Electrical modeling and simulation for stockpile stewardship
XRDS: Crossroads, The ACM Magazine for Students - Scientific Computing
Amesos2 and Belos: Direct and iterative solvers for large sparse linear systems
Scientific Programming
Scientific Programming - A New Overview of the Trilinos Project --Part 1
| Hi-index | 0.00 |
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 \emph{sub domain 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.