levels of parallelism via hybrid programming (MPI+threads). ShyLU is useful both in shared-memory environments and on large parallel computers with distributed memory. In the latter case, it should be used as a subdomain solver. We argue that with the increasing complexity of compute nodes, it is important to exploit multiple levels of parallelism even within a single compute node. We show the robustness of ShyLU against other algebraic preconditioners. ShyLU scales well up to 384 cores for a given problem size. We also study the MPI-only performance of ShyLU against a hybrid implementation and conclude that on present multicore nodes MPI-only implementation is better. However, for future multicore machines (96 or more cores) hybrid/ hierarchical algorithms and implementations are important for sustained performance.
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References in zbMATH (referenced in 2 articles )
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- Heinlein, Alexander; Klawonn, Axel; Knepper, Jascha; Rheinbach, Oliver: Adaptive GDSW coarse spaces for overlapping Schwarz methods in three dimensions (2019)
- Kopysov, Sergeĭ Petrovich; Kuz’min, Igor’ Mikhaĭlovich; Nedozhogin, Nikita Sergeevich; Novikov, Aleksandr Konstantinovich: Parallel algorithms for constructing and solving the Schur complement on graphics accelerators (2012)