Journal Article10.1137/140968896
Fine-Grained Parallel Incomplete LU Factorization
Edmond Chow,Aftab Patel +1 more
210
TL;DR: Numerical tests show that very few sweeps are needed to construct a factorization that is an effective preconditioner, and the amount of parallelism is large irrespective of the ordering of the matrix, and matrix ordering can be used to enhance the accuracy of the factorization rather than to increase parallelism.
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Abstract: This paper presents a new fine-grained parallel algorithm for computing an incomplete LU factorization. All nonzeros in the incomplete factors can be computed in parallel and asynchronously, using one or more sweeps that iteratively improve the accuracy of the factorization. Unlike existing parallel algorithms, the amount of parallelism is large irrespective of the ordering of the matrix, and matrix ordering can be used to enhance the accuracy of the factorization rather than to increase parallelism. Numerical tests show that very few sweeps are needed to construct a factorization that is an effective preconditioner.
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Citations
A Synchronization-Free Algorithm for Parallel Sparse Triangular Solves
Weifeng Liu,Ang Li,JD Hogg,Iain S. Duff,Brian Vinter +4 more
- 24 Aug 2016
TL;DR: This paper proposes a novel approach for SpTRSV in which the ordering between components is naturally enforced within the solution stage, and is an order of magnitude faster for the preprocessing stage than existing methods.
97
Iterative Sparse Triangular Solves for Preconditioning
Hartwig Anzt,Edmond Chow,Jack Dongarra +2 more
- 24 Aug 2015
TL;DR: This work proposes using an iterative approach for solving sparse triangular systems when an approximation is suitable, and demonstrates the performance gains that this approach can have on GPUs in the context of solving sparse linear systems with a preconditioned Krylov subspace method.
Fast synchronization‐free algorithms for parallel sparse triangular solves with multiple right‐hand sides
TL;DR: Novel approaches for SpTRSV and SpTRSM in which the ordering between components is naturally enforced within the solution stage are proposed, so the cost for preprocessing can be greatly reduced, and the synchronizations between sets are completely eliminated.
54
GHOST: Building Blocks for High Performance Sparse Linear Algebra on Heterogeneous Systems
Moritz Kreutzer,Jonas Thies,Melven Röhrig-Zöllner,Andreas Pieper,Faisal Shahzad,Martin Galgon,Achim Basermann,Holger Fehske,Georg Hager,Gerhard Wellein +9 more
TL;DR: GHOST is a collection of building blocks that targets algorithms dealing with sparse matrix representations on current and future large-scale systems and implements the “MPI+X” paradigm, has a pure C interface, and provides hybrid-parallel numerical kernels, intelligent resource management, and truly heterogeneous parallelism.
49
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