面向能耗优化的面积(核数)-功率(频率)分配问题是当前众核处理器研究热点之一.通过性能-功耗模型了解其在核数-频率空间的分布规律,然后在核数和频率级别这2个维度上通过实测执行逐步搜索,可以获取"核数-频率"配置的最优解,...面向能耗优化的面积(核数)-功率(频率)分配问题是当前众核处理器研究热点之一.通过性能-功耗模型了解其在核数-频率空间的分布规律,然后在核数和频率级别这2个维度上通过实测执行逐步搜索,可以获取"核数-频率"配置的最优解,从而达到能耗优化的目的;然而本领域现有方法在核数-频率空间内实测搜索最低能耗时收敛速度慢、搜索开销大、可扩展性差.针对此问题,提出了一种基于求解最优化问题的经典数学方法——可行方向法的最低能耗搜索方法(energy-efficient optimization based on feasible direction method,EOFDM),每次执行都能从核数和频率2个维度上同时减小搜索空间,在迭代执行中快速收敛至最低能耗点.该方法与现有研究中最优的启发式爬山法(hill-climbing heuristic,HCH)进行了对比实验,平均执行次数、执行时间和能耗分别降低39.5%,46.8%,48.3%,提高了收敛速度,降低了搜索开销;当核数增加一倍时,平均执行次数、执行时间和能耗分别降低48.8%,51.6%,50.9%;当频率级数增加一倍时,平均执行次数、执行时间和能耗分别降低45.5%,49.8%,54.4%,在收敛速度、搜索开销和可扩展性方面均有提高.展开更多
This paper presents the dimension split element-free Galerkin （DSEFG） method for three-dimensional potential problems, and the corresponding formulae are obtained. The main idea of the DSEFG method is that a three-d...This paper presents the dimension split element-free Galerkin （DSEFG） method for three-dimensional potential problems, and the corresponding formulae are obtained. The main idea of the DSEFG method is that a three-dimensional potential problem can be transformed into a series of two-dimensional problems. For these two-dimensional problems, the improved moving least-squares （IMLS） approximation is applied to construct the shape function, which uses an orthogonal function system with a weight function as the basis functions. The Galerkin weak form is applied to obtain a discretized system equation, and the penalty method is employed to impose the essential boundary condition. The finite difference method is selected in the splitting direction. For the purposes of demonstration, some selected numerical examples are solved using the DSEFG method. The convergence study and error analysis of the DSEFG method are presented. The numerical examples show that the DSEFG method has greater computational precision and computational efficiency than the IEFG method.展开更多
文摘面向能耗优化的面积(核数)-功率(频率)分配问题是当前众核处理器研究热点之一.通过性能-功耗模型了解其在核数-频率空间的分布规律,然后在核数和频率级别这2个维度上通过实测执行逐步搜索,可以获取"核数-频率"配置的最优解,从而达到能耗优化的目的;然而本领域现有方法在核数-频率空间内实测搜索最低能耗时收敛速度慢、搜索开销大、可扩展性差.针对此问题,提出了一种基于求解最优化问题的经典数学方法——可行方向法的最低能耗搜索方法(energy-efficient optimization based on feasible direction method,EOFDM),每次执行都能从核数和频率2个维度上同时减小搜索空间,在迭代执行中快速收敛至最低能耗点.该方法与现有研究中最优的启发式爬山法(hill-climbing heuristic,HCH)进行了对比实验,平均执行次数、执行时间和能耗分别降低39.5%,46.8%,48.3%,提高了收敛速度,降低了搜索开销;当核数增加一倍时,平均执行次数、执行时间和能耗分别降低48.8%,51.6%,50.9%;当频率级数增加一倍时,平均执行次数、执行时间和能耗分别降低45.5%,49.8%,54.4%,在收敛速度、搜索开销和可扩展性方面均有提高.
基金supported by the National Natural Science Foundation of China (Grants 11571223, 51404160)Shanxi Province Science Foundation for Youths (Grant 2014021025-1)
文摘This paper presents the dimension split element-free Galerkin （DSEFG） method for three-dimensional potential problems, and the corresponding formulae are obtained. The main idea of the DSEFG method is that a three-dimensional potential problem can be transformed into a series of two-dimensional problems. For these two-dimensional problems, the improved moving least-squares （IMLS） approximation is applied to construct the shape function, which uses an orthogonal function system with a weight function as the basis functions. The Galerkin weak form is applied to obtain a discretized system equation, and the penalty method is employed to impose the essential boundary condition. The finite difference method is selected in the splitting direction. For the purposes of demonstration, some selected numerical examples are solved using the DSEFG method. The convergence study and error analysis of the DSEFG method are presented. The numerical examples show that the DSEFG method has greater computational precision and computational efficiency than the IEFG method.
