.The geometric multigrid method(GMG)is one of the most efficient solving techniques for discrete algebraic systems arising from elliptic partial differential equations.GMG utilizes a hierarchy of grids or discretizati....The geometric multigrid method(GMG)is one of the most efficient solving techniques for discrete algebraic systems arising from elliptic partial differential equations.GMG utilizes a hierarchy of grids or discretizations and reduces the error at a number of frequencies simultaneously.Graphics processing units(GPUs)have recently burst onto the scientific computing scene as a technology that has yielded substantial performance and energy-efficiency improvements.A central challenge in implementing GMG on GPUs,though,is that computational work on coarse levels cannot fully utilize the capacity of a GPU.In this work,we perform numerical studies of GMG on CPU–GPU heterogeneous computers.Furthermore,we compare our implementation with an efficient CPU implementation of GMG and with the most popular fast Poisson solver,Fast Fourier Transform,in the cuFFT library developed by NVIDIA.展开更多
基金the assistance provided by Mr.Xiaoqiang Yue and Mr.Zheng Li from Xiangtan University in regard in our numerical experiments.Feng is partially supported by the NSFC Grant 11201398Program for Changjiang Scholars and Innovative Research Team in University of China Grant IRT1179+4 种基金Specialized research Fund for the Doctoral Program of Higher Education of China Grant 20124301110003Shu is partially supported by NSFC Grant 91130002 and 11171281the Scientific Research Fund of the Hunan Provincial Education Department of China Grant 12A138Xu is partially supported by NSFC Grant 91130011 and NSF DMS-1217142.Zhang is partially supported by the Dean Startup Fund,Academy of Mathematics and System Sciences,and by NSFC Grant 91130011.
文摘.The geometric multigrid method(GMG)is one of the most efficient solving techniques for discrete algebraic systems arising from elliptic partial differential equations.GMG utilizes a hierarchy of grids or discretizations and reduces the error at a number of frequencies simultaneously.Graphics processing units(GPUs)have recently burst onto the scientific computing scene as a technology that has yielded substantial performance and energy-efficiency improvements.A central challenge in implementing GMG on GPUs,though,is that computational work on coarse levels cannot fully utilize the capacity of a GPU.In this work,we perform numerical studies of GMG on CPU–GPU heterogeneous computers.Furthermore,we compare our implementation with an efficient CPU implementation of GMG and with the most popular fast Poisson solver,Fast Fourier Transform,in the cuFFT library developed by NVIDIA.
