论文标题
数据驱动的启发式启发式启发式，用于快速的计划放松雅各比方案的快速收敛
A data driven heuristic for rapid convergence of Scheduled Relaxation Jacobi schemes
论文作者
论文摘要
预定的放松雅各比（SRJ）方法是可行的候选者，作为椭圆形部分微分方程（PDE）的高性能线性求解器。该方法通过在每个算法的每个循环中应用$ M $选择的过度递延和不足因子来大大提高标准雅各比迭代的收敛性，从而有效地减弱了溶液误差。在先前的工作中，已得出最佳的SRJ方案（一组松弛因子），以加速收敛以获得椭圆PDE的特定离散化。在这项工作中，我们开发了一个SRJ方案系列，无论采用哪种特定的离散化，都可以应用于求解椭圆PDES。为了获得有利的收敛，我们基于从将这些方案应用于一维泊松方程中收集的收集数据，训练该算法以在线性求解过程的每个周期中选择该家族中的哪个方案。发现基于此有限数据开发的自动选择启发式方法可为各种问题提供良好的收敛性。
The Scheduled Relaxation Jacobi (SRJ) method is a viable candidate as a high performance linear solver for elliptic partial differential equations (PDEs). The method greatly improves the convergence of the standard Jacobi iteration by applying a sequence of $M$ well-chosen overrelaxation and underrelaxation factors in each cycle of the algorithm to effectively attenuate the solution error. In previous work, optimal SRJ schemes (sets of relaxation factors) have been derived to accelerate convergence for specific discretizations of elliptic PDEs. In this work, we develop a family of SRJ schemes which can be applied to solve elliptic PDEs regardless of the specific discretization employed. To achieve favorable convergence, we train an algorithm to select which scheme in this family to apply at each cycle of the linear solve process, based on convergence data collected from applying these schemes to the one-dimensional Poisson equation. The automatic selection heuristic that is developed based on this limited data is found to provide good convergence for a wide range of problems.
