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Persistent URL http://purl.org/net/epubs/work/39440019
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Record Id 39440019
Title Parallelization of the solve phase in a task-based Cholesky solver using a sequential task flow model
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Abstract We describe the parallelization of the solve phase in the sparse Cholesky solver SpLLT [Duff, Hogg, and Lopez. Numerical Algebra, Control and Optimization. Volume 8, 235237,2018]when using a sequential task flow(STF)model. In the context of direct methods, the solution of a sparse linear system is achieved through three main phases: the analyse, the factorization and the solve phases. In the last two phases which involve numerical computation, the factorization corresponds to the most computationally costly phase, and it is therefore crucial to parallelize this phase in order to reduce the time-to-solution on modern architectures. As a consequence, the solve phase is often not as optimized as the factorization in state-of-the-art solvers and opportunities for parallelism are often not exploited in this phase. However, in some applications, the time spent in the solve phase is comparable or even greater than the time for the factorization and the user could dramatically benefit from a faster solve routine. This is the case, for example, for a CG solver using a block Jacobi preconditioner. The diagonal blocks are factorized once only but their factors are used to solve subsystems at each CG iteration. In this study we design and implement a parallel version of a task-based solve routine for an OpenMP version of the SpLLT solver. We show that we can obtain good scalability on a multicore architecture enabling a dramatic reduction of the overall time-to-solution in some applications.
Organisation STFC , SCI-COMP
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Language English (EN)
Type Details URI(s) Local file(s) Year
Report RAL Technical Reports RAL-TR-2018-008. STFC, 2018. RAL-TR-2018-008.pdf 2018
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