Approximating a Multi-Grid Solver
Approximating a Multi-Grid Solver
复制标题
逼近多重网格求解器
DOI：
10.1109/pmbs.2018.8641651
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
Marc Casas
中科院分区：
文献类型：
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作者：
Valentin Le Fèvre;L. Bautista;O. Unsal;Marc Casas
多重网格方法是用于并行和分布式处理的数值算法。多重网格求解器的主要思想是通过多次将问题简化为较粗糙的网格来加速迭代方法的收敛。多重网格方法在许多应用领域得到广泛应用，因此提高其性能和能源效率非常重要。本文旨在基于以下观察来实现这一目标：鉴于中间步骤不需要完全准确，可以通过降低某些步骤的精度来节省时间和精力，同时将最终结果保持在目标精度范围内。为了实现这一目标，我们首先引入与多网格求解器中使用的经典 V 循环不同的循环形状。然后，我们建议根据每个中间步骤所需的精度动态更改运行时使用的浮点精度。我们对最先进的多网格求解器实施的评估表明，可以用临时精度来换取完成时间，而不会损害最终结果的质量。特别是，我们能够达到与全双精度相同的精度结果，同时获得 15% 到 30% 的执行时间改进。
Multi-grid methods are numerical algorithms used in parallel and distributed processing. The main idea of multigrid solvers is to speedup the convergence of an iterative method by reducing the problem to a coarser grid a number of times. Multi-grid methods are widely exploited in many application domains, thus it is important to improve their performance and energy efficiency. This paper aims to reach this objective based on the following observation: Given that the intermediary steps do not require full accuracy, it is possible to save time and energy by reducing precision during some steps while keeping the final result within the targeted accuracy. To achieve this goal, we first introduce a cycle shape different from the classic V-cycle used in multi-grid solvers. Then, we propose to dynamically change the floating-point precision used during runtime according to the accuracy needed for each intermediary step. Our evaluation considering a state-of-the-art multi-grid solver implementation demonstrates that it is possible to trade temporary precision for time to completion without hurting the quality of the final result. In particular, we are able to reach the same accuracy results as with full double-precision while gaining between 15% and 30% execution time improvement.