Numerical study of geometric multigrid methods on CPU-GPU heterogeneous computers

Chunsheng Feng, Shi Shu, Jinchao Xu, Chen Song Zhang

Research output: Contribution to journalArticle

6 Citations (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)1-23
Number of pages23
JournalAdvances in Applied Mathematics and Mechanics
Volume6
Issue number1
DOIs
StatePublished - Jan 1 2014

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Multigrid Method
Graphics Processing Unit
Program processors
Numerical Study
Natural sciences computing
Fast Fourier transforms
Scientific Computing
Partial differential equations
Energy efficiency
Elliptic Partial Differential Equations
Fast Fourier transform
Energy Efficiency
Burst
Siméon Denis Poisson
Discretization
Graphics processing unit
Grid

All Science Journal Classification (ASJC) codes

  • Mechanical Engineering
  • Applied Mathematics

Cite this

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Numerical study of geometric multigrid methods on CPU-GPU heterogeneous computers. / Feng, Chunsheng; Shu, Shi; Xu, Jinchao; Zhang, Chen Song.

In: Advances in Applied Mathematics and Mechanics, Vol. 6, No. 1, 01.01.2014, p. 1-23.

Research output: Contribution to journalArticle

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