## ShyLU: A hybrid–hybrid solver for multicore platforms (2012)

Venue: | IN PROC. OF 26TH IEEE INTL. PARALLEL AND DISTRIBUTED PROCESSING SYMP. (IPDPS’12). IEEE |

Citations: | 1 - 1 self |

### BibTeX

@INPROCEEDINGS{Rajamanickam12shylu:a,

author = {Sivasankaran Rajamanickam and Erik G. Boman and Michael A. Heroux},

title = {ShyLU: A hybrid–hybrid solver for multicore platforms},

booktitle = {IN PROC. OF 26TH IEEE INTL. PARALLEL AND DISTRIBUTED PROCESSING SYMP. (IPDPS’12). IEEE},

year = {2012},

publisher = {}

}

### OpenURL

### Abstract

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 sharedmemory 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.