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

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

Year:    2014

Author:    Chunsheng Feng, Shi Shu, Jinchao Xu, Chen-Song Zhang

Advances in Applied Mathematics and Mechanics, Vol. 6 (2014), Iss. 1 : pp. 1–23

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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.2013.m87

Advances in Applied Mathematics and Mechanics, Vol. 6 (2014), Iss. 1 : pp. 1–23

Published online:    2014-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    23

Keywords:    High-performance computing CPU–GPU heterogeneous computers multigrid method fast Fourier transform partial differential equations.

Author Details

Chunsheng Feng

Shi Shu

Jinchao Xu

Chen-Song Zhang

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