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Numerical Study of Geometric Multigrid Methods on CPU-GPU Heterogeneous Computers

Published online by Cambridge University Press:  03 June 2015

Chunsheng Feng ,
Shi Shu ,
Jinchao Xu  and
Chen-Song Zhang
Chunsheng Feng*
Affiliation:
Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan 411105, China
Shi Shu*
Affiliation:
Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education, Xiangtan University, Xiangtan 411105, China
Jinchao Xu*
Affiliation:
Department of Mathematics, Pennsylvania State University, PA, USA
Chen-Song Zhang*
Affiliation:
NCMIS and LSEC, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100190, China
*
Email: spring@xtu.edu.cn
Corresponding author. Email: shushi@xtu.edu.cn
Email: xu@math.psu.edu
Email: zhangcs@lsec.cc.ac.cn
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Abstract

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.

Keywords

65M1078A48High-performance computingCPU–GPU heterogeneouscomputersmultigrid methodfast Fourier transformpartial differential equations
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 6 , Issue 1 , February 2014 , pp. 1 - 23
Copyright
Copyright © Global-Science Press 2014

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